The effects of photon inertia on the determination of its trajectory were verified and the representation of a displacement mass characterized by the flow of the number of wavefronts and the decomposition of photon inertia into parts associated with translation and rotation motions was considered. It was found that with the relativistic increase of the photon's resistance to change its directional properties, it inhibits the relativistic trajectory of the second torque, of Minkowski, in an angular range of incidence. After synchronizations, in the OAM inversions, there are reductions of the inertia associated to the translational part that assumes classical predominance, where the relativistic trajectory is allowed while the photon offers less resistance to changes in its directional properties. The classical-relativistic variability of the photon inertia characterizes the classical or relativistic profile of the energy distribution in forms of motion, where adjustments of the rotational and translational parts can be performed as a function of the refractive index rate, temperature and angle of incidence. It was found that with increasing temperature of the refringent medium, the synchronizations displacement in the sense of the normal incidence. A specific vacuum temperature for the refringent medium was characterized, where the photon exhibits a classical-relativistic synchronization under all angles of incidence, characteristic of its immaterial state in vacuum.

Open Inertia Modelling (OpInMod) is a modelling framework designed to create unit commitment and economic inertia dispatch optimisation problems. Present energy system modelling generators do not consider power system inertia in unit commitment and economic dispatch modelling to assess future energy system pathways. However, maintaining sufficient power system inertia in power systems is the foundation for power frequency controllability. The work at hand describes the functionality and approaches of open source tool OpInMod. The softwares universal design approach increases reuse potential. OpInMod is distributed with a set of examples to test and understand OpInMod

A non-relativistic theory of inertia based on Mach's principle is presented as has been envisaged but not achieved by Ernst Mach in 1872. Central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element $dm$ to the inertia of a particle $m_0$ experiencing an acceleration from rest is proportional to $\cos^2\alpha$, where $\alpha$ is the angle between the line connecting $m_0$ and $dm$ and the direction of the acceleration. Apsidal precession for planets circling around a central star is not a consequence of this theory, thereby avoiding the prediction of an apsidal precession with wrong sign as is done by Mach-like theories with isotropic inert mass.

This paper studied the solar PV frequency control in the U.S. Eastern Interconnection (EI) and Texas Interconnection (ERCOT) systems. The studied frequency control approaches include droop frequency control, inertia control, and droop-inertia-combined frequency control. The control effects of different frequency controls of PV in the EI and ERCOT are studied using actual high PV penetration interconnection grid models to provide suggestions to the future revision of future PV frequency control standards.

Microgrids can be islanded to improve the reliability of the electrical energy supply during contingencies such as faults. It is still unclear what stability phenomena can occur in microgrids without inertia during and immediately after the fault-initiated islanding transient, and how the stability should be evaluated. To allow robust planning and operation, a stability analysis methodology should be able to take into account the inherent uncertainty of load and renewable energy sources. Therefore, this paper proposes a probabilistic stability analysis methodology for fault-initiated islanding of microgrids based on a thorough analysis of the root causes of instability during islanding transients. To perform stability analysis within reasonable time and allow control actions during operation, dynamical microgrid models in the dq reference frame are described and validated by comparing time-domain simulations results to previously validated component-based models. The stability analysis methodology is demonstrated in a case study of a generic microgrid. The instability phenomena and the dq microgrid models are successfully validated, and the results indicate that the stability analysis methodology can assist the microgrid operator to improve fault-initiated islanding capability in order to improve reliability of supply.

The paper presents a method for estimating the inertia tensor components of a spacecraft that has expired its active life using measurement data of the Earth's magnetic field induction vector components. The implementation of this estimation method is supposed to be carried out when cleaning up space debris in the form of a clapped-out spacecraft with the help of a space tug. It is assumed that a three-component magnetometer and a transmitting device are attached on space debris. With the help of this measuring system, the parameters for the rotational motion of space debris are estimated. Then the known controlled action from the space tug is transferred to the space debris. Next, measurements for the rotational motion parameters are carried out once again. Based on the available measurement data and parameters of the controlled action, the space debris inertia tensor components are estimated. It is assumed that the measurements of the Earth's magnetic field induction vector components are made in a coordinate system which axes are parallel to the corresponding axes of the main body axis system. Such an estimation makes it possible to effectively solve the problem of cleaning up space debris, to calculate the costs of the space tug working body and the parameters of the space debris removal orbit. Examples of numerical simulation using the measurement data of the Earth's magnetic field induction vector components on the Aist-2D small spacecraft are given. The results of the work can be used in the development and implementation of missions to clean up space debris in the form of clapped-out spacecraft.

