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The comments provided in this document are a response to a study conducted by Professor Jean-Pierre Pascal on the inertia forces in roller test rigs. The comments address concerns raised by Professor Pascal regarding a statement made in a previous paper. The comments highlight the limitations of using roller test rigs for longitudinal wheelset motion and emphasize the need for three-dimensional models to accurately capture the effects of inertia forces on contact forces. The document also points out several fundamental problems with the planar example used in Professor Pascal's paper. Overall, the comments suggest that further research is needed to fully understand the impact of longitudinal velocity on motion trajectories and contact forces. [Extracted from the article]

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This paper assesses thermoelastic damping (TED) in circular nanoplates by incorporation of the small-scale effect into structural and thermal domains. The nonlocal elasticity theory and dual-phase-lag (DPL) heat conduction model are exploited for achieving the size-dependent coupled thermoelastic equations. By choosing time-harmonic and asymmetric form for deflection and temperature change, and solving the size-dependent thermoelastic eigenvalue problem, the damped natural frequency of circular nanoplate is extracted. On the basis of the complex frequency approach, an analytical relation, for the description of TED in circular nanoplates, is derived. For different boundary conditions and vibration modes, a comparison study is performed between the size-dependent results and those provided by classical continuum mechanics and heat conduction theories. Outcomes show a discrepancy between results acquired by the size effect on the structure and heat conduction. It is elucidated that how nonlocal and DPL characteristic parameters can represent the size-dependent phenomenon and can affect the magnitude of TED. A comprehensive parametric study is conducted to specify the influence of boundary constraints, vibration mode and the type of material on the amount of energy loss from TED. [ABSTRACT FROM AUTHOR]

Friction is not an inherent attribute in natural science. Indeed, there are various friction phenomena present in social systems. In this study, the researchers developed the general concept of social friction and distinguished the two-dimensional structure of explicit-implicit social friction phenomena. Specifically, explicit friction includes institutional friction, economic friction, behavioral friction, and migration friction. Implicit friction includes cultural friction, cognitive friction, interpersonal friction, technological friction, and information friction. Physical theories such as friction force, classical mechanics, and functional principles have been introduced to construct a social friction force model. This paper describes the emergence and evolution of social friction phenomena from the mechanics perspective and clarifies the various characteristics of social friction force in different areas. This study also provides a new theoretical perspective for examining social friction phenomena and adds innovative content to intersection studies in physics and the social sciences. [ABSTRACT FROM AUTHOR]

Physics is a tricky subject to learn, especially when it comes to students applying physics knowledge to the real world and its application. This paper aims to study the effectiveness of the integrated science, technology, engineering, and mathematics project-based learning (iSTEM-PjBL) module in physics on students’ belief-specific categories, i.e., real-world connection, conceptual connection and applied conceptual understanding. This research used the quasi-experimental model, employing a two-group pre-survey-post-survey design. Quantitative data were collected using the Colorado Learning Attitude about Science Survey (CLASS) instrument at two selected schools in Sabah, Malaysia, and Seoul, Korea. The sample size was 88 from Malaysia and 66 from Korea who learned classical mechanics. The students were divided into two groups, respectively, i.e., the experimental group (Malaysia=44, Korea=33) and the control group (Malaysia=44, Korea=33). Participants in the experimental group were intervened with the integrated STEM-PBL physics module, whilst participants in the control group learned physics through a conventional approach for eight weeks. Participants in both groups were then administered a pre-survey before and post-survey after the intervention. This research showed that the integrated STEM-PjBL physics module significantly improved students’ real-world connections, conceptual connections, and applied connections after the intervention. The implications and suggestions were also discussed to extend the research further. [ABSTRACT FROM AUTHOR]

There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of S e t s are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences. [ABSTRACT FROM AUTHOR]

