In this paper we have defined the effect of bulk viscosity on Quintessence model and scaler field potential as well as on classical field. We have shown the same effect for modified gravity with f(R,T)= R+f(T). In the derivation we have predicted the possibility of time dependent evolution of gravitational constant G and anisotropy.

Three body systems in which one of the bodies is ejected without escaping the binary system have previously been studied in various restricted forms. However, none of these studies dwells on the problem in a general setting. Thus, to study this phenomenon qualitatively, we try to expand this problem's scope to unequal mass systems and generalize them by considering various configurations of fixed initial points with precisely calculated initial velocities, some zero velocity models and some optimized models. We will see the use of terminology similar to the previous studies done in this domain but incorporate different analytical and evaluation methods.

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the lat- ter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the gen- eral definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg's and others' un- certainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

Our goal in this paper is to study the relationship between the linear approximation of Einstein's equations to the Klein-Gordon’s equation. The part one presents what the Klein-Gordon’s equation and the integration of the theory of quantum information in it. The Part two deals with the Stress Energy tensor quantum, wherein the detail I linearized gravity of Einstein equation, and wherein I develop the tensor quantum energy pulse from the equivalence of equation einstein the linearized gravity and the Schrödinger equation relativistic described by Klein-Gordon’s equation.

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

In this paper, we examine the mathematical and physical consistencies of the three primary couple stress theories: original Mindlin-Tiersten-Koiter couple stress theory (MTK-CST), modified couple stress theory (M-CST) and consistent couple stress theory (C-CST). As has been known for many years, MTK-CST suffers from some fundamental inconsistencies, such as the indeterminacy of the couple-stress tensor. Therefore, despite the fact that MTK-CST has a fundamental position in the evolution of size-dependent continuum mechanics, it is not a reliable theory within continuum mechanics, for example, in developing new size-dependent multi-physics formulations. We also observe that M-CST not only inherits all inconsistences from the original MTK-CST, but also suffers from new additional inconsistencies, such as the introduction of a new non-physical governing equation. These inconsistencies refute the claim of those who state that the couple-stress tensor may be chosen symmetric. Therefore, the apparent success of MTK-CST and M-CST in describing a size-effect for some problems, such as two-dimensional plate and beam bending, is not enough to justify these theories as suitable for general cases. In fact, the symmetric couple-stresses in M-CST create torsional or anticlastic deformation, not bending. On the other hand, C-CST, with a skew-symmetric couple-stress tensor, is the consistent continuum mechanics suitable for solving different size-dependent solid, fluid and multi-physics problems.

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.

We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé-Hoover dynamics aims to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the loss of reality, the behavior of micro particles shows randomness and hopping. The second is the loss of certainty, the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will change the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell's inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell's inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not parallel relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which show the wave-particle duality simultaneously and provide intuitionistic teaching materials for the new interpretation of quantum theory.

A new utilization of entropy in the context of buckling is presented. The novel concept connecting strain energy and entropy for a pin-ended strut is derived. This concept rationalizes the ranking of buckling modes based on strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of buckling modes that coincide with the measurement of initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for given energy roughly decreases with the inverse square of the mode index. For practical engineering, the study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

Recent advances in understanding the Planck scale have led to a new, straightforward method for quantizing the general theory of relativity. This results in a theory of gravity that predicts the same outcomes as general relativity with greater fundamental comprehension connected directly to the Planck scale.

In order to study the acoustic emission characteristics of sandstone under the action of the high temperature-water cooling cycle, the RMT-150B electro-hydraulic servo rock test system and the DS-5 acoustic emission detection and analysis system were used to conduct a single analysis of the sandstone after the high temperature-water cooling cycle. Experimental study on acoustic emission characteristics under axial compression, analyzing the deformation, strength and acoustic emission characteristics of sandstone under different temperatures and cycles. The results of the study show that the high temperature-water cooling action causes changes in the physical properties of the sandstone. The expansion rate of the rock sample decreases first and then increases when the temperature rises, and the strength first increases and then decreases. The number of cycles has little effect on the physical properties of the rock sample; sandstone acoustic emission ringing count increases with the increase of temperature and cycle times, acoustic emission activities become more frequent with the loading process; with the increase of cycle times and temperature, acoustic emission ringing counts and accumulative acoustic emission energy appear earlier The rock sample enters the elastic deformation stage ahead of schedule, the yielding period increases, and the rock sample presents a trend of transition from brittle failure to ductile failure; the ringing count and cumulative energy increase with the increase in temperature and cycle times, and the high-energy ringing count and cumulative energy increase. The simultaneous sharp increase of the rock sample is the harbinger of the failure and instability of the rock sample.

In the Aharonov-Bohm setup, a double-slit experiment, coherent beams of electrons passing through two slits form an interference pattern on the observing screen. However, when a long but thin solenoid of current is introduced behind the slits between the two electron beams, an extra phase difference between them appears, as shown by a shift in the interference pattern. This happens even though there is no magnetic field outside the solenoid, at the location of the beams. This is known as Aharonov-Bohm effect, though the idea was mooted apparently a decade earlier, and the effect sometimes is called Ehrenberg-Siday-Aharonov-Bohm effect. This mysterious effect, purportedly arises owing to an electromagnetic momentum, attributed to the presence at the location of either beam, a vector potential due to the solenoid of current even when there exists no magnetic field outside the solenoid. The first experimental confirmation came soon and It has since been amply verified using clever experimental setups, leaving hardly any doubts that the observed effect is real. However, on the theoretical side the picture is not so clear and a satisfactory physical explanation of the existence of momentum, at least under the aegis of classical electromagnetism, is still missing since inception of the idea more than half a century back. It has remained a puzzle, how just potential, thought to be a mere mathematical tools for calculating electromagnetic field, can give rise to an electromagnetic momentum in a system, in lieu of field itself. We here show that a subtle momentum can be seen to lie in the product of the drift velocities of the current carrying charges and the mass equivalent of their non-localized potential energies in the electric field of the interfering electrons, which manifests, from a classical point of view, a linear momentum in the system. It is this hard-to-pinpoint, additional momentum, reflected through an extra phase difference between the interfering beams of electrons, which exhibits from a classical physics perspective, the presence of an elusive, long sought-after electromagnetic momentum in the system.

A brief (subjective) description of the state of the art of the many-worlds interpretation of quantum mechanics (MWI) is presented. It is argued that the MWI is the only interpretation which removes action at a distance and randomness from quantum theory. Limitations of the MWI regarding questions of probability which can be legitimately asked are specified. The ontological picture of the MWI as a theory of the universal wave function decomposed in a superposition of world wave functions, the important part of which are defined in three-dimensional space, is viewed from the point of view of our particular branch. Some speculations about misconceptions which apparently prevent the MWI to be in the consensus are mentioned.

We show that quantum mechanics can be constructed as a classical field theory that correctly describes all basic quantum effects, by combining the Maxwell and Dirac equations. It is shown that for a self-consistent union of the Maxwell and Dirac equations into a unified classical field theory, it is necessary to introduce an additional short-range tensor field, which compensates the intrinsic electrostatic field of the electron wave inside the atom. For the combined Maxwell-Dirac field, the stress-energy tensor is constructed. We show that in the nonrelativistic limit this theory naturally transforms into the self-consistent Maxwell-Pauli theory and allows describing all basic quantum effects in the framework of classical field theory without any quantization.

Calculation of the pressure field on and around solid bodies exposed to external flow is of paramount importance to a number of engineering applications. However, conventional pressure measurement techniques are inherently linked to problems principally caused by their point-wise and/or intrusive nature. In the present paper, we attempt to calculate the time-averaged two-dimensional pressure field by integrating PIV (Particle Image Velocimetry) velocity measurements into a CFD code and modifying them by the respective correction step of the SIMPLE algorithm. Boundary conditions are applied from the PIV data as a three-layer area of constant velocities, adjacent to the boundaries. A novel characteristic of the approach is the straightforward inclusion of the Reynolds Stresses into the source terms of the momentum equations, calculated directly from the PIV statistics. The methodology is applied to three regions of the symmetry plane parallel to the main boundary layer flow past a surface mounted cube. In spite of findings of deviations from the planar 2D flow assumption, the derived pressure fields and the adjusted velocity fields are found to be reliable, while the intrinsic turbulent nature of the flow is considered without modelling of the Reynolds stresses.

Although lithium-ion batteries have extensively been used in various applications because of their high energy capacity, fracture and failure, the by-products of large strains and stresses caused by fast charging and discharging need yet to be addressed. The size effects on the mechanical behavior of the nano-sized structures are significant; however, the classical elasticity theory may not consider such effects. On the other hand, surface stress theory, as a robust and potential theory, is suitable in considering size effects in nano-scale structures. Therefore, in this paper, in order to involve the surface stress effects on the fracture behavior of Li-ion batteries, the following steps are taken. Firstly, a phase-field model is used to determine the evolution of the concentration profile. Subsequently, the stress distribution is obtained by using the surface stress theory combined with chemical equations for a planar electrode. Afterward, by using the weight function method for an edge crack in the plate, the stress intensity factor is derived for all time steps and possible crack lengths during the process. It is found that with increasing phase boundary thickness parameter or decreasing phase-separation phenomenon, the surface mechanics parameters become more influential. Furthermore, in the presence of positive surface stress, the diffusion-induced stress distribution decreases, which in turn reduces the stress intensity factor. In addition, in this paper, the two states of surface stress are compared either for elastic or total strain. Concerning stresses and concentrations, the results indicate a big difference at the beginning of the deintercalation process showing, in particular, 2% for stresses, but the differences diminish gradually.