In this paper, an adaptive proportional and integral (PI) controller for speed control of electric drives is developed. The adaptive PI controller is designed based on model reference adaptive identification and the Lyapunov function so that the system stability can be proved. To identify the inertia, the viscous friction torque coefficient, and the load torque simultaneously and smoothly, sinusoidal speed reference is usually employed. A modified motion equation considering the low-pass filter for feedback speed and the Coulomb friction torque is introduced and the relationship between the identified parameters and their actual values are clarified. A high-precision digital simulation model is built based on MATLAB/Simulink. The effectiveness of the proposed method is verified by simulations under various conditions.

This paper presents a comparison of two methods to represent variable blade inertia in two codes for aero-servo-elastic simulations of wind turbines: the nonlinear aeroelastic multi-body model HAWC2 and the nonlinear geometrically exact beam model BeamDyn for OpenFAST. The main goal is to enable these tools to simulate the dynamic behavior of a wind turbine with variable blade inertia. However, in order to simulate the structural response of wind turbines with variable blade inertias, the source code of load simulation tools need to be modified. This is due to the fact that, currently, state-of-the-art load simulation tools for wind turbines are unable to simulate variable rotor blade inertias. The validity of the modified codes is proven based on a simple beam model. The validation shows very good agreement between the modified codes of HAWC2, BeamDyn and an analytical calculation. The add-on of variable blade inertias is applied to reduce the mechanical loads of a 5 megawatt reference wind turbine with an integrated hydraulic-pneumatic flywheel in its rotor blades.

This paper presents a numerical two-scale framework for the simulation of fiber reinforced concrete under impact loading. The numerical homogenization framework considers the full balance of linear momentum at the microscale. This allows for the study of microscopic inertia effects affecting the macroscale. After describing the ideas of the dynamic framework and the material models applied at the microscale, the experimental behavior of the fiber and the fiber-matrix bond under varying loading rates are discussed. To capture the most important features, a simplified matrix cracking and a strain rate sensitive fiber pullout model are utilized at the microscale. A split Hopkinson bar tension test is used as an example to present the capabilities of the framework to analyze different sources of dynamic behavior measured at the macroscale. The induced loading wave is studied and the influence of structural inertia on the measured signals within the simulation are verified. Further parameter studies allow the analysis of the macroscopic response resulting from the rate dependent fiber pullout as well as the direct study of the microscale inertia. Even though the material models and the microscale discretization used within this study are still simplified, the value of the numerical two-scale framework to study material behavior under impact loading is shown.

In studies of dynamic stability and power quality, it is necessary to know the mechanical parameters that determine the transient response of a wind turbine. The exact value of these parameters is not as decisive as the power curve can be, but an estimate that is far from reality can distort or even invalidate the simulation results. Despite its importance, this information, especially the inertia, but also the stiffness and damping constant of the drive-train, is hardly available for the turbine model under investigation. In this work, the different bibliographical sources that provide values of blade inertia in kg·m2 will be reviewed, and above all, those that provide a distribution of masses along the span of the blade. With this, different reliable relations will be obtained that allow calculating the inertia of the turbine rotor, based on the mass and length of the blade. When the center of gravity is also available, a very correlated expression is provided to obtain the inertia. The even rarer references to the stiffness and damping constant of the drive-train will also be reviewed.

The performance of a normal-strength SHCC under impact loading was studied using the results obtained from a split Hopkinson tension bar (SHTB). The focus of the investigation is to explain the mechanisms behind the peculiar rate-dependent behavior of SHCC under tensile loading. With the help of frames obtained by high-speed cameras and the subsequent Digital Image Correlation (DIC) analysis, the stress-strain relation of the SHCC obtained in SHTB was analyzed. The investigation of the composite’s behavior was supported by constituent-level experiments on the non-reinforced matrix of the SHCC and on the fiber-matrix bond. In the case of the constituent matrix, the well-known apparent increase in the tensile strength of the cement-based matrix and its influence on the behavior of SHCC was studied. For this purpose, experiments on the SHCC specimens with different geometries were performed in the SHTB. The results obtained from these experiments and those obtained by DIC show that commonly used analytical models, in which the specimen is assumed elastic, cannot capture the effects of structural inertia on the results. Thus, an alternative novel method based on the results of DIC has been used to explain and quantify the contribution of structural inertia. The rate-dependent behavior of the fiber-matrix bond was studied by performing high-speed single fiber pullout tests in a miniaturized split Hopkinson tension bar. This novel experimental technique enabled explanation of the rate-dependent bridging action of the fibers in SHCC. Based on the results, the enhanced behavior of SHCC under impact loading is explained.

