A Berry geometrical phase is identified in a strongly metastable system containing dynamically responsive clathrate hydrate structures within a crystal-fluid material. High energy degeneracy in the associated chemistry produces local stability and false vacuum conditions that lead to non-extensive and non-additive contributions in the fundamental thermodynamic relation. The reciprocating action of a piston expander confirms a net energy gain despite the crystal-fluid material maintaining almost constant density. Application of Ginzburg-Landau theory and the scaling laws reveals a coherence length and a penetration depth for a macro-scale dual superconductor. The coherence length determines non-extensive volume changes whilst its inverse gives the Higgs mass. The penetration depth determines the extent of QCD vacuum suppression whilst its inverse gives the vector boson mass together with indirect manifestation as non-additive hyperbolic curvature. External pressure perturbations of the low-energy system initiate ‘rolling’ critical responses that see energy and momentum conserved across a synchronized U(2) symmetry group whilst a complex gauge field is also exposed. Simultaneous emergence of the Ginzburg-Landau superconducting phase transition is consistent with gauge-invariant coupling of this scalar field to the Yang-Mills action in QCD. The discovery of an energy gap in the gradient energy term of the system Lagrangian is associated with a critical correlation length revealed in the transition from a gapped to a gapless superconducting state. Together with the emergence and absorption of the Higgs-like scalar field, a mechanism for describing the QCD mass gap arises.

The study of photonic crystals has emerged as an attractive area of research in nanoscience in the last years. In this work we study the properties of a two-dimensional photonic crystal composed of dielectric rods. The unit cell of the system is composed of six rods organized on the sites of a C6 triangular lattice. We induce a topological phase by introducing an angular perturbation ϕ in the pristine system. The topology of the system is then determined by using the so-called k.p perturbed model. Our results show that the system presents a topological and a trivial phases, depending on the sign of the angular perturbation ϕ. The topological character of the system is probed by evaluating the electromagnetic energy density and analyzing its distribution in the real space, in particular on the maximal Wyckoff points. We also find two edge modes at the interface between the trivial and topological photonic crystals, which present a pseudospin topological behavior. By applying the Bulk-Edge correspondence, we study the pseudospin edge modes and conclude that they are robust against defects, disorder and reflection. Moreover, the localization of the edge modes leads to the confinement of light and the interface behaves as a waveguide for the propagation of electromagnetic waves. Finally, we show that the two edge modes present energy flux propagating in opposite directions, which is the photonic analogue of the quantum spin Hall effect.

The search for fundamental determinants of bio-molecular chirality is a hot topic in biology, clarifying the meaning of evolution and the enigma of life's origin. Non-biological and biological entities obey the universal laws of nature grounded on space-time symmetry (STS) transformations. The fabric of STS is the immense subject of our review. The symmetry, encompassing behavior of elementary particles and galaxy structure, imposes its fundamental laws on all hierarchical levels of the biological world. Objects across spatial scales may be classified as chiral or achiral concerning a specific space-related symmetry transformation - mirror reflection. Chirality as a symmetry element reflecting the property of asymmetry (or dissymmetry) is the critical structural feature of natural systems, including sub-atomic particles and living matter. The inheritance of molecular symmetry from the symmetry of elementary particles points to the bi-directional causal pathway of prevalent bio-chirality. We assume that both extremities of spatial dimension naturally influence this transitional state of biological matter. The current review promotes an integrative holistic approach to the new experimental results in fast-developing and divergent branches of STS and biological chirality. The generalized view on biological chirality is a necessary and promising avenue for adequately understanding the link between protein folding, cell morphology, neuronal signaling, and laterality of cognitive functions.

Remotely sensed data play a crucial role in monitoring the El-Niño/La-Niña Southern Oscillation (ENSO), which is an oceanic-atmospheric phenomenon occurring quasi-periodically with several impacts worldwide, such as specific biological and global climate responses. Since 1980, Earth has witnessed three strong ENSO events (1982–1983, This study aims, 2015-2016). In September 2022, La-Niña entered its third year and was unlikely to continue through 2023. Instead, since 2022 forecasts pointed to a transition from La-Nina to a Neutral phase in summer or late 2023. The onset of the El-Niño occurred around April 2023, and it is anticipated by sophisticated models to be a strong event through the Northern Hemisphere winter (December 2023 - February 2024). The aim of this study is to demonstrate the ability of the combination of two new methods to improve the accuracy of the above claim because El-Niño apart from climate anomalies, significantly impacts Earth’s ecosystems and human societies, regulating the spread of diseases by insects (e.g., malaria and dengue fever), and influencing nutrients, phytoplankton biomass, and primary productivity. This is done by exploring first the previous major El-Niño events in the period January 1876-July 2023. Our calculations show that the ongoing 2023-2024 El-Niño will not be the strongest.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

In this paper, we consider particles together with the surrounding space as an indivisible system, and then investigate the maximum symmetry of the system at the quantum level. We introduce a new quantity to describe the evolution of this system before and after measurement. The effective mass of gravity is estimated. We also show that a free quantum particle as the source of energy and momentum do not produce gravity.