A two-axis stabilizing gimbal is a device that ensures a sensor is working properly on a moving platform. When classical mechanics (Newton–Euler and Lagrange) is employed to model a two-axis stable gimbal, its limitations can complicate the modeling process. To address this issue, a method for establishing a dynamic model for a two-axis stabilizing platform based on the Kane method is proposed in this paper. The Kane method offers the advantage of a simple model structure and computational efficiency. Initially, utilizing a generalized coordinate system, expressions of the generalized velocities, deflection velocities and angular velocities are derived. Subsequently, the generalized active forces and inertial forces acting on the two-axis stabilized gimbal are analyzed. Finally, by combining force and velocity with the Kane equation, the dynamic model of the two-axis stable platform is obtained, demonstrating the validity of the Kane method for establishing the two-axis stable platform model. To ensure the pointing accuracy stability of the two-axis stabilizing platform, a Novel Particle Swarm Optimization Proportion Integration Differentiation (NPSO-PID) controller is designed using the PSO algorithm. It is then simulated in MATLAB/Simulink and compared with a classical PID controller. Simulation results demonstrate that NPSO-PID exhibits superior object tracking performance compared to classical PID controllers and better optimization of control parameters compared to traditional PSO-PID controllers. [ABSTRACT FROM AUTHOR]

Conical intersection (CI) leads to fast electronic energy transfer. However, Hamm and Stock [Phys. Rev. Lett. 109, 173201 (2012)] showed the existence of a vibrational CI and its role in vibrational energy relaxation. In this paper, we further investigate the vibrational energy relaxation using an isolated model Hamiltonian system of four vibrational modes with two distinctively different timescales (two fast modes and two slow modes). We show that the excitation of the slow modes plays a crucial role in the energy relaxation mechanism. We also analyze the system from a mixed quantum-classical (surface hopping method) and a completely classical point of view. Notably, surface hopping and even classical simulations also capture fast energy relaxation, which is a signature of CI's existence. [ABSTRACT FROM AUTHOR]

This paper investigates the structural changes in the turbulent motion of an incompressible fluid in the hydrodynamic entrance region of plane-parallel pressure motion. Movement in pressure hydromechanical systems usually occurs in a turbulent regime. Studying the patterns of changes in hydrodynamic parameters under conditions of stationary turbulent pressure motion in the inlet region is a very urgent task. The study was carried out on the basis of boundary layer equations. Taking into account the dependence of changes in the kinematic viscosity coefficient that occur between layers of fluid, a boundary value problem was formed. Analytical solutions have been obtained that make it possible to obtain patterns of changes in velocity and pressure in any effective flow section. Based on the general conclusions of the study, solutions were found for two cases: a) the velocity of the fluid entering the cylindrical pipe is constant; b) the velocity of the incoming fluid has a parabolic distribution. For these cases, using computer analysis of the data obtained, general graphs of velocity changes were constructed in various sections along the hydrodynamic entrance region. These graphs, which display the change in velocity along the entire length of the inlet, make it possible to obtain the velocity of fluid movement at any point along the inlet length and estimate the length of the transition zone. The results obtained are among the least studied issues of classical fluid mechanics and are of important theoretical interest. The results obtained are applicable for the correct construction of the hydrodynamic entrance region of machinery. A calculation formula has been obtained to determine the length of the hydrodynamic inlet region. [ABSTRACT FROM AUTHOR]

This paper focuses on Kojève's account of history and philosophy of science. Kojève's understanding of science can be characterized as internalism, which is evident in his holistic view of philosophy, theology, quantum physics, and the history of classical Newtonian mechanics. It precipitates the facilitation of a further inquiry into the Christian genesis, secular evolution, and subsequent de-Christianization of scientific thought. The paper includes a critical scrutiny of Kojève's philosophical tenets, followed by a comparative analysis of the views of Hegel, Koyré, and Kojève. The primary objective of this research is to juxtapose Kojève's doctrines with Hegel's contemplations on the history and philosophy of science. In addition to identifying affinities, notably the emphasis on the Christian concept of God's Incarnation for the advancement of science, I draw the distinctions between the positions of Hegel, Kojève, and Koyré, specifically concerning the valuation of mathematical knowledge. [ABSTRACT FROM AUTHOR]