When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined uniquely apart from a Lorentz transformation if suitable supplementary conditions are imposed. It is known that wave equations keep the same form under Lorentz transformations. Thus, we speculate that Fock's special harmonic reference frames may have provided us a clue to derive the Einstein's equations in some special class of non-inertial reference frames. Following this clue, generalized Einstein's equations in some special non-inertial reference frames are derived based on the theory of vacuum mechanics. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explain all the experiments which support the theory of general relativity. There exist some differences between this theory and the theory of general relativity.

The dynamic development of electromobility poses challenges to designers regarding not only the efficiency of energy transformation but also the battery life, which is influenced by the stability of its operating temperature. Designing cooling systems is connected not only with the optimization of energy management but also with other environmental parameters, such as noise emission. The paper presents the numerical optimization of an innovative radiator for use in electric buses in terms of energy consumption and noise emission. The results of the numerical studies were verified in laboratory and field conditions, showing a very good convergence of the model with the results of the experiments.

In this paper we will show that standard physics to a large degree consists of derivatives of a deeper reality. This means standard physics is both overly complex and also incomplete. Modern physics has typically started from working with first understanding the surface of the world, that is typically the macroscopic world, and then forming theories about the atomic and subatomic world. And we did not have much of a choice, as the subatomic world is very hard to observe directly, if not impossible to observe directly at the deepest level. Despite the enormous success of modern physics, it is therefore no big surprise that we at some point have possibly taken a step in the wrong direction. We will claim that one such step came when one thought that the de Broglie wavelength represented a real matter wavelength. We will claim that the Compton wavelength is the real matter wavelength. Based on such a view we will see that many equations in modern physics are only derivatives of much simpler relations. Second, we will claim that in today’s physics one uses two different mass definitions, one mass definition that is complete or at least more complete, embedded in gravity equations without being aware of it, as it is concealed in GM, and the standard, but incomplete, kg mass definition in non-gravitational physics. First, when this is understood, and one uses the more complete mass definition that is embedded in gravity physics, not only in gravity physics, but in all of physics, then one has a chance to unify gravity and quantum mechanics. Our new theory shows that most physical phenomena when observed over a very short timescale are probabilistic for masses smaller than a Planck mass and dominated by determinism at or above Planck mass size. Our findings have many implications. For example, we show that the Heisenberg uncertainty principle is rooted in a foundation not valid for rest-mass particles, so the Heisenberg uncertainty principle can say nothing about rest-masses. When re-formulated based on a foundation compatible with a new momentum that is also compatible with rest-masses, we obtain a re-defined Heisenberg principle that seems to become a certainty principle in the special case of a Planck mass particle. Furthermore, we show that the Planck mass particle is linked to gravity and that we can easily detect the Planck scale from gravity observations. The Planck mass particle is unique as it only lasts the Planck time, and in that very short time period it can only be observed directly from itself, and it therefore closely linked to absolute rest.

This article attempts to formulate a mathematical model for a potential explanation regarding the unavoidable impact of a rigid body's peculiar shape on the seamless flow over it. The solid body completely immersed in a Newtonian fluid and respectively has a relative open circuit flow on it will typically experience various observable phenomena like flow separation, flow transition, down-wash, stalling at the higher angle of attack, stalling velocity and how cambered airfoil can typically generate lift at a zero incidence angle. This article respectively represents an understanding of the laminar flow over a rigid body's external surface with due respect to its distinctive shape and size. This working paper formulates a more realistic and simplified mathematical model for open circuit laminar flow over a body, based on the historical data of aerodynamics and theoretical mechanics. This is intended to properly estimate forces on the continuous surface of the body in a laminar flow, to properly explain, understand and predict mentioned phenomena. Most of all the mechanism of streamline formation and its deformation with due regards to flow, shape and size of the body in an open-circuit laminar are formulated mathematically to enhance better design theory which can reduce experimentation while designing a streamlined body.

We evaluate the complexity of Colombian climate from extreme behavior of gauge temperature and precipitation, using the the novel Tsallis' non-extensive entropy principle based on physical information through the q-index. We find the spatial structure of non additive universal categories (q-index) and compare with some complex systems with the potential to have some degree of dynamical affinity. Our results evidence the great dynamical variability of regional climate expressed in the large range of values of $q$-index, and the high degree of non-extensitivity for both temperature and precipitation.

For more than eighty years the standard interpretation (SI) has dominated quantum physics. Perspectives that have tried to challenge this domination have been remarkably unsuccessful. As a result, quantum theory (QT) has remained remarkably stagnant. The article offers a critical examination of SI and provides an explanation for its continued domination. It also uses Bohmian mechanics—a theoretical perspective advanced by American physicist David Bohm—as a case study for why alternative interpretations have failed to displace SI. The article sees the main reason for the failure to achieve much progress beyond SI in the unresolved philosophical problem of subject-object relation that continues to plague our study of physics. The article sketches a path to a possible solution and outlines a new science practice that this solution will require.

The objective of this research is to develop an experimental-theoretical analysis about the influence of the cooling medium and the geometry of the welding bead profile in fatigue life and associated parameters with structural integrity of welded joints. A welded joint with cruciform geometry is considered using SMAW, plates in structural steel ASTM A36 HR of 8 mm of thickness and E6013 electrode input. A three-dimensional computational model of the cruciform joint was created using the finite element method. For this model, the surface undulation of the cord and differentiation in the mechanical properties of the fusion zone were considered, the heat-affected zone (HAZ) and base material, respectively. In addition, an initial residual stress field which was established experimentally was considered. The results were a set of analytical expressions for the weld magnification factor Mk. It was found that values for the latter decrease markedly in function of the intensity of the cooling medium used in the post welding cooling phase, mainly due to the effect of the residual compressive stresses. The obtained models of behavior of the weld magnification factor are compared with the results from other researchers with some small differences, mainly due to the inclusion of the cooling effect of the post weld and the variation of the leg of the weld bead. The obtained analytical equations in the present research for Mk can be used in management models of life and structural integrity for this type of welded joint.

Mechanical properties of cardiomyocytes from different transmural regions are heterogeneous in the left ventricular wall. The cardiomyocyte mechanical environment affects this heterogeneity because of mechano-electric feedback mechanisms. In the present study, we investigated the effects of load upon transmural differences in contraction of subendocardial (ENDO) and subepicardial (EPI) single cells isolated from the murine left ventricle. Various loads were applied to the cells using carbon fiber techniques for single myocytes. To simulate experimentally obtained results and to predict mechanisms underlying the cellular response to change in load, our mathematical models of the ENDO and EPI cells were used. Extent of the transmural gradient in the time course of contractions was independent of the loading conditions where unloaded and heavy loaded (isometric) contractions were examined, but the regional gradient of the relaxation time characteristics tended to decrease when the load decreased. Under auxotonic contractions, time to peak contraction (T_max) was significantly longer in ENDO cells than in EPI cells at low preload. An increase in preload (axial stretch) prolonged T_max in both cell types; however, the prolongation was greater in EPI cells, resulting in a decrease in transmural gradient in T_max at high preload. The [Ca²⁺]_i transient decay time constant was consistent with the greater preload dependency in T_max of EPI cells. Our modified mathematical models reproduced experimental results, suggesting that differences in cooperativity of cross bridges and calcium troponin C complex interactions between the ENDO and EPI cardiomyocytes may contribute to the different cellular responses to stretch, which may provide a decrease in transmural dispersion of cellular shortening in the intact heart.

The Dirac and Klein-Gordon equations have proven to be some of the most accurate theories for describing particle behaviour and have laid the foundations of Relatavistic Quantum Mechanics. We extend the formulations to consider a 5 Dimensional spacetime with two time dimensions (as first conceptualised by Sajjad Zahir) and extend the notions to Quantum Field Theory to arrive at the behaviour of particles through the Dirac and Klein-Gordon counterparts of the 5 Dimensional spacetime. The implications of this to anti-matter are discussed.

Consciousness results from comprehending the living creature from its existence in time and space. Thought and consciousness are distinguishing factors between humans and machines having artificial intelligence. No algorithm has been offered for artificial self-awareness based on Thinking. Previous studies have not studied the relationship between consciousness, thinking and time. In this study, the relationship between consciousness, thinking, memories and speech over time has been studied. A deep logical connection exists between consciousness, thinking, and time. An algorithm can be designed for artificial consciousness based on this research findings.

The correspondence between classical and quaternion quantum equations, permits considering the universe (vacuum) as an ideal elastic solid. Elementary particles would have to be standing or soliton-like waves. Tension induced by the compression and twisting of the elastic medium would increase the energy density, consequently generate a gravity forcing and affect the wave speed. Consequently the gravity could be described by an index of refraction. Theory was created by combining the Cauchy model of the elastic continuum with the Planck-Kleinert crystal hypothesis. The quaternion-imaginary Lagrange’an, the quaternion motion equation and the quaternionic oscillator allowed deriving: - The Schrödinger equation from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. - The 2nd order wave equation system describing both the bosons and the gravity in terms of quaternionic Poisson equation. - The first order quaternionic wave equation system. - The family of the second order wave equation systems describing both the particles and the generated quaternionic force-fields (four-potentials). - The fundamental Planck and gravity constants. - The quaternionic continuity equation in an ideal elastic solid.