Particles and photons appear to be total opposites; the former has rest mass which requires space to exist; the latter has kinetic energy which requires time to occur (oscillate). But they do share certain properties (e.g., quantization) that remain invariant when one is transformed (swapped) for the other. This gauge invariance is developed in some detail.The symmetry between particle and photon turns out to be one of inversion. It is the equalities of special relativity that support this inversion and the accompanying invariances: mass transformed to energy; space transformed to time. The great advantage of these symmetries (inversions) is that they provide guidance for an object little understood (the photon) based upon an object well understood (the particle). On this basis, progress can be made in the understanding of some long-standing issues: wave-particle duality, time’s arrow, the constant speed of light and nonlocality.

We use a random gap model to describe a metal-insulator transition in three-dimensional semiconductors due to doping and find a conventional phase transition, where the effective scattering rate is the order parameter. Spontaneous symmetry breaking results in metallic behavior, whereas the insulating regime is characterized by the absence of spontaneous symmetry breaking. The transition is continuous for the average conductivity with critical exponent equal to 1. Away from the critical point the exponent is roughly 0.6, which may explain experimental observations of a crossover of the exponent from 1 to 0.5 by going away from the critical point.

Topological states of matter have attracted significant attention due to their intrinsic wave-guiding and localization capabilities robust against disorders and defects in electronic, photonic, and phononic systems. Despite the above topological features phononic crystals share with their electronic and photonic counterparts, finite-frequency topological states in phononic crystals may not always survive. In this work, we discuss the survivability of topological states in Su-Schrieffer-Heeger models with both local and non-local interactions with larger symmetry perturbation. Although such a discussion is still about ideal mass-spring models, the insights from this study set the expectations in continuum phononic crystals, which can further instruct the applications of phononic crystals for practical purposes.

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum space-time: This is the principle of minimal group that allows to consistently and simultaneously obtain a natural description of the spacetime dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the Metaplectic group Mp(n) , the double covering of SL(2C) in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the Metaplectic group symmetry generators and the physical states (mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov-Klauder type defined by the action of the Metaplectic group which divide the Hilbert space into even and odd states mutually orthogonal. They carry a spin weight 1/4 and 3/4 respectively from which, two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4 and 3/4 spin weight states, plus their symmetric and antisymmetric combinations, have spin contents s = 0, 1/2, 1, 3/2 and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) space-time for n going to infinity. (vii) There emerges a relation between the eigenvalue of our coherent state metric solution and the black hole area (entropy) as A_{bh}/4 l_{p}^{2} = I alpha I relating the phase space of the metric found g_{ab} and the black hole area A_{bh} through the Planck length l_{p}^{2} and the eigenvalue I alpha I of the coherent states. As a consequence of the lowest level of the quantum discrete space-time spectrum, eg the ground state associated to n = 0 and its characteristic length, there exists a minimum entropy related to the black hole history.

Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green’s matrix retrieval and Marchenko-type Green’s matrix retrieval in PT-symmetric materials.

The crystal structure of Pb₁₀(PO₄)₆O, the proposed matrix for the potential room-temperature superconductor LK-99, Pb_10-xCu_x(PO₄)₆O (x = 0.9-1.0), has been reinvestigated by single-crystal X-ray diffraction using crystals prepared by Merker and Wondratschek (The crystal structure is trigonal, P, a = 9.8109(6), c = 14.8403(12) Å, V = 1237.06(15), R₁ = 0.0413 using 3456 unique observed reflections. The crystal structure of Pb₁₀(PO₄)₆O is a superstructure with regard to the ‘standard’ P6₃/m apatite structure type. The doubling of the c parameter is induced by the ordering of ‘additional’ O’ atoms within the structure channels running parallel to the c axis and centered at (00z). The O’ atoms form short bonds to the Pb1 atoms, resulting in splitting the Pb1 site into two, Pb1A and Pb1B. The structural distortions are further transmitted to the Pb phosphate framework formed by four Pb2 sites and PO₄ groups. The structure data previously reported by Krivovichev and Burns (Z. Kristallogr. 2003, 218, 357-365) may either correspond to the Pb₁₀(PO₄)₆O_x(OH)_2-x (x ~ 0.4) member of the Pb₁₀(PO₄)₆O - Pb₁₀(PO₄)₆(OH)₂ solid solution series, or to the high-temperature polymorph of Pb₁₀(PO₄)₆O (with the phase with doubled c parameter being the low-temperature polymorph).