Applied physics and computer methods in biomechanics have been extensively used in sports science research, including performance and biomechanics analysis. The Brachistochrone problem, which expresses the curve that an object draws quickly under gravitational forces in a vertical position, is one of the most widely used studies in classical mechanics. A similar problem arises when a badminton player intends to hit a smash with the shortest shot time. This paper aims to determine the optimal stroke trajectory for a shuttlecock smash in the shortest time. We simulate the badminton smash movement using a computer program after analyzing the shuttlecock smash analytically and numerically for several conditions. The modeling results show that a cycloid trajectory allows badminton players to smash the shuttlecock in the shortest time. Based on the experimental findings of Tsai, Huang, and Jih's study and our models, the ratio of clear speed to smash speed is 0.75, which is still in the range of 0.71 to 0.76, and we find that a cycloid trajectory gives the shortest shuttlecock smash time. We concluded that the experimental data from this study's literature supported our model. The novelty of this study is that we found the first powerful model and simulation of conventional Brachistochrone in the case of a badminton smash of badminton players. For badminton coaches and players, this model formulation is intended as a reference for optimizing shuttlecock shots. Furthermore, another novelty of this research is that it may lead to software that can be used to analyze the muscle strength of badminton players based on their cycloid hand trajectory and shuttlecock speed. [ABSTRACT FROM AUTHOR]

This document is a special issue of AIMS Materials Science focused on peridynamics and its applications. Peridynamics is a new formulation of continuum mechanics that overcomes the limitations of classical continuum mechanics. It uses integro-differential equations to represent material points and does not rely on spatial derivatives. This makes it particularly useful for analyzing cracks and representing material behavior that cannot be properly defined in classical continuum mechanics. The special issue includes six journal papers that cover topics such as fractional peridynamic mechanics, dynamic fracture, structural analysis, and optimization of reinforced concrete beams. [Extracted from the article]

In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue of classical mechanics. Another one is a shape resonance model which is a perturbation of a quantum walk with a non-penetrable barrier. [ABSTRACT FROM AUTHOR]

The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed, but a comparison with results for the dynamics in the framework of classical statistical mechanics is useful. Analytical results are presented when the initial and final potentials are harmonic oscillators. When the final potential vanishes, the problem reduces to the broadening of wave packets. A simple introduction to the concept of the Wigner function is presented, which allows a better understanding of the dynamics of general wave packets. It is pointed out how special the broadening of Gaussian wave packets is, the only example usually presented in quantum mechanics textbooks. Quantum quenches occur when the Hamiltonian of a system is suddenly changed, so that the system is driven out of equilibrium. This paper, appropriate for graduate-level quantum mechanics classes, examines the similarities and differences of quantum quenches compared to their classical counterparts for three one-dimensional examples: the harmonic oscillator, the linear potential, and the zero potential for which the broadening of a non-Gaussian wave packet is addressed. [ABSTRACT FROM AUTHOR]

Georgiy (George) Albertovich Krasinsky was one of the scientists who made Soviet and later Russian science both advanced and competitive by arousing interest in it with the leading researchers around the world. Having received his education in the Department of Mathematics and Mechanics at Leningrad State University, for a long time he was engaged in research in the field of classical celestial mechanics, where he performed a number of first-class studies whose results are still in demand at present. The onset of the Space Age, with its sharp jump in the accuracy of astronomical observations, caused by the rapid development of technology, made Krasinsky realize that the classical methods of celestial mechanics and astrometry could no longer cope with the processing of up-to-date measurements, as these were unable to provide the accuracy of the ephemerides of the Solar System bodies at a level demanded by the new requirements. As a result, under his expert guidance and with his active participation, the ERA (Ephemeris Research in Astronomy) software system was developed, which became the basis for all of the later work at the Institute of Applied Astronomy of the Russian Academy of Sciences (IAA RAS) on processing modern high-precision measurements and formulating relativistic numerical theories of the orbital motion of the Solar System bodies. While working at the IAA RAS, George got deeply involved in such issues as the fundamental coordinate-time system, thus becoming one of those who were active in building up the quasar radio-interferometric network. During the last years of his life, George developed a numerical theory of the rotation of a deformable Earth with a liquid core, and theories of the evolution of both the rotational motion of the Earth and of the Moon's orbit. [ABSTRACT FROM AUTHOR]

In this paper, we investigate stability and optimization of an axially loaded nonlocal beam that is simply supported at one end and elastically restrained against rotation on the other. Nonlocal continuum mechanics is a theoretical framework that extends classical continuum mechanics to account for the influence of small length scales, especially in nanostructures. We analyze elastically buckling nanobeam based on Eringen's nonlocal elasticity theory. The Euler method of adjacent equilibrium configuration is used to derive the nonlinear governing equations. The critical axial force and postbuckling shape are obtained for the beam with the unit cross-sectional area. The shape of the nonlocal beam stable against buckling that has minimal volume is determined by using Pontryagin's maximum principle. The optimality conditions are derived. The cross-sectional area for optimally designed beam is found from the solution of a nonlinear boundary value problem. New numerical results are obtained. The first integral (Hamiltonian) is used to monitor the accuracy of the integration. The numerical analysis includes the influence of the characteristic parameter of the small length scale on the critical load, the postbuckling shape and the optimal shape of the analyzed beams. It is shown that there are the saving materials for optimally designed nanobeam in all numerical examples. [ABSTRACT FROM AUTHOR]