In a series of recent papers we developed a formulation of general relativity in which spacetime and the dynamics of matter evolve with a Poincaré invariant parameter τ. In this paper we apply the formalism to derive the metric induced by a `static’ event evolving uniformly along its t-axis at the spatial origin x=0. The metric is shown to vary with t and τ, as well as spatial distance r, taking its maximum value for a test particle at the retarded time τ=t−r/c. In the resulting picture, an event localized is space and time produces a metric field similarly localized, where both evolve in τ. We first derive this metric as a solution to the wave equation in linearized field theory, and discuss its limitations by studying the geodesic motion it produces for an evolving event. By then examining this solution in the 4+1 formalism, which poses an initial value problem for the metric under τ-evolution, we clarify these limitations and indicate how they may be overcome in a solution to the full nonlinear field equations.

This article proposes a novel formulation of quantization, which considers the Koopman-von Neumann formulation (KvN) and ordinary non-relativistic quantum mechanics (OQM) as unitarily inequivalent representations of the same underlying structure. The approach is grounded in the notion that contextuality, rather than occurrence if Plank's constant, is the fundamental aspect of quantum mechanics. The motivation for this novel view arises from the limitations of traditional approaches to quantization, combined with previous research demonstrating contextuality in KvN. Using a representation-theoretic approach, both KvN and OQM are regarded as valid quantum theories, separated by a superselection rule.

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

This paper aims to provide an overall review of degradation, damage evolution and fatigue models in the literature of various engineering materials, mostly metals, and composites.

Data on the seasonally dry tropical forests of Mexico have been examined in the light of statistical mechanics. The results suggest a division into two classes of species. There are drifting populations of a cosmopolitan class capable of existing in most dry forest sites; these have a statistical distribution previously only observed (globally) for populations of alien species. A high proportion of species found only at a single site are endemic and these prefer sites comparatively low in species richness.

We numerically study surface models defined on hexagonal disks with a free boundary. 2D surface models for planer surfaces have recently attracted interest due to the engineering applications of functional materials such as graphene and its composite with polymers. These 2D composite meta-materials are strongly influenced by external stimuli such as thermal fluctuations if they are sufficiently thin. For this reason, it is very interesting to study the shape stability/instability of thin 2D materials against thermal fluctuations. In this paper, we study three types of surface models including Landau-Ginzburg (LG) and Helfirch-Polyakov models defined on triangulated hexagonal disks using the parallel tempering Monte Carlo simulation technique. We find that the planer surfaces undergo a first-order transition between the smooth and crumpled phases in the LG model and continuous transitions in the other two models. The first-order transition is relatively weaker compared to the transition on spherical surfaces already reported. The continuous nature of the transition is consistent with the reported results, although the transitions are stronger than that of the reported ones.

We propose a generalization of Nambu-Hamilton equation in superspace $\mathbb R^{3|2}$ with three real and two Grassmann coordinates. We construct the even degree vector field in the superspace $\mathbb R^{3|2}$ by means of the right-hand sides of proposed generalization of Nambu-Hamilton equation and show that this vector field is divergenceless in superspace. Then we show that our generalization of Nambu-Hamilton equation in superspace leads to family of ternary brackets of even degree functions defined with the help of Berezinian. This family of ternary brackets is parametrized by the infinite dimensional group of invertible second order matrices, whose entries are differentiable functions on the space $\mathbb R^{3}$. We study the structure of ternary bracket in a more general case of a superspace $\mathbb R^{n|2}$ with $n$ real and two Grassmann coordinates and show that for any invertible second order functional matrix it splits into the sum of two ternary brackets, where one is usual Nambu-Poisson bracket, extended in a natural way to even degree functions in a superspace $\mathbb R^{n|2}$, and the second is a new ternary bracket, which we call $\Psi$-bracket, where $\Psi$ can be identified with invertible second order functional matrix. We prove that ternary $\Psi$-bracket as well as the whole ternary bracket (the sum of $\Psi$-bracket with usual Nambu-Poisson bracket) is totally skew-symmetric, satisfies the Leibniz rule and the Filippov-Jacobi identity (Fundamental Identity).

The diffraction-like process displayed by a spatially localized matter wave is here analyzed in a case where the free evolution is frustrated by the presence of hard-wall-type boundaries (beyond the initial localization region). The phenomenon is investigated in the context of a nonrelativistic, spinless particle with mass m confined in a one-dimensional box, combining the spectral decomposition of the initially localized wave function (treated as a coherent superposition of energy eigenfunctions) with a dynamical analysis based on the hydrodynamic or Bohmian formulation of quantum mechanics. Actually, such a decomposition has been used to devise a simple and efficient analytical algorithm that simplifies the computation of velocity fields (flows) and trajectories. As it is shown, the development of space-time patters inside the cavity depends on three key elements: the shape of the initial wave function, the mass of the particle considered, and the relative extension of the initial state with respect to the total length spanned by the cavity. From the spectral decomposition it is possible to identify how each one of these elements contribute to the localized matter wave and its evolution; the Bohmian analysis, on the other hand, reveals aspects connected to the diffraction dynamics and the subsequent appearance of interference traits, particularly recurrences and full revivals of the initial state, which constitute the source of the characteristic symmetries displayed by these patterns. It is also found that, because of the presence of confining boundaries, even in cases of increasingly large box lengths, no Fraunhofer-like diffraction features can be observed, as happens when the same wave evolves in free space. Although the analysis here is applied to matter waves, its methodology and conclusions are also applicable to confined modes of electromagnetic radiation (e.g., light propagating through optical fibers).

When phenomena in quantum mechanics are interpreted from the perspective of bio-psychology, wave function collapse from several to a single eigenstate must be plausibly explained. Quantum mechanics requires a context, yet the context of an observer is rarely considered. On the other hand, in bio-psychology, the observer context is examined to explain superposition and collapse by different mental functions used in everyday life. Three mental functions are described, one of which is responsible for observation, and the others for conservation and treatment of information in mental representation. Whereas observation produces information with certainty, the subsequent processes result in uncertain potentiality. In order to encompass uncertainty, multiple possibilities are simultaneously considered in mental superposition, one of which should represent the unknown future outcome. During observation, all suggested potentialities necessarily collapse to one real outcome. The collapse of superposition does not occur in observable physical reality, but in its mental representation. Some physical principles—such as superposition, infinity and nothingness before the Big Bang—are pure phenomena of mental representation, which will always remain unverifiable by observation. This argument proves that mental representation brought about by the observer context participates in the production of mental models for the best approximation of physical reality.

Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc…Using the PBN, many formulas, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions, easy to expand by inserting a proper P-identity. The time evolution of homogeneous Markov processes can also be formatted in such a way. Our system P-kets are identified with probability vectors and our P-bra system is comparable with Doi’s state function or Peliti’s standard bra. In the Heisenberg picture of the PBN, a random variable becomes a stochastic process, and the Chapman-Kolmogorov equations are obtained by inserting a time-dependent P-identity. Also, some QM expressions in Dirac notation are naturally transformed to probability expressions in PBN by a special Wick rotation. Potential Applications show the usefulness of the PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT.

Differences between the quantum mechanical and relativistic concepts of time observed in GPS satellites are accounted for by applying the equivalence principle to the transitioning electron of an atomic clock. It allows a differential equation of motion to be derived for the electron in the Minkowski space between electron shells. Using Hamilton’s principle we transform the differential equation relativistically into an integral equation of motion, the time integral of a Lagrangian. This newly derived equation accounts for the abstract mathematics of the more familiar non-relativistic model by means of a physical interpretation. Abstract rotations in Hilbert space are replaced by the rotations of real particle field geometries in Minkowski space. Because the properties of energy are universal the same equations are then used to describe the field geometry of galaxies despite vast differences in lifetime. They reveal a symmetry between the electromagnetic fields of atoms and the gravitational fields of galaxies due to similarities in the exchange of energy by radial and transverse fields. Our analysis reveals that the conjugate variables energy and time permit differences between atomic and galactic structure to be compared in a more intuitive way than by means of the differential equations of motion which use the conjugate variables position and momentum.

The Planetary Roller Screw Mechanisms (PRSMs), alongside Ball Screw Mechanisms (BSMs) and Electromechanical Actuators (EMAs), occupies a pivotal role in advancing the precision and efficiency of various industrial applications, including aerospace, automotive, and high-precision machining tools. Despite their critical advantages such as high load capacity, superior precision, and extended lifespan, the deployment of PRSMs in complex operational conditions reveals a landscape rife with challenges and opportunities for further research. This comprehensive review endeavors to dissect the multifaceted aspects of PRSMs, focusing on their mechanics and dynamics, tribology and thermal behavior, and the paramount importance of reliability and condition monitoring. By synthesizing current research findings, this paper highlights the significant advancements in understanding the static and dynamic characteristics of PRSMs, the intricate interplay between lubrication conditions and wear mechanisms, and the critical role of thermal effects on operational performance. Moreover, it delves into the dynamic models that address the impact of manufacturing imperfections, such as waviness and defects, on the reliability of these mechanisms. Despite the strides made, the review identifies critical gaps in the existing literature, particularly under conditions of extreme temperatures, large deformations, and multifaceted loads, advocating for a holistic approach to research. By proposing integrated thermo-mechanical models and emphasizing the need for empirical validations, this paper outlines a roadmap for future studies aimed at facilitating the development of more robust and reliable PRSMs, capable of meeting the demands of complex operational scenarios and advancing the field of high-precision applications in aerospace, robotics, and beyond.