The Supersymmetry Genetic code (SSyGC) table is based on five physicochemical symmetries: 1) double mirror symmetry on the principle of the horizontal and vertical mirror symmetry axis between all bases (purines [A, G) and pyrimidines (U, C)], and 2) of bases in form of codons 3) direct – complement like codon/anticodon symmetry in the sixteen alternating boxes of the genetic code columns, 4) A+T rich and C+G rich alternate codons in the same row between both columns of the genetic code, 5) the same position between divided and undivided codon boxes in relation to horizontal mirror symmetry axes. The SSyGC table has a unique physicochemical purine – pyrimidine symmetry net which is as the core symmetry common for all, more than thirty different nuclear and mitochondrial genetic codes. This net is present in the SSyGC table of all RNA and DNA living species. None of these symmetries is present in the Standard Genetic Code (SGC) table which is constructed on the alphabetic horizontal and vertical U-C-A-G order of bases. Here we show that the free energy value of each codon incorporated as fundamentally mapping the “energy code” in the SSyGC table is compatible with mirror symmetry. On the other hand, in the SGC table the same free energy values of codons are dispersed and a mirror symmetry between them is not recognizable. At the same time the mirror symmetry of the SSyGC table and the DNA quadruplets together with our classification of codons/trinucleotides are perfectly imbedded in the mirror symmetry energy mapping of codons/trinucleotides and point out in favor of maintaining the integrity of the genetic code and DNA genome. We also argue that physicochemical symmetries of the SSyGC table in the manner of the purine – pyrimidine symmetry net, the quadruplet symmetry of DNA molecule and the free energy of codons have remined unchanged during all of evolution. The unchangeable and universal symmetry properties of the genetic code, DNA molecule and energy code are decreasing disorder between codons/trinucleotides and shed a new light on evolution. Diversity in all living species on Earth is broad, but the symmetries of the Supersymmetry Genetic Code as the code of life and the DNA quadruplets related to the” energy code” are unique, unchangeable and have the power of natural laws.

In this article, we give a brief review of the origin of the neutrino mass in some interesting non-linear supersymmetric models with R-symmetry. These models are able to address and solve the most important problems of the particle physics and provide mechanisms for neutrino mass generation and their mixing parameters in agreement with the current experimental data. Their prediction could be experimentally tested in the near future by collider experiments.

A new mesogenic non-symmetric dimeric monomer with a terminal olefin function, forming a twist bend nematic (Ntb) as well as a nematic (N) phase was synthesized, using an enhanced synthetic methodology, which avoids isomerization of the terminal double bond in the preparation of the dimer. This monomer was attached to a pentamethyldisiloxane group, resulting in SmA LC phase behaviour of the ensuing material. Linking the monomer to a siloxane main chain resulted in nematic phase behaviour. Detailed studies with the Ntb phase forming dimer DTC5C7 show full miscibility of the dimer and the new LC polymer in the LC state, suggesting that the side-chain LC polymer forms a Ntb phase as the low temperature nematic phase. Copolymerizing the monomer with a cyanobiphenyl based monomer allows to tune the glass transition and phase behavior further.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

A time interval only description necessarily needs its own independent definitions, without one moment time coordinates to it. In this paper derived are time interval only set properties, including commutation relations, addition, multiplication and derivatives. Time interval only set commutation relations, consistent with one moment time set properties, are introduced by defining correspondence relations for these sets. Time development and equilibrium within the time interval description depend on the well-known ‘mean velocity theorem’ and the time interval version of the Legendre transform. In contrast, usually applied is only the traditional vector and one moment time coordinate kinematic approach from Newton’s laws. The main results of this paper are correspondences and time interval only set commutation relations. All other properties are derived from these results, while for the time interval only set, different from the one moment time set the canonical property is not valid. The time interval only description can be applied assuming spherical symmetric star-source radiation propagation, with finite time intervals for realistic measurement events. From time development with (a-)symmetry of time intervals, and from Curie’s principle, change can be described with a set theoretic approach. Time interval only set properties include the time interval only version of Noether charges and structure constants. A time interval only description for wave propagation, including group-velocity, for zero and non-zero mass wave particles, relates to the properties of the time interval only set. A second result in terms of the time interval only description is propagation wave energy equivalence with gravitation energy, derived from time interval only set commutation relations. A time interval approach, however including one moment time description dependence, was introduced in earlier publications of this author. In part 1 investigated are the time interval only set and its properties, a forthcoming part 2 to application of the time interval only description to specific groups of stars as emission sources.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