In the present paper we study the nonlinear system ut + [ϕ(u)]x + v = 0, vt + ψ(u)vx = 0 as a model for the one-dimensional dynamics of dark matter. We prove that under certain conditions this system, such as the Gurevich-Zybin system, can also explain why the observed rotation speed (relative to the galactic center) of stars near galactic halos do not coincide with what it is expected in classical mechanics. The solutions are obtained in fully explicit formulas, in a convenient space of distributions, without using any result within the classical framework. For such purpose we use the α-solution concept which is defined within a product of distributions. Such a concept generalizes the classical solution concept and for evolution equations may also be seen as an extension of the weak solution concept to the nonlinear setting. [ABSTRACT FROM AUTHOR]

• The compressive buckling analysis of cracked nanosheets is performed by XFEM, considering small-scale effect. • The contribution of this work is the study of buckling of nanosheets in the presence of a crack. • The studied variables include small-scaling parameter, crack length, nanosheet dimensions, and boundary supports. • The results show that the cracking phenomenon and the increase of its length intensify the nonlocal effect. The process used to produce nanosheets may cause damage such as cracks in them. These cracks can adversely affect the buckling capacity of nanosheets. The main contribution of this research endeavor is to extend the previous studies on undamaged nanosheets to the cracked ones concerning the size-dependent effect. On the nanoscale, the assumption of material continuity, which is the fundamental assumption in classical continuum mechanics, is not valid. In this case, nonlocal non-classical theories are employed to analyze nanosheets. The present paper examines the nonlocal buckling of cracked graphene sheets under uniaxial and biaxial loads. To this end, the governing equations are developed based on the first-order shear deformation theory and using Eringen's nonlocal elasticity theory. Moreover, cracked nanosheets with various boundary conditions are analyzed via the extended finite element method. The variables under study are the small scaling parameter, crack length, nanosheet dimensional parameters, and support conditions. The results indicate that while the small scaling parameter reduces the critical buckling capacity of nanosheets, the presence of a crack in the nanosheet and the increase in its length intensify the nonlocal effect. In addition, as the aspect ratio of the nanosheet increases from one, the nonlocal effect decreases gradually. The small-scale effect increases by constraining the edges of the cracked nanosheets. [ABSTRACT FROM AUTHOR]

The paper presents the numerical calculation of the group resistance to the incident particle impact on the supramolecular structure comprising rotating carbon nanotori. Methods of classical molecular mechanics are used to study the interaction between the particle and toroidal cluster in a columnar phase. The analysis is given to the influence of the nanotorus rotation frequency and the supramolecular structure dimensions on its resilience. [ABSTRACT FROM AUTHOR]

In this paper, we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing a constraint, and apply our theory to Gaussian model and black hole thermodynamics. Thus, we demonstrate how deformation of gradient flows leads to more general Randers–Finsler metrics, describe Hamiltonian mechanics that derive from a constraint, and prove duality via canonical transformation. We also verified our theories for a deformation of the Gaussian model, and described dynamical evolution of flat metrics for Kerr and Reissner–Nordström black holes. [ABSTRACT FROM AUTHOR]

In the 3rd century B.C.E., Archimedes wrote his treatise on the quadrature of the parabola, in which he laid out his solution to the problem of finding the area of a parabolic segment. Archimedes attacks the problem from two sides; first, he uses classical mechanics to derive an area formula, and then he uses pure geometry to prove his formula is correct. In this paper, we will present two modern approaches to this problem using calculus. The first approach can be presented to a calculus class that has learned about optimization methods and convergent geometric sequences, and the second can be presented after they have learned the Fundamental Theorem of Calculus. [ABSTRACT FROM AUTHOR]