The phenomenon of interference is a characteristic of all waves. This paper reviews the interference of classical waves and of matter waves in quantum mechanics. In quantum mechanics, there are two interference mechanisms between identical particles. One is that the de Broglie wavelengths of two interference waves are the same, which is called the equal wavelength interference mechanism. The other is that the wavelengths of interference waves can also be different, in which case there should be an exchange term in additional to the direction term in the wave function. There is a fixed phase difference between the two terms, which causes interference. This is called exchange effect interference mechanism. We propose an experiment, which is simpler to what has been done, to show the exchange effect interference. There is a special case where two interference waves can satisfy both the two mechanisms. We propose an experiment to discriminate that in this case which mechanism plays a role on earth.

Polyhedral oligomeric silsesquioxane (POSS) is a suitable nanoscale reinforcement for thermosetting polymers, such as epoxy resin systems in order to modify its mechanical, thermal, and chemical properties. The inclusion of POSS in the epoxy resin at higher loading (greater than 1 wt.%), however, introduces the ductility during the fracture behavior of these nanocomposites. Consequently, the J-integral is used to quantify the fracture behavior of these materials and characterize the crack growth resistance curve against stable crack growth. A range of nanocomposites is prepared by adding 0.5, 1, 3, 5, and 8 wt.% of glycidyl POSS into DGEBF epoxy resin cured with an amine-based curing agent. From the fracture toughness experiment the load-displacement result confirms that when the POSS reinforcement is greater than 1 wt.%, the fracture behavior of the nanocomposite changes from brittle to ductile. For both brittle and ductile nanocomposites, the addition of POSS molecules improves the crack initiation toughness. The development of POSS–POSS compliant domains are reported previously, is attributed for this change in the failure behavior. The fractured images of POSS–epoxy nanocomposites, obtained using scanning electron microscopy, show that the increase in fracture resistance at higher values of POSS loading occurs due to the extensive shear yielding. Meanwhile, the increased fracture toughness at lower values of POSS loading occurs due to crack pinning and crack deflection.

The interpretation of optical spectra requires thorough comprehension of quantum mechanics, especially understanding the concept of angular momentum operators. Suppose now that a transformation from laboratory-fixed to molecule-attached coordinates, by invoking the correspondence principle, induces reversed angular momentum operator identities. However, the foundations of quantum mechanics and the mathematical implementation of specific symmetries assert that reversal of motion or time reversal includes complex conjugation as part of anti-unitary operation. Quantum theory contraindicates sign changes of the fundamental angular momentum algebra. Reversed angular momentum sign changes are of heuristic nature and are actually not needed in analysis of diatomic spectra. This work addresses sustenance of usual angular momentum theory, including presentation of straightforward proofs leading to falsification of the occurrence of reversed angular momentum identities. This review also summarises aspects of a consistent implementation of quantum mechanics for spectroscopy with selected diatomic molecules of interest in astrophysics and in engineering applications.

At present there is a renewed interest in theories of ”modified” gravity. Here, under a more drastic modification enforced by Galilei group, we obtain a completely new gravitational structure, and which exists in addition to the already available general relativity of today. Correlated with this, we show that in addition, there is a new ”modified” quantum mechanics, in as much as it exists as an independent and new ”pure” non-relativistic quantum me- chanics, and which has no relativistic counterpart. This is in addition to the present quantum mechanics, where the relativistic and non-relativistic structures are counterparts of each other. The above holds, firstly due to the correlation between Galilei group and quantum mechanics. These math- ematical conclusions are consolidated by the fact that there exists a physical Majorana interaction between each neutron- proton pairs in nuclei. Galilei invariance of Majorana exchange in Majorana interaction, shows that the mass here is of pure gravitational nature, and which is immune to the other three forces. This makes an amazing connection between the gravitational force and the quantum mechanics. This pure gravitational mass would man- ifest itself as dark matter of the universe. It is our new modified gravity that generates the dark matter.

Damage in concrete structures initiates as the growth of diffuse microcracks that is followed by damage localisation and eventually leads to structural failure. Weak changes such as diffuse microcracking processes are failure precursors. Identification and characterisation of these failure precursors at an early stage of concrete degradation and application of suitable precautionary measures will considerably reduce the costs of repair and maintenance. To this end, a reduced order multiscale model for simulating microcracking-induced damage in concrete at the mesoscale levelis proposed. The model simulates the propagation of microcracks in concrete using a two-scale computational methodology. First, a realistic concrete specimen that explicitly resolves the coarse aggregates in a mortar matrix was generated at the mesoscale. Microcrack growth in the mortar matrix is modelled using a synthesis of continuum micromechanics and fracture mechanics. Model order reduction of the two-scale model is achieved using clustering technique. Model predictions are calibrated and validated using uniaxial compression tests performed in the laboratory.

The maximization of entropy S within a closed system is accepted as an inevitability (as the second law of thermodynamics) by statistical inference alone. The Maximum Entropy Production Principle (MEPP) states that not only S maximizes, but $\dot{S}$ as well: a system will dissipate as fast as possible. There is still no consensus on the general validity of this MEPP, even though it shows remarkable explanatory power (both qualitatively and quantitatively), and has been empirically demonstrated for many domains. In this theoretical paper I provide a generalization of entropy gradients, to show that the MEPP actually follows from the same statistical inference, as that of the 2nd law of thermodynamics. For this generalization I only use the concepts of super-statespaces and microstate-density. These concepts also allow for the abstraction of 'Self Organizing Criticality' to a bifurcating local difference in this density, and allow for a generalization of the fundamentally unresolved concepts of 'chaos' and 'order'.

This article objectively assesses, the hypothesis of the streamline's shape theory and its formulated equation. The deduction of proof uses algebra rather than first-order partial differential equations to address the specific hypothesis of "Streamline's shape theory" from the fundamental perspective of applied mathematics and scientifically derives mathematical relations of the axioms and corollaries in the field of fluid dynamics. The algebraic methods employed provide progressively more distinct and precise solutions compared to first-order partial differential equations. The foremost objective of this work is to evaluate if the formulations of the streamline's shape theory can have solutions for inviscid-incompressible and viscid-compressible flows of Newtonian fluids and to identify their nature. Secondly, to understand how the topology of the body and the free-stream conditions affect these solutions with due regards to the shape and size of the body interacting with the fluid flow. Finally, to explore the possibility of this theory to develop a CFD solver for streamline simulation to reduce the experimentation in the analysis of flow-structure interactions of Newtonian fluids and also to identify its scope of applications and limitations.

We refute a recently proposed thought experiment namely the Dead-Alive Physicist (DAP) whose authors claim it to be the falsification of the von Neumann interpretation in Quantum Mechanics. We discover major flaws in their model and our justification serves the purpose of disregarding further claims and assertions made in the paper at various stages. Thus, in a yet another situation, it is proven that the formalism advanced by von Neumann is non-trivial and non-falsifiable.

Planck’s constant and the gravitational constant are comprised of more fundamental quantities of length, mass, and time. Reformulating traditional equations in terms of these fundamental units offers a more granular view of the physical transformations encoded in the equations of physics. The composite structure of h and G conceals a simple model in which maximum unit potentials are reduced by dimensionless proportionality operators. Natural symmetries correlate the three unit dimensions, yielding predictable quantities of physical dynamics. Insights are organized into a New Foundations Model of physics that reformulates traditional constants and equations in elementary form. The New Foundations Model offers a common language for describing quantum mechanical, gravitational, and electromagnetic phenomena.

The loss of integrity and adverse effect on mechanical properties can be concluded as attributing miro/macro-mechanics damage in structures, especially in composite structures. Damage as a progressive degradation of material continuity in engineering predictions for any aspects of initiation and propagation requires to be identified by a trustworthy mechanism to guarantee the safety of structures. Besides the materials design, structural integrity and health are usually prone to be monitored clearly. One of the most powerful methods for the detection of damage is machine learning (ML). This paper presents the state of the art of ML methods and their applications in structural damage and prediction. Popular ML methods are identified and the performance and future trends are discussed.

This work has its origin in intuitive physical and statistical considerations. The problem of optimizing an artificial neural network is treated as a physical system, composed of a conservative vector force field. The derived scalar potential is a measure of the potential energy of the network, a function of the distance between predictions and targets. Starting from some analogies with wave mechanics, the description of the sys-tem is justified with an eigenvalue equation that is a variant of the Schr˜odinger equation, in which the potential is defined by the mutual information between inputs and targets. The weights and parameters of the network, as well as those of the state function, are varied so as to minimize energy, using an equivalent of the variational theorem of wave mechanics. The minimum energy thus obtained implies the principle of minimum mutual information (MinMI). We also propose a definition of the potential work produced by the force field to bring a network from an arbitrary probability distribution to the potential-constrained system, which allows to establish a measure of the complexity of the system. At the end of the discussion we expose a recursive procedure that allows to refine the state function and bypass some initial assumptions, as well as a discussion of some topics in quantum mechanics applied to the formalism, such as the uncertainty principle and the temporal evolution of the system. Results demonstrate how the minimization of energy effectively leads to a decrease in the average error between network predictions and targets.