Gait variability (GV) is a crucial measure of inconsistency of muscular activities or body seg-mental movements during repeated tasks. Hence, GV might serve as a relevant and sensitive measure to quantify adjustments of walking control. However, has not been clarified whether GV is associated with walking speed to exploit effective better coordination level. Fourteen male stu-dents (age 22.4 ± 2.7 years, body mass 74.9 ± 6.8 kg, body height 1.78 ± 0.05 m) took part in this study. After three days of walking 1 km each day at a self-selected speed (SS) on asphalt with Apple Watch S. 7 (AppleTM), the participants were randomly evaluated on a treadmill at three different walking speed intensities for 10 minutes each one, at SS-20% / SS+20% of SS, with 5 minutes of passive recovery in-between. Heart rate (HR) was monitored beat-to beat and nor-malized as HR%MAX, while the rate of perceived exertion (RPE) (CR-10) was asked after each trial. Kinematic analysis was performed assessing the Contact Time (CT), Swing Time (ST), Stride Length (SL), Stride Cycle (SC) and Gait Variability as Phase Coordination Index (PCI). RPE and HR increased with higher walking speed (P = 0.005 and P = 0.035, respectively). CT and SC decreased as the speed increased (P = 0.0001 and P = 0.013, respectively), while ST remained un-changed (P = 0.277). SL increased with higher walking speed (P = 0.0001). Conversely, PCI was 3.81 ± 0.88 % (high variability) at 3.96 ± 0.47 km·h-1, 2.64 ± 0.75 % (low variability) at SS (4.94 ± 0.58 km·h-1), 3.36 ± 1.09 % (high variability) at 5.94 ± 0.70 km·h-1 (P = 0.001). These results indi-cate that while the metabolic demand and kinematics variables changing linearly with increasing speed, the most effective GV was observed at SS. Therefore, SS could be a new methodological approach to choose the individual walking speed, normalize the speed intensity, and avoid a gait pattern alteration.

Analytical modeling has symmetries and aesthetic-mathematical characteristics that distinguish it from numerical computation. Nanoscience plays an extremely important role in unification efforts that also include holistic aspects of reality. In this paper I present new discovered results about the complete analytical quantum relativistic form of the mean square deviation of position false related to a lately appeared Drude-Lorentz-like model (DS model), already performed at classical, quantum and relativistic level. The function false gives precise information about the distance crossed by carriers (electrons, ions, etc.) inside a nanostructure, considering both quantum effects and relativistic velocities. The model has a wide scale range of applicability; the nanoscale is considered in this paper, but it holds from sub-pico-level to macro-level because of the existence of a gauge factor, making it applicable to every oscillating processes in Nature. Examples of application and suggestions supplement the paper, as well as interesting developments to be studied related to the model and to one of the basic elements of a current unified holistic approach based on the vacuum energy.

In physics, symmetry is mostly about the symmetry between elementary particles, between matter and antimatter. In the universe, we have two fundamental types of energy: energy of matter and energy of space. These two energies have a symmetry that is not geometry type, not electric charge type, it is energy type. Every physical object with mass m symmetrically diminishes the energy density of space in its center exactly for the amount of its mass. This symmetry of matter and space energies is the physical source of gravity that is also valid in the centre of black holes.

A comprehensive review on symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics and even when the symmetry is broken, symmetric pairs of coexisting attractors are born annotating the symmetry in another way. The polarity balance can be recovered by the combinations of the polarity reverse of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reverse from their functions. In this case, conditional symmetry is constructed giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reverse of some of the system variables, which brings more alternatives of chaotic signal and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic system and those of conditional symmetry provide sufficient system options for chao-based applications.

Time-modulated sparse circular array (TMSCA) with elements uniformly excited is designed and synthesized in this paper. By utilizing rotationally symmetric structure, the array geometry and the time modulation of the TMSCA is presented, and the radiation patterns in frequency domain are formulated. In order to achieve the desired radiation pattern at the operating frequency and suppress the sideband radiation, the synthesis problem is established and solved by the proposed harmony search-convex programming (HS-CP) algorithm in two dependent optimizations. Two designs are presented, and the numerical results indicate that the TMSCA with rotationally symmetric structure has the advantages of designing time-modulated sparse arrays with superior performance.