It is often said in physics that if two models of a theory are related by a symmetry, then the two models provide (or could provide) two different representations of the very same situation, alike the case of two maps of different color for the very same city. It is also said that the situations represented by two models of a theory are indiscernible in some ways when the models in question are related by a symmetry of the theory, just like the situation in the interior of the cabin of a train when the train is at rest in the station is empirically indiscernible from the situation in the interior when the train is moving uniformly (in classical mechanics, these two situations are represented by two models related by a boost). In recent years, philosophers of physics have focused a lot of attention in developing various principles that aim to elucidate these and similar remarks on symmetries, models, physical equivalence, and representation that are widespread in physics practice. The goal of the current article is to provide a critical review of these principles, and suggest a new framework for thinking about these kinds of questions. One important upshot of the paper is that questions of indiscernibility, and questions of the representational capacity of models, must be distinguished from one another. [ABSTRACT FROM AUTHOR]

Quantum coherence is an important feature that distinguishes quantum mechanics from classical physics. In this paper, we study the coherence of a quantum state with respect to a quantum channel, and introduce a coherence measure in terms of the generalized Wigner–Yanase–Dyson skew information. The basic properties and operational significance of the measure are expounded in detail, which shows that it is indeed a veritable quantity and satisfies many desirable conditions intuitively required for the coherence measures. We illustrate the significance of characterizing channels from the coherence perspective through some examples. Finally, we consider the average coherence of a state based on the generalized Wigner–Yanase–Dyson skew information with respect to any complete mutually unbiased bases in prime power dimensional systems, as well as with respect to all orthonormal bases, and show that these two averages are equivalent since they both can be seen as the coherence of the quantum state with respect to the depolarizing quantum channel. [ABSTRACT FROM AUTHOR]

Peridynamic theory is the reformulation of classical mechanics mathematical theory compatible with cracks while performing structural analysis. The present study models the tubular joints having T, Y, K, and X configurations in the peridynamic framework by implementing peridynamic shell governing equations. The linear response of the structure is validated by comparing the magnitude of deformations under static loading and the displacement variation at the subsequent load steps varying in a sinusoidal and irregular manner with the abaqus results. The crack initiation location at the stress-concentrated region and the crack growth path leading to fracture under linearly increasing loads for the considered tubular joints can be inferred from this approach. A comparative study is performed among the joint configurations based on the linear displacement variation and critical loads for the unstable deformation due to damaged material points at the joint intersection. In the present paper, apart from validating the implementation of novel theory in the offshore structure, the drawbacks and intricacies of the classical approach for studying crack initiation and growth in complex tubular joint structures are resolved by the peridynamic approach. [ABSTRACT FROM AUTHOR]

In this paper, the equation of motion of a projectile in a resistive medium is revisited in view of quantum calculus. Quantum calculus, abbreviated as q-calculus is a recently recognized unconventional type of calculus in which q-derivatives of a real function can be obtained without limit. In order to describe the motion of a 2-D projectile, vertical and horizontal components of velocity in terms of q-differential equations are presented in accordance with the exact classical expressions. The solutions are obtained in terms of the small q-exponential function. Features of a projectile are also deducted one by one for relevance. It is also found that, when the parameter q→1, the present solutions and all the features take the form as they are in general Newtonian classical mechanics. [ABSTRACT FROM AUTHOR]

• The proposed model only places the PD subdomain in the crack initiation region of porous material, which greatly improves the computational efficiency while ensuring the calculation accuracy. • The displacement vector and mass matrix are reconfigured to ensure the calculation consistency in the process of adaptive expansion of the PD subdomains. • The fracture phenomenon of porous materials based on this model is well reproduced and interesting results are obtained. Predicting the dynamic failure process of porous materials is a challenging task due to their complex structure. To minimize the use of time-consuming peridynamic (PD) models and to avoid surface effect issues in the dynamic failure of complex porous materials, this paper proposes a strength-induced PD model. The paper first presents the dynamic formula and relevant finite element discrete equation of the coupled PD and classical continuum mechanics (PD-CCM) model based on the Morphing method. The Morphing function is implemented to control the material parameters and enable the free transformation of PD and CCM models. Based on the coupled PD-CCM model, the strength-induced PD model is established to adaptively expand the PD subdomain in porous materials by controlling the Morphing function value through the strength state of the structure. This model enables the PD subdomain to appear automatically when the porous materials reach the critical stress state. The proposed model accurately predicts the location of crack initiation and path while minimizing computational costs and improving efficiency. Three two-dimensional numerical examples are used to verify the effectiveness, efficiency, and accuracy of the model. The results of the simulation suggest that the location where the crack initiates in the porous materials is strongly influenced by the amplitude of the dynamic load. Cracking is dependent on the pores and typically occurs through them. [ABSTRACT FROM AUTHOR]