A convenient practical model for accurately estimating the total entropy (ΣSi) of atmospheric gases based on physical action is proposed. This realistic approach is fully consistent with statistical mechanics, but reinterprets its partition functions as measures of translational, rotational and vibrational action or quantum states, to estimate the entropy. With all kinds of molecular action expressed as logarithmic functions, the total heat required for warming a chemical system from 0o K (ΣSiT) to a given temperature and pressure can be computed, yielding results identical with published experimental third law values of entropy. All thermodynamic properties of gases including entropy, enthalpy, Gibbs energy and Helmholtz energy are directly estimated using simple algorithms based on simple molecular and physical properties, without resource to tables of standard values; both free energies are measures of quantum field states and of minimal statistical degeneracy, decreasing with temperature and declining density. We propose that this more realistic approach has heuristic value for thermodynamic computation of atmospheric profiles, based on steady state heat flows equilibrating with gravity. Potentially, this application of an action principle can provide better understanding of emergent properties of many natural or evolving complex systems, including modelling of predictions for global warming.

Inspired by amazing result obtained by Semay [1], this study revisits generalised Kepler's third law of an n-body system from the perspective of dimension analysis. To be compatible with Semay's quantum n-body result, this letter reports a conjecture which had not be included in author's early publication [2] but formulated in the author's research memo. The new conjecture for quantum N-body system is proposed as follows: Tq|Eq|^3/2 = πG/√2[(Σ^N_i=1 Σ^N_j=i+1 m_im_j)³/(Σ^N_k=1 m_k)]^1/2. This formulae is, of course, consistent with the Kepler's third law of 2-body system, and exact same as Semay's quantum result for identical bodies.

If "quantization is an art" then it can be greatly rened by adopting cyclic time formalism. In past papers we have proven the effectiveness of a formulation of physics based on cyclic relativistic time. Now we can demonstrate in a general way, by using theorems of Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics directly imply the ordinary canonical commutation relations and the other Dirac's rules of canonical Quantum Mechanics. In other words, according to our result, canonical quantization is an implicit way of imposing intrinsically cyclic time dynamics without explicitly saying that time is a cyclic dimension.

The Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and ensure that the predictions are consistent and stable with the physical laws. PINNs opens up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar-Gross-Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts the equilibrium control equations in different discrete velocity directions within SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling inference of the fluid's non-equilibrium characteristics. The third component, a physics informed function translates the outputs of the first two networks into physical infor-mation. By minimizing the residuals of the physical partial differential equations (PDEs), the physics informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models applicable to different dimensions, named PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physical informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into the neural network through the interpretation function. Therefore, PINN-SRT-LBM allows the neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Experimental results confirm the accurate prediction of flow infor-mation at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.

At the highest level of endurance sports, the differences in finishing times are small, so equipment is constantly being constantly improved to enhance the athletes' performance. For instance, one dominant resistive force in connection with cross-country skiing is the friction between the skis and snow and since the 1930s, research designed to understand and reduce this friction has been ongoing. The mechanisms involved in ski-snow friction include compaction, micro-ploughing, adhesion, viscosity, and water-bridging. Of these, adhesive and viscous friction have been most studied, while much less is presently known about compaction, micro-ploughing, and water-bridging. At the macro-scale, the ski-camber profile plays a key role in determining whether, with respect to friction, a particular cross-country ski is suitable for use under a given set of conditions. Through its influence on where ski-snow contact occurs, this ski-camber profile has a profound impact on adhesive and viscous friction, micro-ploughing, the formation of water bridges, and the rate of compaction. Different contact zones with different apparent areas of contact and pressure have been found to be most suitable for different conditions. In addition, the micro-scale texture of the ski base is also an important determinant of ski-snow friction. Topographical measurements of this texture can be achieved with white-light interferometer and recent characterisation has focused on the mechanical properties of contact. In numerous tribological studies the interactions between features at different scales are modelled. In most tribological systems, features on several scales influence friction and ski-snow contact is certainly no exception. Accordingly, the current investigation was designed to evaluate the multi-scale properties of different combinations of two skis with two different base textures. The real area of contact and the average interfacial separation and total average reciprocal interfacial separation between the ski and snow were taken into consideration. We found that different macro- and micro-scale properties of the ski favour different mechanisms of friction. Both the profile of the ski camber and texture of the base play decisive roles in determining viscous friction. At the same time, the texture of the ski base exerts a greater impact on the average real contact pressure, real contact area and minimal average interfacial separation between the ski and snow than does the ski-camber profile.

This study aimed to investigate the effects of forearm postures and elbow joint angles on muscle torque and mechanomyography (MMG) signals. The torque about the elbow and MMG of the biceps brachii (BB) muscle were measured in 36 healthy subjects using an in-house elbow flexion testbed and Neuromuscular electrical stimulation (NMES) of the BB muscle. The BB muscle received stimulation intensity while the forearm was positioned in the neutral, pronation or supination. The elbow was flexed at angles 10°, 30°, 60° and 90°. (0° = full elbow extension). The study analyzed the impact of forearm posture(s) and elbow joint angle(s) on the root mean square value of torque (TQ_RMS). Subsequently, MMG parameters such as the root mean square value (MMG_RMS), the mean power frequency (MMG_MPF), and the median frequency (MMG_MDF), were analyzed in the longitudinal, lateral, and transverse axes of the BB muscle fibers. Forearm posture and elbow flexion angle were found to significantly influence TQ_RMS (P < 0.05). Similarly, MMG_RMS, MMG_MPF and MMG_MDF exhibited a significant difference for all postures and angles (P < 0.05). However, the combined main effect of forearm postures and elbow joint angles was insignificant in the longitudinal axis (P > 0.05). The study also found that MMG_RMS and TQ_RMS increased with the joint angle to 60° and decreased to the other angle(s). However, during this investigation,MMG_MPF and MMG_MDF exhibited a consistent decrease in response to joint angles. This finding suggests that the muscle contraction evoked by NMES may be influenced by the interplay between actin and myosin filaments, which are responsible for muscle contraction and are in turn influenced by muscle length. As restoring the function of limbs is a common goal in rehabilitation services, it becomes imperative to develop methods that may enable the real-time tracking of exact muscle dimensional changes and activation levels.

In cross-country skiing the time difference between a race winner and the person coming second is typically very small. Since much of the energy is spent on overcoming resistive forces, a relatively small reduction of these can have a significant impact on the results. The resistive forces come partly from the friction in the tribological interface, between the ski and the snow, and as with many tribological applications the characterisation of its origin, plays an important role in determining the frictional properties. Also in cross-country ski friction, there are several scales impacting the frictional performance, with the major contributors being the ski-camber profile and ski-base structure. Macro-scale measurements of the ski's camber profile under load, are often used to determine how adequate the ski is for a specific condition. The characteristic properties usually obtained are, the force required to collapse the ski to a certain camber height, the topography of the kick-wax zone, and by simple means a determined lengths of the frictional interface, i.e., the apparent contact length. To this date, there are some mathematical models, but there is no robust way of determining the macro-scale contact properties between a cross-country ski and a counter surface using simulations. In the present paper an Artificial neural networks (ANN) is trained to predict the ski-camber profile for various loads placed at different positions, and a well established deterministic approach is used to simulate the contact between the ANN-predicted ski-camber profile and a linearly elastic body with a flat surface, representing the snow. The results suggest that this method is feasible for the determination of the apparent contact characteristics of different skis. Moreover, we show that the apparent contact area does not linearly depend on the load, and that the elastic properties of the counter surface also has a large impact on the apparent contact area and the average apparent contact pressure.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

Economics has long sought to bridge the principles of microeconomics into the realm of macroeconomics. This paper presents a formal attempt to do so by using a maximum entropy based approach derived from statistical mechanics coupled with subjective game theory and elements from political philosophy. This approach is then applied to income distributions and to the Cobb-Douglas production function, to create a framework for future applications, and to illustrate where past work had made implicit assumptions regarding the system. The paper then explores the consequences of the approach, illustrating self-contradictions in the political philosophy of distributive justice, formally deriving an equation of state for the transactions on the Bitcoin network, and deriving from this the ideal gas law and polytropic process for an economy proving that expansionary monetary policy is not stimulative.

We show that the quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems allowing exposing its falsity.

Total hip arthroplasty is a complex procedure. The achievements of implantology enabled the development of a faithful representation of hip joint physiology as well as the production of materials that can successfully replace damaged natural tissues. A very important issue is the correct selection of the geometry of the endoprosthesis adequate to the load of the joint. Materials used for endoprosthesis are a metal head and a polymer cup (e.g. PE-UHMW). The main interactions in the endoprosthesis are friction and surface pressure, which must be limited, exceeding them causes the destruction of the biomechanical system - plastic deformation of the polymer and the formation of too large and unacceptable radial clearances. Based on the author's developed calculation method of hip joint endoprosthesis contact parameters, the impact on maximum contact pressure and the angle of contact of the joint load was estimated depending on the diameter of the endoprosthesis and radial clearance. The correctness of changing the values of maximum contact pressure from the mentioned parameters was determined. Correspondingly: an increase in joint load causes a linear increase in the maximum contact pressure; increasing the diameter of the endoprosthesis head - their non-linear decrease, and increasing radial clearance - their increase

The asymmetry in the dynamics of an electro-pneumatic actuating device consisting of an electro-pneumatic transducer and a single-action pneumatic actuator was unexpectedly found experimentally. This asymmetry manifests in response to large step excitations. The dynamic asymmetry effect is understood as a change in the shape of the response of an actuator depending on the direction of the actuators stem movement. The questions appears: How to explain this effect? Does this phenomenon reflect thermodynamic air processes? Is it connected with air-to-mechanical energy conversion? Together, six working hypotheses explaining this effect were formulated. The asymmetry was studied in detail using analytical and simulation modeling, as well as experimental research. In this respect, a nonlinear analytical model was developed, tuned, and later solved using simulations. The simulation model was verified based on the experiment data. In addition, the problem of the efficiency in the energy conversion of a single-action actuator was discussed and, in result, the maximum theoretical energy efficiency was determined. Subsequently, all six working hypotheses were verified. Finally, the hypothesis explaining asymmetry as an effect of the different thermodynamic air processes in both actuator’s stem travel directions was confirmed.