Application of the Ramsey Theory to the set of the points placed in the plane is discussed. Consider a set of N points located in the same plane. The straight lines connecting these points are yikx=αikx+βik i,k=1...N. Listed below values of slopes αik are possible: αik>0; αik=0; αik is not defined; αik<0. Following coloring procedure is introduced: we connect the pairs of points for which αik>0, αik=0 or αik is not defined, with the red links, and the pairs of points for which αik<0 place with green links. The suggested coloring procedure enables building of the complete bi-colored graph for any set containing N points located in the same plane. We apply the Ramsey theorem to the complete graph emerging from the suggested coloring. For the set containing N=6 points at least one monochromatic triangle will necessarily appear in the graph. The values of the slopes αik depend on the chosen coordinate system. The rotation of coordinate axes changes the coloring of the graph; however, at least one monochromatic triangle will be present for N=6. The introduced coloring procedure diminishes the order of the symmetry group of the regular hexagon, irrespectively to the orientation of the coordinate axes. We hypothesized that this will be true for arbitrary regular n-polygon, independently on the orientation of coordinate axes. The inverse bi-color Ramsey graphs arise, when we replace red links appearing in the source graph with red ones, and vice versa. The total number of triangles in the “direct” and “inverse” Ramsey graphs is the same. We considered the particular case of the set of points for which αik>0 or αik<0 is true in the given coordinates. In this particular case, the rotation of the Cartesian coordinate axes to the angle θ=π2 yields the inverse complete graph. Generalization of this coloring for an arbitrary number and arbitrary location of the source points is introduced.

This paper explores the Wilsonian renormalization group of probe-D-branes, focusing on the Dirac-Born-Infeld (DBI) action. The analysis involves deriving the constant of motion and formulating the Wilsonian renormalization group equation. The study extends to the infrared regime, considering both zero and non-zero temperatures. Additionally, thermodynamic aspects related to the functional form of the grand potential are discussed. The investigation provides insights into the renormalization of probe-D-branes and their thermodynamic properties.

Symmetry-breaking is a phenomenon that is observed in various contexts, from the early universe to complex organisms, and is considered a key puzzle in understanding the emergence of life. The presence of enantiomeric amino acids and proteins highlights its critical role. However, the origin of symmetry-breaking has yet to be comprehensively explained, particularly from an energetic standpoint. This article explores a novel approach by considering energy dissipation, specifically lost free energy, as a crucial factor in elucidating symmetry-breaking. Through a thorough thermodynamic analysis applicable to enantiomeric systems at various scales, from elementary particles to aggregated matter like crystals, we present experimental findings that establish a direct correlation between non-equilibrium free energy and energy dissipation during formation processes. Results emphasize the pivotal role of energy dissipation not only as an outcome but as the trigger for symmetry-breaking. This insight suggests that understanding the origins of complex systems, from cells to living beings and the universe itself, requires a lens focused on non-equilibrium processes, ultimately facilitating the formation of non-racemic systems.

We demonstrate that the black hole evaporation can be modelled as a process where one symmetry of the system is spontaneously broken continuously. We then identify three free-parameters of the system. The sign of one of the free-parameters, governs whether the particles emitted by the black-hole are fermions or bosons. The present model explains why the Black Hole evaporation process is so universal. Interestingly, this universality emerges naturally inside certain modifications of gravity.

The nucleon-pair shell model (NPSM) with broken symmetry basis is studied. The results demonstrate the validity of NPSM with symmetry broken basis, which leads to a significant reduction in the dimensionality of the multi-pair configuration space. We have observed that the axial-deformed basis provides a satisfactory description of the low-lying spectrum, even without the need for the projection procedure. In the case of the triaxial-deformed basis, we have investigated the variation after angular momentum projection, indicating the potential for NPSM to find exact solutions in the half-closed system.

By this contribution we would like to briefly highlight the problems in conceiving the “Hydrogen Bond” (HB) as a real short-range, directional, electrostatic, attractive interaction and to reframe its nature through the non-approximated view of condensed matter offered by a Quantum Electro-Dynamic (QED) perspective. We focus our attention on water, as the paramount case to show the effectiveness of this 40-years’ old theoretical background, which depicts water as a two-fluid system (where one of the two phases is coherent). The HB emerge to be the result of the electromagnetic field gradient in the coherent phase of water, whose vacuum level is lower than the non-coherent (gas-like) fraction. Thus, the HB can be properly looked at, i.e. no more as a “dipolar force” among molecules, but as the phenomenological effect of their collective thermodynamic tendency to occupy a lower ground-state, compatibly with temperature and pressure. This perspective allows to account for many “anomalous” behaviours of water and to understand why the calculated energy associated to HB should change when considering two molecules (water-dimer), or the liquid state, or the several kinds of ice. The emergence of a condensed, liquid, phase at room temperature is indeed the consequence of the boson condensation as described in the framework of spontaneous symmetry breakings (SSB). The switch from a still semi-classical Quantum Mechanical (QM) in the 1st quantization to a Quantum Field Theory (QFT) view embedded in the 2nd quantization is advocated for a more realistic and authentic description of water, condensed matter and living systems.