The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behaviour of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behaviour can emerge based on the geometric features of the waveguide. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class which we call normal, and a non-generic abnormal class. The eigenvalues of the locked inertia tensor descend to shape-space and endow it with the geometric structure of a three-web with the property that any normal relative equilibrium occurs as a critical point of the potential restricted to a leaf from the web. To demonstrate the utility of this web structure we show how the spherical three-body problem gives rise to a web of Cayley cubics on the three-sphere, and use this to fully classify the relative equilibria for the case of equal masses. [ABSTRACT FROM AUTHOR]

Due to the existence of microstructures involving characteristic length scales, micropolar materials such as bones, rocks and foam materials usually have complex fracture behaviors. The near-tip fields of an anti-plane crack in micropolar media and the local cracking modes, however, remain unclear. In this paper, the Williams asymptotic solutions of the near-tip fields of an anti-plane crack in micropolar elasticity are derived. A force stress intensity factor (FSIF) and two couple stress intensity factors (CSIFs) are the key fracture parameters characterizing the anti-plane crack-tip fields. And the energy release rate for an anti-plane crack is similar to the Rice's J-integral for classical continua. Then, six crack modes are introduced for a three-dimensional micropolar solid, i.e., three global modes controlled by the FSIFs and three local modes controlled by the CSIFs. Different from classical isotropic elasticity, a material constant appears in the singular terms of the crack-tip force stress and couple stress fields of isotropic micropolar materials. In addition, there are six constant terms in the asymptotic solutions of the crack-tip fields, i.e., three constant force stresses and tree constant couple stresses similar to the T-stress in classical fracture mechanics. Sequentially, the J-integral for three-dimensional micropolar solids is expressed concisely by the FSIFs and CSIFs. It can be observed that the CSIFs normalized by the torsion and bending characteristic lengths are dimensionally equivalent to the FSIFs. This work provides a theoretical basis for studying the fracture performance and crack propagation criterion of micropolar materials. • The asymptotic solutions of the near-tip fields of an anti-plane crack for micropolar elasticity are provided. • Three global and three local crack modes are deeply elucidated for micropolar elasticity. • The J-integral is expressed concisely by three force stress intensity factors and three couple stress intensity factors. [ABSTRACT FROM AUTHOR]

We study the problem of the hydrogen atom submitted to a circularly polarized microwave field. This problem, analyzed from a classical mechanics approach, can be modeled by an autonomous Hamiltonian depending on one parameter K > 0. The paper is focused on the so called n -ejection–collision orbits (n -EC orbits), that is orbits that the electron describes when it ejects from the nucleus and collides with it at the n relative minimum in the distance with respect to the nucleus. In this work, we analyze the evolution of the families of n -EC orbits. We conduct a comprehensive numerical analysis of the bifurcations, which involves multiple precision computations, to characterize the successive bifurcation families that emerge. Additionally, we examine the periodic and quasi-periodic motion of the n -EC orbits belonging to these bifurcation families. • First analytical proof of n–ejection–collision orbits in the CP problem. • Numerical simulations require quadruple and even multiple precision. • Characterization of an n–EC orbit is provided, valuable for analysis and computation. • Families of n–EC orbits are continued, with an analysis of successive bifurcations. [ABSTRACT FROM AUTHOR]

The motion of a rigid body (a gyroscope) is one of the key issues in classical mechanics. It remains a significant challenge, as evidenced by its extensive practical implementations in various scientific disciplines and engineering operations. It is important to obtain analytical solutions, as they provide solutions that depend directly on the system's parameters, which can be definitively interpreted. The coupling of numerical and analytical solutions allows for a more precise representation of the real phenomenon. The main objective of the article was to formulate analytical solutions for the motion of a Cardan suspension gyroscope subjected to controlling torque moments. Analytical solutions for the proposed mathematical model were developed using the Laplace transform and Green's function. Subsequently, they were validated by numerical tests. The obtained analytical solutions are universally applicable, regardless of the type of controlling moments. [ABSTRACT FROM AUTHOR]