This paper uncovers that quantum uncertain principle makes the single particle with global property have no certain path, and then wave of quantum particle can simultaneously do pass the double slits. The two subwaves after passing Young’s double slits are entanglement, they may form interference of subwaves. Consequently, we find a kind of quantum probabilistic entanglements with Wheeler's delayed choice. Quantum particles such as photons, electrons, neutrons, protons etc mean that wave of the quantum particle can simultaneously do pass through Young's double slits, rather than individual quantum particle may pass through Young's double slits at the same time. When considering wave property, we cannot consider particle property (Just as in the photoelectric effect, considering the particle nature of the system, people cannot consider wave property, otherwise the photoelectric effect cannot appear). Therefore, this paper discovers that the ability of single photon to hit electrons out in photoelectric effect is complementarily equivalent to the ability of wave of the single photon to simultaneously pass through Young's double slits in wave-particle duality. Objective criteria for distinguishing classical and quantum particles are discovered and objectively give the applicable realm of quantum mechanics for the first time. The crisis of the single particle’s simultaneously passing through Young's double slits, which has been plaguing physicists in the whole world up to now for decades, is solved, in which the studies are classified as classical and quantum particles, the classical particle and quantum particle wave cannot and can pass the Young’s slits, respectively. This paper discovers both the new physics mechanism of passing the double slits of the wave with the amplitude of 4-dimensional momentum representation wave function reflecting particle nature and the principle of self-adaptive emergence of wave-particle duality, and then using the principle, this paper gives both direct explanations to the current experiments and new predictions of new some experiments for wave-particle duality. All the deduced results here are consistent with all relevant physics experiments.

In quantum approaches to consciousness, the authors try to propose a model and mechanism for the mind-brain interaction using modern physics and some quantum concepts which do not exist in the classical physics. The independent effect of mind on the brain has been one of the challenging issues in the history of science and philosophy. In some recent mind-brain interaction models, the direct influence of mind on matter is either not accepted (as in Stapp’s model) or not clear, and there have not been any clear mechanism for it (as in Penrose-Hameroff’s model or in Eccles’s model). In this manuscript we propose a model and mechanism for mind’s effect on the matter using an extended Bohmian quantum mechanics and Avicenna’s ideas. We show that mind and mental states can affect brain’s activity without any violation of physical laws. This is a mathematical and descriptive model which shows the possibility of providing a causal model for mind’s effect on matter. It is shown that this model guarantees the realistic philosophical constraints and respects the laws of nature. In addition, it is shown that it is in agreement with the Libet style experimental results and parapsychological data. To propose this model, we obtained a modified (non-unitary) Schrödinger equation via second quantization method which affects the particle through a modified quantum potential and a new term in the continuity equation. At the second quantized level, which is equivalent to quantum field theory level (QFT), we can use the path integral formalism of Feynman. We show that there are three methods to extend Bohmian QM via path integral formalism, which has different interpretations. By numerical simulation of trajectories in the two-slits experiment, we show their differences and choose one of these methods for our mind-brain model which can be the basis for explaining some phenomena which are not possible to explain in the standard Bohmian QM.

Rigid-hulled inflatable boats are extremely practical and popular nowadays. They offer a effective conciliation among usability and costs. Their stable and seaworthy behaviour is guaranteed by performing hydroplaning hulls coupled with unsinkable inflated tubes. At the same time, their design is often based on tradition and preconceptions. Rarely, the design assumptions are validated by the reality or, even, by deeper investigations. In this article, both numerical methods and experimental mechanics techniques are proposed as an essential way for supporting the designers in their decisive tasks. Three different situations are detailed where a numerical or an experimental approach shows its benefit inside the engineering design process: firstly permitting to investigate the behaviour of materials driving the fiberglass selection; then measuring the levels of stress and strain in the hull during sailing; finally, using all available information as a base for developing numerical models of the hull slamming in waves. Even if the discussion is focused on a rigid inflatable boat, large part of its considerations is relevant beyond this special case.

In recent years, cemented tailings/paste backfill (CPB) become more and more important to maintain mine structure and keep mining stope to be stable in deep underground mining. Deep mining process often accompanied by blasting, rock burst and other high-speed dynamic loading. So it’s important to make research on dynamic behavior and characteristics of CPB. In this paper, a series of dynamic loading tests on CPB specimens by SHPB were taken to study the characteristic of stress-strain, dynamic strength, deformation and failure of CPB. The experimental results revealed that some CPB specimens have 1~2 lower stress peaks after reaching the peak stress before getting completely failed. The greater the cement-sand ratio was, the more obvious of strain reaction was. This property mainly showed like follows. The greater the cement-sand ratio was, the greater the dynamic compressive strength was under similar velocity impact; the dynamic compressive strength and the average strain rate were quadratic equation relationship, and the greater the cement-sand ratio was, the higher increase rate of dynamic compressive strength caused by strain rate. The dynamic compressive strength enhancement factor increased with the increase of the strain rate, and is larger than that of rock samples. The failure forms of CPB specimens under low-speed impact were almost the same as them under static uniaxial and triaxle compression. The CPB specimens were crushed broken under the critical strain rate, similar to the failure mode of low strength concrete. The experimental research results will improve our understanding the dynamic mechanical property of CPB and help to guide the strength design of deep mining backfill.

This article is some review of results that were obtained at 2007-2021 years development of “The Information as Absolute” concept and the informational physical model, which is based on the concept; including a number of fundamental physical problems are briefly considered in framework of the conception and the model. Recently in physics there are several publications, that present lists of the problems. However, those lists are essentially incomplete, for at least two reasons. Firsts of all, a number of phenomena are studied traditionally by philosophy, and so corresponding problems are usually considered to be “metaphysical”. However, they relate also to some concrete physical phenomena. For example, physics evidently studies Matter, and so the metaphysical problems “what is ontology of Matter”, “what is “Space”, “Time” and a few other physical phenomena and notions as well, are really a Meta-physical problems “what does physics study?” There are other fundamental physical problems, which are not considered as such in physics, and are absent in the “fundamental problems lists”. Those include the problems, which really exist, yet are incorporated into standard physical theories, and so are fundamental “implicitly”, which in physics are “solved by default” ‒ and mostly erroneously. Note, though, that a number of “Meta-physical”, and concrete fundamental, problems more in detail are considered in the paper “The Informational Conception and Basic Physics”, https://arxiv.org/abs/0707.4657, v5 (2021), so this paper is, in certain sense, an expanded conclusion of this paper, which includes, correspondingly, more in detail consideration of some more general physical problems; and, besides, in this article, the problem “what are Gravity and Electric Forces” is essentially clarified comparing with the arXiv 2021 paper version above. Besides, the concrete problem “What is Life”, and the rational cosmological model, where a few vague points in standard cosmology rather probably are rationally clarified, while the fundamental problem “matter – antimatter asymmetry” in Matter is solved practically for sure, are considered, and one of recently published rather complete “lists of fundamental problems” is commented in Appendix.

Several mathematicians and physicists are working all over the globe to get a unified theory. However, most of them are discarding Einstein’s view at the very first step of their theories. This article provides a brief description about this. Also, on the basis of Koga’s theory we point out two reasons which might have caused Einstein’s failure to get a unified theory.

Developing detailed Finite Element Models related to aerospace, automobile, civil, material science etc could be a very challenging task, especially generating a mesh that could produce accurate results. This review article provides an overview of different types of structural mechanics problems which are of interest to researchers and recent developments in meshing methodology related to each type of problems. The article also describes an automatic 2D mesh generation framework leverag- ing the capabilities of commercial FEA software MSC.PATRAN

This paper attempts to describe the large-scale (solar system-like, astronomical-scale) systems of the known world using the physical models and mathematical tools of relativistic quantum mechanics. The value of H_x can be introduced and approximated as an analogue of the constant ℏ. Based on the quantum mechanical approach, the proper time scale of the solar system can be determined.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1^st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

In this article we study the presence of chaos in supersymmetric(SUSY) quantum mechanics. For that purpose we present a form of 4-point out of time order correlator(OTOC) for SUSY quantum mechanical systems using tensor product formalism. We calculate the 4-point OTOC for SUSY 1D harmonic oscillator and find that the OTOC is exactly equal to that of 1D bosonic harmonic oscillator system. In similar manner using the eigenstate representation of supersymmetric systems we calculate the generalized higher order out of time order correlator. The higher order OTOC is a more sensitive measure of chaos than the usual 4-point correlator used in literature. Finally, we calculate the generalized 2N-point OTOC for SUSY 1D harmonic oscillator.