In this non-exhaustive review, we discuss the importance of invariant vectors in atomic physics, such as the Laplace-Runge-Lenz vector, the Redmond vector in the presence of an electric field, the Landau-Avron-Sivardière vector when the system is subject to a magnetic field, and the supergeneralized Runge-Lenz vector for the two-center problem. Application to Stark and Zeeman effects are outlined. The existence of constants of motion in the charge-dyon system is also briefly mentioned.

When discussing the gauge symmetries of any theory, the Henneaux-Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important role in understanding the structure of the full gauge symmetry group of any theory, especially regarding the subgroup of diffeomorphisms. We give a review of the Henneaux-Teitelboim transformations and the resulting gauge group in the general case, and then discuss its role in the applications to the class of topological theories called nBF models, relevant for the constructions of higher gauge theories and quantum gravity.

The aim this text to present the confined covariant quark model (CCQM) and review its applications to the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we review also. The physics principles are in detail exposed for the CCQM, the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering successively three categories of decay processes: leptonic, semileptonic and non-leptonic.

We discuss the neutron skins of 48Ca and 208Pb. We review and critically examine modern predictions and empirical constraints, with special attention to the dierent interpretations of the ndings from the PREX-II experiment and the recently reported value of the neutron skin in 48Ca extracted from the CREX experiment. We argue that, in the spirit of the ab initio philosophy, the path to understanding the behavior of dense neutron-rich matter must not circumvent fundamental nuclear forces. Based only on that argument, a thick neutron skin in 208Pb is highly unlikely.

We report on recent experimental results on β decay into self-conjugate (N=Z) nuclei with mass number 58≤A≤70. Super-allowed β decays from the Jπ=0+ ground state of a Z=N+2 parent nucleus are to the isobaric analogue state, through so-called Fermi transitions, and to Jπ=1+ states, by way of Gamow–Teller (GT) transitions. The operator of the latter decay is a generator of Wigner’s SU(4) algebra and as a consequence GT transitions obey selection rules associated with this symmetry. Since SU(4) is progressively broken with increasing A, mainly as a consequence of the spin–orbit interaction, this symmetry is not relevant for the nuclei considered here. We argue, however, that the pseudo-spin–orbit splitting can be small in nuclei with 58≤A≤70, in which case nuclear states exhibit an approximate pseudo-SU(4) symmetry. To test this conjecture, GT decay strength is calculated with use of a schematic Hamiltonian with pseudo-SU(4) symmetry. Some generic features of the GT β decay due to pseudo-SU(4) symmetry are pointed out. The experimentally observed GT strength indicates a restoration of pseudo-SU(4) symmetry for A=70.

The behaviour and bifurcations of solutions to three-dimensional (three-phase) quadratic polynomial dynamical systems (DSs) are considered. The integrability in elementary functions is proved for a class of autonomous polynomial DSs. The occurrence of bifurcations of the type twisted fold is discovered on the basis and within the frames of the elements of the developed DS qualitative theory. The discriminant criterion applied originally to two-phase quadratic polynomial DSs is extended to three-phase DSs investigated in terms of their coefficient matrices. Specific classes of D- and S-vectors are introduced and complete description of the symmetry relations inherent to the DS coefficient matrices is performed using the discriminant criterion.

We present three reduced integrable hierarchies of nonlocal integrable NLS type equations from a vector integrable hierarchy associated with a matrix Lie algebra, not being A type. Three similarity transformations are taken to keep the invariance of the transformed zero curvature equations. The key step is to formulate a solution to a reduced stationary zero curvature equation so that the zero curvature formulation works for a reduced case.

Boron nitride clusters play an important role as precursors in the formation of ultra-hard thin solid boron nitride films, which have received considerable attention in material science. In this contribution, we investigated the ground and low-lying electronic states of B₂N^(∓,0) and N₂B^(∓,0). Triatomic NBN and BNB have been previously investigated using a variety of spectroscopic and calculational methods, and it is generally agreed that both of them are linear in their ground electronic states. The six ions including B₂N ^(-), B₂N ⁽⁺⁾, B₂N ⁽⁰⁾ , BN₂ ^(-), BN₂ ⁽⁺⁾ and BN₂ ⁽⁰⁾ have been studied and been also compared with one another in terms of various basis sets and predication of the symmetry breaking (SB) phenomenon. Artifactual symmetry breaking along the v3 coordinate is observed in the ab initio wave functions for the neutral ground state up to the coupled-cluster level of theory, even when Brueckner orbitals are used. In the D_∞h point group of B₂N^(∓,0) and N₂B^(∓,0) variants, the unpaired electrons are delocalized, while in the asymmetric C_∞v point group, they are localized on either one of the B atoms or N atoms of B₂N^(∓,0) and N₂B^(∓,0) , respectively. Structures with broken symmetry,C_∞v, can be stable by interaction to the D_∞h point group. In viewpoint of quantum chemistry, the second-order Jahn-Teller effect permits the unpaired electron to localize on boron atom, rather than being delocalized. Finally, from a statistical thermodynamical analysis, we calculated the thermochemical stabilities of those six ions.