The axiomatic structure of the κ -statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the κ -entropy and its special limiting case, the classical Boltzmann–Gibbs–Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from κ -entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the κ -formalism, which emerges from the κ -entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on κ -entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the κ -statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized. [ABSTRACT FROM AUTHOR]

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical structures of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories. [ABSTRACT FROM AUTHOR]

As an important indicator for measuring the effectiveness and level of oil and gas field development, recovery rate has always been a focus in the research of oil and gas fields. Reservoirs of tight sandstone gas formations have significant characteristics of low porosity, high permeability, and high water content, which leads to greater difficulty in their development and makes it challenging to evaluate the recovery rate. Newtonian mechanics, as an important component of the mechanical system, is an innovative application of classical mechanics in the field of seepage mechanics when applied to the two-phase flow of gas and water. Firstly, starting from the perspective of mechanics analysis, we derive a steady-state model for gas–water two-phase infiltration and obtain the productivity equation based on this model. Then, according to the steady-state model, we establish a method to calculate the effective control radius of gas reservoirs under different production conditions and reservoir physical properties. Finally, using Matlab 2018a programming based on the productivity equation, we calculate the gas recovery under different conditions during constant pressure drop production and constant production rate production. The results indicate that the effective control radius of the reservoir decreases with an increase in the economic ultimate daily gas production, increases with an increase in production pressure difference, slightly decreases with an increase in startup pressure gradient, and correspondingly increases with an increase in microtube radius and quantity. Regardless of whether it is production with a fixed pressure drop or production with a fixed production rate, the gas recovery decreases as the production pressure drop and bottomhole abandonment pressure increase, but it increases as the proportion of the single-well control radius increases. In production with a fixed pressure drop, the gas recovery remains consistent across different reservoir quality indices. However, in production with a fixed production rate, the gas recovery initially increases rapidly and then gradually slows down as the reservoir quality index increases, and there is an obvious critical permeability (0.1 mD). The research findings are based on the mechanical analysis of porous media, delving into the laws governing fluid flow during infiltration. The derived infiltration model can be used to calculate the effective control radius and evaluate recovery rates, providing practical guidance for reservoir development. [ABSTRACT FROM AUTHOR]

Bragg reflectors are essential for beam transport in X-ray free-electron laser (XFEL) facilities. On interaction with Bragg reflectors, a part of the pulse energy will be absorbed, causing the propagation of displacement waves due to rapid thermal expansion. It is suspected that these waves may cause stability problems for XFELs operating with megahertz repetition rates. Here, we experimentally investigate the displacement of a diamond Bragg reflector induced by an optical ultra-violet laser pulse, simulating XFEL pulses with mJ pulse energy, both at room temperature and cryogenic temperatures. Our experiment shows negligible damping of the displacement waves on µs timescales, which could cause disruption for subsequent XFEL pulses. We compare our measurements to a simulation framework based on the assumptions of local thermodynamic equilibrium and classical mechanics, observing reasonable agreement. Our results show that thermoelastic effects are critical for a reliable stability assessment of Bragg reflectors, but are often overlooked. While MHz repetition rates at modern X-ray free-electron laser (XFEL) facilities achieve remarkable capabilities for imaging, the high repetition rates may also lead to new stability problems. The authors experimentally demonstrate that thermoelastic displacements between successive pulses can be detrimental to the performance of cavity-based XFEL [ABSTRACT FROM AUTHOR]

Introduction: Classical mechanics concepts are vital for understanding traffic safety, encompassing speed, acceleration, stopping distance, impact speed, deformation, kinetic energy, and their effects on vehicle occupants. Statistical physics principles are also employed to study multiple vehicles as a many-particle system. This study examines the effectiveness of using a damaged car and structured instruction in road safety initiatives. Methods: Participants engaged with a damaged car and discussed deformation caused by excessive speed. They participated in role simulations, envisioning and solving risky traffic scenarios, while considering the potential boomerang effect resulting from excessive fear appeals within the campaign. Results: Combining emotional appeals with solution-focused, action-oriented, and self-esteem-enhancing interventions is essential to mitigate the boomerang effect and encourage safety-compliant behavior. Educational institutions must implement tailored follow-ups to emotionally charged prevention campaigns. Using Design-Based Research, we developed effective methods for knowledge acquisition and transfer, drawing from cognitive behavioral therapy and established traffic safety programs. Discussion: This publication explores non-standardized social training within focus groups, focusing on negative emotional states following an emotionalizing campaign similar to "Crash Kurs NRW," targeting upper-level courses in North Rhine-Westphalian schools. Methods from cognitive behavioral therapy and social learning initiated, observed, and documented changes in participants' norms, values, and attitudes, discussed herein. Additionally, we investigated whether the presence of police officers in prevention campaigns influences reactive behavior. Comparing pre- and post-surveys confirmed reactance after emotionalizing campaigns, and our structured post-survey effectively influenced stage-event-induced behavior. Surprisingly, police officers' presence did not significantly impact reactive behavior. Furthermore, our follow-up tool extends its applicability to similar emotionalizing prevention campaigns, broadening its potential reach. Our future research will delve into students' physics literacy during traffic space analysis of accident hotspots, advancing traffic safety initiatives. [ABSTRACT FROM AUTHOR]