We have shown that according to the predictions of the standard quantum theory, signaling is possible using a postponed compensation Hong-Ou-Mandel interferometer, although it violates Lorentz invariance. We argue that new physics is required to deal with such a paradox. Either quantum principles or relativity needs reassessment. We propose an experiment that can decide whether relativity rules over quantum or vice versa.

This is a short introductory review on quantum-like modeling of cognition with applications to decision making and rationality. The aim of the review is twofold: a) to present briefly the apparatus of quantum information and probability theory useful for such modeling; b) to motivate applications of this apparatus in cognitive studies and artifical intelligence, psychology, decision making, social and political sciences. We define quantum rationality as decision making that is based on quantum information processing. Quantumly and classically rational agents behaves differently. A quantum-like agent can violate the Savage Sure Thing Principle, the Aumann theorem on impossibility of agreeing to disagree.Such an agent violates the basic laws of classical probability, e.g., the law of total probability and the Bayesian probability inference. In some contexts, ``irrational behavior'' (from the viewpoint of classical theory of rationality) can be profitable, especially for agents who are overloaded by a variety of information flows. Quantumly rational agents can save a lot of information processing resources. At the same time, this sort of rationality is the basis for quantum-like socio-political engineering, e.g., social laser. This rationality plays the important role in the process of decision making not only by biosystems, but even by AI-systems. The latter equipped with quantum(-like) information processors would behave irrationally, from the classical viewpoint. As for biosystems, quantum rational behavior of AI-systems has its advantages and disadvantages. Finally, we point out that quantum-like information processing in AI-systems can be based on classical physical devices, e.g., classical digital or analog computers.

In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained by the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion.

Mathematics first is a logical system. But, the Mathematics Crisis showed that we cannot have a logical self-consistent mathematics system. Physics is a kind of applied science. It first need be valid to invent new production and understand new observation. In one theory of physics, the studied object is usually defined as an abstract concept. For example, the Sun is defined as a point particle in the Newtonian theory of gravity. In different theories of physics, the abstract concept for a same object is different. It determines that logical self-consistent is not needed for different theories of physics. Physics only can be developed from observation and experiment. But, in the past a century, physicists’ main attempt is to have a standard model, such as the Grand Unification or the Theory for Everything, from mathematics derivation. Therefore, the current attempt to develop new physics is questioned. In recent, the strong gravitational field was studied. It is found that the fundamental physical constants which are measured in the weak field shall be varied in a super strong field. For the two reasons, modern physics need be advanced greatly.

n this article a first attempt at formalizing a new approach to the grand unified theory is introduced. This theory named NUVO is based primarily on considering two aspects of inertia. The first aspect is how a mass couples to space, introducing definitions to distinguish massive particles from massless particles. The second aspect is space’s availability to couple to massive particles. In essence these are the two contributions of inertia; mass and space. Postulates, clarifications, and a mathematical structure are introduced. Part 1 covers the physics of the very large (cos- mic), laying ground work for part two which applies the structure to the very small (quantum). The cosmic application of the theory will show a strong correlation to empirical data and correspondence to General Rela- tivity, including; time dilation, length contraction, and orbital advances. Departing from the canonical findings of General Relativity by predicting a quantization of physical units under the effect of acceleration and or gravity.

The paper is a continuation of another paper (https://philpapers.org/rec/PENFLT-2) published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense (https://dx.doi.org/10.2139/ssrn.3656179), in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem.

In previous work, a quantum mathematical formalism associated an element of experience with a single sensory neuron, as a local reduction of a global mental state. In contrast to the binary objective states of neuronal polarisation/depolarisation, neuronal experience was modeled as a continuous variable, the instantaneous value of which could only be estimated statistically from an ensemble of evoked responses to stereotyped stimulus presentation. In the present work, the quantum operations formalism of energy dissipation through amplitude damping is adopted to explain how smooth evolution of conscious experience might arise from discrete spikes and discontinuous synaptic transmission between neurons.

Quantum mechanics could be studied through polynomial algebra, as has been demonstrated by a work (“An approach to first-principles electronic structure calculation by symbolic-numeric computation” by A. Kikuchi). We carry forward the algebraic method of quantum mechanics through algebraic number theory; the basic equations are represented by the multivariate polynomial ideals; the symbolic computations process the ideal and disentangle the eigenstates as the algebraic variety; upon which one canbuild the Galois extension of the number field, in analogy with the univariate polynomial case, to investigate the hierarchy of solutions; the Galois extension is accompanied with the group operations, which permute the eigenstates from one to another, and furnish the quantum system with a non-apparent symmetry. Besides, this sort of algebraic quantum mechanics is an embodiment of the class field theory; some of the important consequences of the latter emerge in quantum mechanics. We shall demonstrate these points through simple models; we will see the use of computational algebra facilitates such sort of analysis, which might often be complicated if we try to solve them manually.

Time, traditionally viewed as a linear, non-dynamic parameter, is re-envisioned in this study as a Hyperdimensional concept. This paper conducts a cross-disciplinary examination, critically analysing the conceptualization of time in classical mechanics, quantum mechanics, and cosmology to propose a ground breaking reconceptualisation that extends beyond conventional frameworks. In classical mechanics, time is perceived as an absolute, continuously progressing backdrop, largely independent of events. Quantum mechanics treats time as a static parameter that does not influence quantum states but provides a framework for their evolution. In cosmology, time is considered a dimension that emerges from the Big Bang and serves as a measure for the universe's expansion, yet it does not interact with the structural dynamics of the cosmos. Challenging the transformative insights of Einstein’s relativity, which merges time with spatial dimensions under extreme conditions, we advocate for a perspective that views time as a Hyperdimensional and universal constant. This perspective posits that time, despite its unique and intrinsic properties, does not dynamically interact with or alter physical phenomena. Instead, it underpins our understanding of phenomena across different scales—from the minutiae of quantum states to the macroscopic dynamics of cosmology—without direct causation or change. A critical examination of time dilation and relativistic assumptions reveals significant discrepancies in traditional interpretations, particularly in how they are applied across different physical contexts. Our findings challenge the uniform applicability of time dilation, suggesting that observed phenomena often attributed to relativistic effects might better be explained through non-relativistic mechanisms such as phase shifts or changes in wavelength rather than temporal dilation. By synthesizing insights from various scientific domains, we advocate for a unified theory that recognizes time as a fundamental, universal dimension that is conceptual and non-interactive. Our goal is to bridge existing gaps between diverse scientific interpretations and promote a more integrated, profound understanding of time's autonomous and intrinsic nature.

With simple but rigorous arguments we prove that the ordinary second quantization of bosonic and fermionc fields is formally equivalent to constraining the elementary degrees of freedom of the classical fields to have intrinsically periodic dynamics in time. This result confirms and extends the formal equivalence obtained in previous papers for general Hamiltonian systems in terms of canonical quantization, for elementary relativistic particles also in terms of the Feynman Path Integrals, as well as other remarkable correspondences of both phenomenological and theoretical fundamental interest.

The fatigue life of welded joints under cyclic loading is a complex process that can be roughly divided into fatigue crack initiation, crack propagation and final fracture. Usually, these phases are evaluated separately. Several methods are available to estimate the extent of the different phases in welded components, such as stress-based fatigue concepts for crack initiation or linear elastic fracture mechanics for crack propagation; however, distinguishing these phases in welded components is a complex procedure and often relies on assumptions such as transition crack sizes. The objective of this study is to investigate the relationship between fatigue crack initiation and propagation in welded joints using artificially notched specimens with welded joints characteristics of different notch acuity (different radii and opening angle). The experiments show that the investigated relationship basically depends on the notch acuity, the load level and the stress ratio.

The mechanisms of natural oscillations and resonance are described, considering the peculiarities of the transformation of elastic and kinetic energy in the implementation of the law of conservation of energy in local and integral volumes of the body, using the concept of mechanics based on the concepts of space, time and energy. When describing the motion in the Lagrange form, the elastic deformation energy of the particles is determined by the quadratic invariant of the tensor, whose components are the partial derivatives of Euler variables with respect to Lagrange variables. The increment of the invariant due to elastic deformation is represented as the sum of two scalars, one of which depends on the average value of the relative lengths of the edges of the particles in the form of an infinitesimal parallelepiped, the second is equal to the standard deviation of these lengths from the average value. It is shown that each of the scalars can be represented in the form of two dimensionless kinematic parameters of elastic energy, which participate in different ways in the implementation of the law of conservation of energy. One part of the elastic energy passes into kinetic energy and participates in the implementation of the law of conservation of energy for the body as a whole, considering external forces. The second part is not converted into kinetic energy but changes the deformed state of the particles in accordance with the equations of motion while maintaining the same level of the part of the elastic energy of the particles used for this. The kinematic parameters differ from the volume density of the corresponding types of energy by a factor equal to the elastic modulus, which is directly proportional to the density and heat capacity of the material and inversely proportional to the volume compression coefficient. Transverse, torsional, and longitudinal vibrations are considered free and under resonance conditions. The mechanisms of transformation of forced vibrations into their own after the termination of external influences and resonance at the superposition of free and forced vibrations with the same or similar frequency are considered. The formation of a new free wave at each cycle with an increase in the amplitude, which occurs mainly due to internal energy sources, and not external forces, is justified.

In this work, we propose a transition wave equation from quantum to classical regime in the framework of the von Neumann formalism for ensembles and then obtain an equivalent scaled equation. This leads us to develop a scaled statistical theory following the well-known Wigner-Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in-between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities including probability density plots, scaled trajectories and arrival times are analyzed.