This study investigates via Lie symmetry analysis the Hunter-Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation derived from first-order multipliers. Conservation laws of the Hunter-Saxton equation, in combination with the Lie point symmetries of the equation, enable us to perform symmetry reductions through employment of the double reduction method. The method exploits the relationship between Lie point symmetries and conservation laws to effectively reduce both the number of variables and the order of the equation. Five nontrivial conservation laws of the Hunter-Saxton equation are derived, four of which are found to have associated Lie point symmetries. Applying the double reduction method to the Hunter-Saxton equation results in a set of first-order ordinary differential equations, the solutions of which represent invariant solutions for the equation.

The time evolution of the continuous measure symmetry for the system built of the three bodies interacting via the potential U(r)~1/r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the case of the pure gravitational interaction the three-body-system deviated from its initial symmetrical location, described by the Lagrange equilateral triangle, comes to collapse, accompanied by the growth of the continuous measure of symmetry. When three point bodies interact via the Coulomb repulsive interaction, the time evolution of CMS is quite different. CMS calculated for all of studied initial configurations of the point charges and all of their charge-to-mass ratios always comes to its asymptotic value with time, evidencing the stabilization of the shape of the triangle, constituted by the interacting bodies.

Symmetry, as a key concept in geometry and the foundational principle of mathematical concepts, is a fundamental part of geometry and nature, creating patterns that help us conceptually organize our world. It is often linked with aesthetic beauty and can be observed in both natural phenomena and human-made objects, such as artworks and manufactured products, across the globe. The automorphism group of a graph is a mathematical structure that captures all the symmetries of the graph. symmetry refers to the property of a graph, indicating that it can be transformed without changing its structure, while the automorphism group is the collection of all permutations of the vertices that preserve the graph's adjacency relationships. In graph theory, the concepts of symmetry group and automorphism group play fundamental roles in understanding the symmetries and structural properties of graphs. This paper aims to explore the relationship between symmetry groups and automorphism groups, shedding light on their interconnected nature and their significance in graph theory. We delve into the definitions and properties of both symmetry groups and automorphism groups, highlighting their similarities and distinctions. Furthermore, we discuss their applications in various fields, including computer science, chemistry, and network analysis. Through this exploration, we aim to provide a comprehensive understanding of the relationship between symmetry groups and automorphism groups, deepening our comprehension of the symmetries and structures inherent in graphs.

In this paper, a regression model between neutron star crust-core pressure and the symmetry energy characteristics was estimated using the Akaike information criterion and the adjusted coefficient of determination Radj2. Based on the obtained regression function, the most probable value of the transition density, which should characterize the crust-core environment of the sought physical neutron star model, was determined. An anti-correlation was found between this transition density and the main characteristic of the symmetry energy, i.e., its slope L.

Aminoacyl-tRNA synthetases (aaRSs) originated from an ancestral bidirectional gene (mirror symmetry) and through the evolution of the genetic code the twenty aaRSs exhibit a symmetrical distribution in a 6-dimensional hypercube of the Standard Genetic Code. In this work, we assume a primeval RNY code, and the Extended Genetic RNA code type II which includes codons of the type YNY, YNR and RNR. Each of the 4 subsets of codons can be represented in a 4-dimensional hypercube. Altogether these 4 subcodes constitute the 6-dimensional representation of the SGC. We identify the aaRSs' symmetry groups in each of these hypercubes. We show that each of the four hypercubes contains the following sets of symmetries for the two known Classes of synthetases: RNY: dihedral group D2; YNY: binary group Z2; YNR: amplified octahedral group Oh; and RNR: binary group Z2. We demonstrate that for each hypercube, the group of symmetries of Class 1 is the same as the group of symmetries of Class 2. The biological implications of these findings are discussed.