Bifidobacterium is the most beneficial flora of the human gastrointestinal tract, but there is a concentration threshold for Bifidobacterium to exert its beneficial properties. In this work, the effect of several simple culture methods on the number of viable bifidobacteria was discussed to improve its viable concentrations, and we unexpectedly discovered that bifidobacteria have inert growth. The concentration of viable bacteria of two isolated Bifidobacterium animalis subsp. lactis, BZ11 and BZ25 and Lactobacillus plantarum SQ-4 were investigated using solid-liquid-liquid circulation subculture, solid-liquid-liquid subculture and solid-liquid-liquid circulation subculture. These 3 subculture methods increase the viable cell concentration, and the best is the solid-liquid-liquid subculture. The highest concentrations of third-generation BZ11 and BZ25 were 9.62 × 109 CFU/mL and 1.21 × 1010 CFU/mL in order by solid-liquid-liquid subculture method, which was 10.38 times and 42.31 times higher (P<0.05) than those of the first generation, respectively. However, none of these three subculture methods increased the concentration of SQ-4. These results suggested that Bifidobacterium has growth inertia and Solid-liquid-liquid passage culture inhibiting the growth inertia. This finding is valuable in promoting the industrial application of probiotic bifidobacteria to potential probiotic food production.

Minimal rotating thermodynamic systems are addressed. Particle m placed into the rotating symmetrical double-well potential (bowl), providing binary logical system is considered. The condition providing the transfer of the particle from one frictionless half-well to another, and in this way possibility to record 1 bit of information is derived. The procedure of recording turns out to be irreversible; it is impossible to return the particle to its initial state under rotation about the same axis. The same rotating double-well system exerted to the thermal noise is considered. Minimal rotating thermal engine built of the rotating chamber, movable partition and the particle confined within the chamber is treated. Rotation of the system displaces the partition; thus, enabling erasing of one bit information. Erasing of 1 bit of information is due to the inertia (centrifugal force) acting on the partition. Isothermal expansion of the “minimal gas” expectedly gives rise to the Landauer bound. Compression of the “gas” with the rotation around the same axis is impossible and demands the additional axis of rotation. The interrelation between the possibility of recording/erasing information and the symmetry of the system is considered.

First, this paper broaches the epistemological status of scientific tenets and approaches: phenomenological (descriptive only), well-founded (solid first principles, conducive to deep understanding), provisional (can be falsified if universal and verified if existential), and imaginary (fictitious entities or processes, conducive to empirically unsupported beliefs). The ΛCDM “concordance model” involves such beliefs: the emanation of the universe out of a non-physical stage, cosmic inflation (invented ad hoc), Λ (fictitious energy), and exotic dark matter. Big Bang cosmology further faces conceptual and pragmatic problems in delimiting what expands from what does not. The problems dissolve after untying inertia from space. The cosmology that emerges appears immediately compatible with the considered observations and the ‘perfect cosmological principle’. Waves and field perturbations that propagate at c expand exponentially with distance (a gravitational effect). The cosmic web of galaxies does not. Potential -Φ varies as H/(cz) instead of 1/r. Inertial forces arise from the gravitational action of the rest of the universe. Due to dilatation, they are reduced disproportionately at low accelerations. A cut-off value a₀ = 0.168 cH is deduced. This explains the successful description of galaxy rotation curves by MoND. A fully elaborated physical theory is still pending. Wider implications are briefly discussed.

The relativistic effects of the dynamical properties of light at angular incidence were analyzed from the perspectives of Bohr indeterminacy and Heisenberg uncertainties and statistical dispersion. It was found that these effects report minimal uncertainties that agree with one or the other according to the angular range of incidence and that decrease with increasing refringence of the medium, constituting a specific relativistic uncertainty at angular incidence. An anomaly is indicated for the uncertainty principle in the Quantum Theory (QT) setting for small angles of incidence, where the accuracy of the angular position does not imply an increase in the uncertainty of the linear momentum. The anomalies arise because TQ does not predict the alternation between the classical and relativistic regimes of photon inertia at angular incidence. Specific relativistic uncertainty particularizes the uncertainty principle in the transmission of light between media pairs at angular incidence for the relativistic scenario, considering an observer that registers the relativistic effects of measurements that interfere with the observed system, in another inertial referential.