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

A new framework in quantum chemistry has been proposed recently ("An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The indeterminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Grröbner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this article, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geometry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in quantum mechanics. We solve simple problems in "quantum chemistry in algebraic variety'' by means of algebraic approach. Finally, we review several topics related to polynomial computation, whereby we shall have an outlook for the future direction of the research.

The shortage of quantum computers, and their current state of development, constraints research in many fields that could benefit from quantum computing. Although the work of a quantum computer can be simulated with classical computing, personal computers take so long to run quantum experiments that they are not very useful for the progress of research. This manuscript presents an open quantum computing simulation platform that enables quantum computing researchers to have access to high performance simulations. This platform, called QUTE, relies on a supercomputer powerful enough to simulate general purpose quantum circuits of up to 38 qubits, and even more under particular simulations. This manuscript describes in-depth the characteristics of the QUTE platform and the results achieved in certain classical experiments in this field, which would give readers an accurate idea of the system capabilities.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.

In previous studies we found that generalized functions can be smooth, discrete, periodic or discrete periodic and they can either be local or global and they are regular or generalized functions. We also saw that these properties were related to Poisson’s summation formula on one hand and to Heisenberg’s uncertainty principle on the other. In this paper, we interlink these studies and show that scalars (real or complex numbers) considered as trivial functions are discrete and periodic, local and global as well as regular and generalized, simultaneously. However, this is also a paradox because it means that Dirac’s δ and 1 (its Fourier transform) coincide. They both are unity. We show that δ and 1 coincide in the sense of scalars (real or complex numbers) but they differ in the sense of (generalized) functions. This result can moreover be related to Max Born’s principle of reciprocity. It also answers an open question in present-day quantum mechanics because it means that the Dirac delta squared is simply delta.

In this article, we investigate both the Schrödinger and continuity equations in the presence of nonlocal potential that arising from electron-electron interaction and local one in the context of minimal uncertainty in momentum within commutative and noncommutative frameworks. Furthermore, the Frahn–Lemmer potential type is used. Interestingly, the combined effects of both the phase-space noncommutativity and nonlocality on the current density while considering a minimal uncertainty in momentum are examined. We find that the current density, as conventionally defined, does not fulfil the condition of current conservation, thus, a new definition of the current density that encompasses the aforementioned contributions is given. Thereafter, it is shown that the computed current using the new definition of the current density satisfies the current conservation. Noting that using both the $★$product and linear Bopp-Shift, the noncommutativity is inserted.

The effect of elastic constants, cij, on the nature (easy or difficult) of a cleavage system in YBa2Cu3O7−δ is investigated, by employing a novel three-dimensional eigenfunction expansion technique, based in part on separation of the thickness-variable and partly a modified Frobenius type series expansion technique in conjunction with the Eshelby-Stroh formalism. Out of the available three complete sets of elastic constants, the first constitutes an estimate, while the second assumes tetragonal symmetry. This leaves only the experimental measurements by resonant ultrasound spectroscopy, despite reported values of c12 and to a lesser extent, c66, being excessively high. The present investigation considers six through-thickness crack systems weakening orthorhombic YBCO mon-crystalline plates. More important, the present approach predicts whether a crack would propagate in its original plane/direction or deflect to a different one. This fracture mechanics criterion is then employed for accurate determination of the full set of elastic constants of mono-crystalline YBCO. Finally, generally unavailable results, pertaining to the through-thickness variations of stress intensity factors and energy release rates for a crack corresponding to symmetric and skew-symmetric hyperbolic cosine loads that also satisfy the boundary conditions on the bounding surfaces of an orthorhombic monocrystalline plate bridge a longstanding gap in the field.

This article will continue ansatz gage matrix of Iyer Markoulakis Helmholtz Hamiltonian mechanics points’ fields gage to Pauli Dirac monopole particle fields ansatz gage general formalism at Planck level, by constructing a Pauli Dirac Planck circuit matrix field gradient of particle monopole flow loop. This circuit assembly gage (PDPcag) that maybe operating at the quantum level, demonstrates the power of point fields matrix theoretical quantum general formalism of Iyer Markoulakis Helmholtz Hamiltonian mechanics transformed to Coulomb gage metrics, to form eigenvector fields of magnetic monopoles as well as electron positron particle gage metrics fields. Eigenvector calculations performed based on Iyer Markoulakis quantum general formalism are substituted for gage values of typical eigenvectors of dipolar magnetically biased monopoles with their conjugate eigenvectors, as well as eigenvector fields that are of the electron and positron particles. Then they are compiled to form combinatorial eigenvector matrix bundle of the monopole particle circuit field constructs assembly. Evaluation of this monopole particle fields matrix provided eigenvector fields results like SUSY, having Hermitian quantum matrix with electron-positron annihilation alongside north and south monopoles collapsing to dipolar “stable” magnetism, representing electromagnetic gaging typical metrics fields. Applying experimental observations on magnetic poles with measuring magnetic forces John Hodge’s results were showing asymmetrical pole forces; author has mathematically constructed asymmetric\strings\gage\metrics to characterize electromagnetic gravity, putting together while integrating with stringmetrics gravity that author has been reporting in earlier published articles. Physical Analysis with generalization of mass-charge and charge-fields gage metrics to quantum relativity gage metrics fields are proposed based on author’s proof formalism paper providing derivational algorithmic steps, to determine gage parametric values within the equation of Coulomb gage. Vortex fields’ wavefunctions and the scalar potential characterized by a function and a coupling constant having quantum density matrix together define the gage metrics quantifiable observable measurement physics of electron-positron cross-diagonal fields; contrastingly, diagonal terms of PDPcag matrix characterizes electron-positron particle eigenvector fields, while Hilbert Higgs mass metrics characterizes eigen-matter. Author is already working with Christopher O’Neill about magic square symmetry configurations to quantitatively understand symmetry, structure, and the real space geometry that are expected to form out of vacuum quanta point fields’ quantitative quantum general formalism theory of Iyer Markoulakis. In addition, author is currently collaborating with Manuel Malaver’s astrophysical Einstein Minkowski modified space time metrics evaluations of the sense-time-space relativistic general metrics to have means to account for curving or shaping of spacetime topology of a five-dimensional sense-time-space. Manuel Malaver’s specialization with modified Einstein Maxwell equations for modeling galaxies and stars cosmological physics, utilizing Einstein-Maxwell-Tolman- Schwarzschild and Reissner-Nordström spacetime and black holes theoretical formalisms have author of this paper collaboratively model quantum astrophysics of dark energy Star’s theory with Einstein-Gauss-Bonnet gravity equations.

We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for perfect fluid. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. This definition helps us to explain the cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved.Part II is contained with some analysis of the lagrangian ; derived in Part I ; on the quintessence model.

The paper discusses the 2022 Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by the 2022 Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview.

Ontological premises have profound theoretical implications. This analysis posits a single, universal structure composed of two ontic entities: discrete, quantized units of space ("Planck Spheres") and a State of Absolute Nothingness (the "SOAN"). Planck Spheres and the SOAN form a physical, ultra-high (3 x N) dimensional space ("Planck Space") and a discrete 3D space (or "4D spacetime"). Together, Planck Space and 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the "Dual Ontology"). Critically, a one-to-one mapping and identity exists between the Planck Spheres comprising 4D spacetime and Planck Space. The Dual Ontology conjecture supports radically simplified physical explanations for three distinct areas of theoretical physics: First, the conjecture reconciles fundamental issues in Special Relativity and quantum mechanics by explaining why single and N-body quantum states (a) dynamically evolve in 4D spacetime subject to the speed of light and (b) instantaneously collapse in a physical Planck Space that is not subject to Special Relativity. Second, the temporal and physical asymmetry between the dynamic evolution of quantum states in 4D spacetime subject to Special Relativity and the instantaneous collapse of quantum states in a Planck Space where Special Relativity is inapplicable explains quantum path irreversibility and the arrow of time. Third, at or near the heat death of 4D spacetime, the instantaneous collapse of the energy content of Planck Space and the simultaneous transition of 4D spacetime's extremely widely dispersed energy content to a non-singular, generally localized volume at t = 0 explains 4D spacetime's isotropy, homogeneity, extremely high energy, pressure, and temperature, flatness, and low gravitational entropy. It also explains the horizon and fine-tuning problems.

In this paper, we review a new treatment of classical radiation damping, which resolves a well-known contradiction in the Abraham-Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicizing quantum mechanics by replacing the canonical commutation relation in quantum mechanics with the Poisson bracket relation in classical mechanics. As an application of our new approach, we will analyze the anomalous damping experienced by electrons undergoing cyclotron motion inside a waveguide near the cut-off frequency. This anomalous damping cannot be described using the existing Abraham-Lorentz equation.

Design and advancement of the durable urban train infrastructures are of utmost importance for reliable mobility in the smart cities of the future. Given the importance of urban train lines, tunnels, and subway stations, these structures should be meticulously analyzed. In this research, two-dimensional modeling and analysis of the soil-structure mass of the Alan Dasht station of Mashhad Urban Train are studied. The two-dimensional modeling was conducted using Hashash’s method and displacement interaction. After calculating the free-field resonance and side distortion of the soil mass, this resonance was entered into PLAXIS finite element program, and finally, stress and displacement contours together with the bending moment, shear force and axial force curves of the structure were obtained.