Abstract Using the Pauli algebra version of the Dirac equation six symmetric but non-equivalent copies of the QED Lagrangian are constructed. The group of symmetries is the group of outer automorphisms of the finite quaternion group, isomorphic to the group of permutations on three letters. Solutions to corresponding Dirac equations form six sectors of fermion fields. The intersections between different sectors can only contain massless fields, implying that the sectors are distinct. If the symmetry could be extended to the full Standard Model Lagrangian it would predict the ratio of dark matter to ordinary matter of 5 : 1 which is close to the ratio of 5.2 : 1 according to current observations.

The structures of Ag complexes with dimethyl amino phenyl substituted phtalocyanine m[dmaphPcAg]q of various charges q and in two lowest spin states m were optimized using the B3LYP method within the D4h symmetry group and its subgroups. The most stable reaction intermediate in the supposed photoinitiation reaction is 3[dmaphPcAg]-. Group-theoretical analysis of the optimized structures and of their electron states reveals two symmetry-descent mechanisms. Stable structures of maximal symmetry of complexes 1[dmaphPcAg]+, 3[dmaphPcAg]+, 2[dmaphPcAg]0 and 4[dmaphPcAg]2- correspond to the D4 group as a consequence of the pseudo-Jahn-Teller effect within unstable D4h structure. Complexes 4[dmaphPcAg]0, 1[dmaphPcAg]-, 3[dmaphPcAg]- and 2[dmaphPcAg]2- with double degenerate electron ground states in D4h symmetry structures undergo a symmetry descent to stable structures corresponding to maximal D2 symmetry not because of a simple Jahn-Teller effect but due to hidden pseudo-Jahn-Teller effect (strong vibronic interaction between excited electron states). The reduction of the neutral photoinitiator causes symmetry descent to its anionic intermediate because of vibronic interactions that must significantly affect the polymerization reactions.

We study in detail the influence of different chemical potentials (baryon, charged, strange, and neutrino) on how and how fast a free gas of quarks in the zero-temperature limit reaches the conformal limit. We discuss the influence of non-zero masses, the inclusion of leptons, and different constraints, such as charge neutrality, zero-net strangeness, and fixed lepton fraction. We also investigate for the first time how the symmetry energy of the system under some of these conditions approaches the conformal limit. Finally, we briefly discuss what kind of corrections are expected from perturbative QCD as one goes away from the conformal limit.

The description of the electron-electron interactions in two-dimensional materials has a dimensional mismatch, where electrons live in (2+1)D while photons propagate in (3+1)D. In order to define an action in (2+1)D, one may perform a dimensional reduction of quantum electrodynamics in (3+1)D (QED4) into Pseudo quantum electrodynamics (PQED). The main difference between this model and QED4 is the presence of a pseudo-differential operator in the Maxwell term. However, besides the Coulomb repulsion, electrons in a material are subjected to several microscopic interactions, which are inherent in a many-body system. These are expected to reduce the range of the Coulomb potential, leading to a short-range interaction. Here, we consider the coupling to a scalar field in PQED for explaining such mechanism, which resembles the spontanoues symmetry breaking (SSB) in Abelian gauge theories. In order to do so, we consider two cases: (i) By coupling the gauge field to a Higgs field in scalar quantum electrodynamics in (3+1)D and, thereafter, performing the dimensional reduction and; (ii) By coupling a Higgs field to the gauge field in PQED and subsequently calculating its effective potential. In case (i), we obtain a model describing electrons interacting through the Yukawa potential and, in case (ii), we show that SSB does not occur at one-loop approximation. The relevance of the model for describing electronic interactions in two-dimensional materials is also adressed.

Developing a dependable gas and condensate value chain is vital for the ongoing prosperity of the oil and gas industries. To achieve this, NNPC is enhancing its production facilities by employing process modeling and simulation with the assistance of Symmetry iCON®. As a part of this initiative, a simulation model was created using the Symmetry iCON® pipe plexus solver to simulate the dynamic environment of the gas and condensate pipeline network in the Nigerian Southern region. To validate the model, data from a single month, specifically December 2022, was utilized. Furthermore, the algorithm was utilized to generate projections for the month of January 2023, providing valuable insights into its effectiveness. The study also highlighted the significance of accurately estimating the characteristics and properties of a pseudo component of C6+ in relation to thermodynamics and material properties, which was a particularly insightful finding. he assessment of this property has transitioned from being relatively unimportant to becoming critically important, primarily due to the lack of condensate data monitoring at specific terminals. However, it's worth noting that the model currently has an error margin of 4-6% when predicting the data. As more information becomes available in the future, the model can be easily fine-tuned to better align with the actual conditions, allowing for more accurate predictions.

A one-dimensional model for fluid and solute transport in poroelastic materials (PEM) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary case, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.