This paper presents findings of a study on continuous feed-in management and continuous synthetic inertia contribution with wind turbines. A realistic case study, based on real measurements, is outlined. A wind turbine feeds into a weak feeder, such that its power has to be adapted to the permissible loading of this feeder. At the same time the wind turbine is to provide inertia to the grid by applying the previously published variable inertia constant controller. It is discussed that optimal grid utilisation and simultaneous inertia contribution are mandatory for the frequency control in power systems that are heavily penetrated with renewable energies. The study shows that continuous feed-in management can be combined well with continuous inertia provision. There are hardly any negative consequences for the wind turbine. The benefits for the grid are convincing, both in terms of increased system utilisation and in terms of provided inertia. It is concluded that wind turbines can enhance angular stability in a power system to a larger extent than conventional power plants.

A four-parameter kinematic model for the position of a fluid parcel in a time-varying ellipse is introduced. For any ellipse advected by an arbitrary linear two-dimensional flow, the rates of change of the ellipse parameters are uniquely determined by the four parameters of the velocity gradient matrix, and vice-versa. This result, termed ellipse/flow equivalence, provides a stronger version of the well-known result that a linear velocity field maps an ellipse into another ellipse. Moreover, ellipse/flow equivalence is shown to be a manifestation of Stokes' theorem. This is done by deriving a matrix-valued relationship, called the geometric Stokes' theorem, that involves a spatial integral over the velocity gradient tensor, thus accounting for the two strain terms in addition to the divergence and vorticity. General expressions for various physical properties of an elliptical ring of fluid are also derived. The ellipse kinetic energy is found to be composed of three portions, associated respectively with the circulation, the rate of change of the moment of inertia, and the variance of parcel angular velocity around the ellipse. A particular innovation is the use of four matrices, termed the IJKL basis, that greatly facilitate the required calculations.

An exact solution is obtained for the kinetic energy in the general case of the spatial motion of solids with arbitrary rotation, which differs from the Koenig formula by three additional terms with centrifugal moments of inertia. The description of motion in the Lagrange form and the superposition principle are used, which provides a geometric summation of the velocities and accelerations of the joint motions in the Lagrange form for any particle at any time. The integrand function in the equation for kinetic energy is represented by the sum of the identical velocity components of the joint plane-parallel motions. The moments of inertia in the Koenig formula do not change during movement and can be calculated from the current or initial state of the body. The centrifugal moments change and turn to 0 when rotating relative to the main central axes only for bodies with equal main moments of inertia, for example, for a ball. In other cases, the difference in the main moments of inertia leads to cyclic changes in the kinetic energy with the possible manifestation of precession and nutation, the amplitude of which depends on the angular velocities of rotation of the body. An example of using equations for a robot with one helical and two rotational kinematic pairs is given.

The shallow water equations are widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. From a mathematical point of view, they are a hyperbolic system of nonlinear partial differential equations, whose numerical integration is sometimes computationally burdensome. For this reason, the interest of many researchers has been focused on the study of simplified forms of the original set of equations, which requires less computational effort. One of the most commonly applied simplifications consists in neglecting the inertial terms, which changes the hyperbolic model to a parabolic one. The effects of such a choice on the outputs of the simulations of flooding events are controversial and an important topic of debate. In the present paper, two numerical models, recently proposed for the solution of the complete and zero-inertia forms of the shallow waters equations, are applied to several unsteady flow routing scenarios. We simulate synthetic and laboratory studies, starting from very simple geometries and moving towards complex topographies. Analyzing the role of the terms in the momentum equations, we try to understand the effect, on the computed results, of neglecting the inertial terms in the zero-inertia formulation. We analyze the computational costs.

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.

Chronic diseases, such as type 2 diabetes (T2D), are difficult to manage because they demand continuous therapeutic review and monitoring. Beyond achieving the target HbA1c, new guidelines for the therapy of T2D have been introduced with the new groups of antidiabetics (GLP-1ra and SGLT2-in). Despite new guidelines, clinical inertia, that can be caused by physicians, patients or healthcare system, results in T2D not being effectively managed. This opinion paper explores the shift in T2D treatment, challenging assumptions and evidence-based recommendations, particularly for family physicians, considering the patient's overall situation in decision-making. We looked for the possible reasons of clinical inertia and poor application of guidelines in the management of T2D. Guidelines for antidiabetic drugs should be more precise, providing case studies and clinical examples to define clinical contexts and contraindications. Knowledge communication can improve confidence and should include clear statements on areas of decision-making not supported by evidence. Precision medicine initiative in diabetes aims to identify subcategories of T2D patients (including frail patients) using clustering techniques from data science applications, focusing on CV and poor treatment outcomes. Clear, unconditional recommendations for personalized T2D management may encourage drug prescription, especially for family physicians dealing with diverse patient contexts and clinical settings.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

This study presents an exact solution to the free vibration analysis of a uniform Timoshenko beam, with a harmonic vibration being assumed. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. In this paper, a moment-shear force-circular frequency-curvature relationship was presented. The complete study was based on this relationship and closed-form expressions of efforts and deformations were derived. The free vibration response of single-span systems and spring-mass systems was analyzed; closed-form formulations of matrices expressing the boundary conditions were presented and the natural frequencies were determined by solving the eigenvalue problem. Systems with intermediate mass, spring, or spring-mass system were also analyzed. Furthermore, first-order dynamic stiffness matrices in local coordinates were derived. Finally, a second-order analysis of beams resting on an elastic Winkler foundation was conducted. The results obtained in this paper were in good agreement with those of other studies.

We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.

This article lays the foundation for Extended Relativity (ER) – a unified geometric approach to the electromagnetic and gravitational field and relativistic dynamics in them. We explain here the basic tenets of ER, including the influenced spacetime of an object and the Extended Principle of Inertia. These two new ideas enable a unified theory of these fields. We introduce local scaling functions for describing the geometry of a spacetime influenced by a field and construct a simple, universal local scaling function which unifies electromagnetism and gravity. We recover the full electromagnetic theory, including Maxwell’s equations. For gravitation, ER passes all of the tests of General Relativity. Despite the non-linearity of relativistic gravitation, we obtain a method of combining fields from multiple sources. Finally, we identify the differences in the relativistic treatment of the electromagnetic field by Special Relativity and of the gravitational field by General Relativity and indicate how these differences are resolved in ER.

The aim of this study is to investigate transient dynamic flow characteristics of the fluid flow through 5-way electric coolant valve (PCCV : Penta-Control Coolant Valve). To achieve this goal, the present paper attempts the three-dimensional dynamic simulation of the fluid flow through the valve using a commercial CFD solver with moving mesh technique to consider flow inertia and dynamic flow in the opening and closing stages of the ball valve rotating motion. Firstly, dynamic flow characteristics and the thermal mixing inside the PCCV ball valve during the opening and closing stage was analyzed. It is found that the discrepancies between dynamic and steady state simulation is remarkable when fluxes with different levels of enthalpy and momentum flow into the PCCV leads to strong flow interference and flow inertia, while the discrepancies are relatively small at low rotation speed and weak flow interference. Then, the effect of dynamic flow characteristics of the valve on dynamic thermal mixing characteristics at two different ball valve rotational speeds and rotational directions were investigated. It was found that the dynamic flow and thermal mixing characteristics inside the PCCV are greatly affected by the rotation speed, rotation direction, and degree of flow interference between fluxes. It is helpful for the design of the better coolant control strategies and the improvement of the FCEV thermal management system.

The transport and entanglement of photons is becoming prominent in optics applied to information and quantum computing, where the angular momentum of light stands out in the exchange and inversion of quantized states, with prospects for several technological applications, such as the transport and storage of quantum information. In order to contribute to the understanding of quantized states in photon-matter interaction, we describe a quantized state equation in multidimensional Hilbert space for the diagnosis of OAM states, where probabilities arise in a relativistic setting. It was found that the classical-relativistic variability of the probabilities constitutes a resultant capable of describing the quantized states of light, where the state variable is the variation of the angular momentum of the photon, capable of estimating the orbital angular momentum inversion points at angular incidence. It was found that the chances of finding the quantized states of light at angular incidence can be treated by purely relativistic probabilities, explaining that when both states have equal chances of being found and the angular momentum variation is zero, the source-observer synchronizations occur at the step of increasing relativistic regime of the photon dynamics. We found that the relativistic effect from the perspective of the source referential is able to alter the chances of an event occurring, dilating and contracting the probabilities of finding a quantized state of light at angular incidence.