Determining the oxidation potential (OP) of lithium-ion battery (LIB) electrolytes using theoretical methods will significantly speed up and simplify the process of creating a new generation high-voltage battery. The algorithm for calculating OP should be not only accurate but also fast. Our work proposes theoretical principles for evaluating the OP of LIB electrolytes by considering LiDFOB solutions with different salt concentrations in EC/DMC solvent mixtures. The advantage of the new algorithm compared to previous versions of the theoretical determination of the oxidation potential of electrolyte solutions used in lithium-ion batteries for calculations of statistically significant complexes, the structure of which was determined by the molecular dynamics method. This approach significantly reduces the number of atomic–molecular systems whose geometric parameters need to be optimized using quantum chemical methods. Due to this, it is possible to increase the speed of calculations and reduce the power requirements of the computer performing the calculations. The theoretical calculations included a set of approaches based on the methods of classical molecular mechanics and quantum chemistry. To select statistically significant complexes that can make a significant contribution to the stability of the electrochemical system, a thorough analysis of molecular dynamics simulation trajectories was performed. Their geometric parameters (including oxidized forms) were optimized by QM methods. As a result, oxidation potentials were assessed, and their dependence on salt concentration was described. Here, we once again emphasize that it is difficult to obtain, by calculation methods, the absolute OP values that would be equal (or close) to the OP values estimated by experimental methods. Nevertheless, a trend can be identified. The results of theoretical calculations are in full agreement with the experimental ones. [ABSTRACT FROM AUTHOR]

We study the motion of a test particle in a conservative force field. In the framework of the 2D inverse problem of Newtonian dynamics, we find 2D potentials that produce a preassigned monoparametric family of regular orbits f (x , y) = c on the x y -plane (where c is the parameter of the family of orbits). This family of orbits can be represented by the "slope function" γ = f y f x uniquely. A new methodology is applied to the basic equation of the planar inverse problem in order to find potentials of a special form, i.e., V = F (x + y) + G (x − y) , V = F (x + i y) + G (x − i y) and V = P (x) + Q (y) , and polynomial ones. According to this methodology, we impose differential conditions on the family of orbits f (x , y) = c. If they are satisfied, such a potential exists and it is found analytically. For known families of curves, e.g., circles, parabolas, hyperbolas, etc., we find potentials that are compatible with them. We offer pertinent examples that cover all the cases. The case of families of straight lines is referred to. [ABSTRACT FROM AUTHOR]

The present article pertains to the assessment of thermoelastic damping (TED) in rectangular nanoplates by incorporation of size effect within the constitutive and heat conduction relations. With the purpose of establishing size-dependent coupled thermoelastic equations, nonlocal elasticity theory and dual-phase-lag heat conduction model are utilized. By considering time-harmonic vibrations, nonclassical frequency equation affected by thermoelastic coupling is derived. By solving this equation and extracting the real and imaginary parts of damped natural frequency via some mathematical operations, an explicit expression for description of TED in circular nanoplates is obtained. With the goal of better understanding the small-scale effect on TED, a comparison is made between the results predicted by the size-dependent formulation and those determined according to classical continuum mechanics and heat conduction theories for two kinds of boundary constraints. Considerable difference between classical and nonclassical results, especially at smaller sizes, implies the necessity of incorporating small-scale effect into both structural and thermal areas. [ABSTRACT FROM AUTHOR]

We study the motion of a test particle in a conservative force-field. Our aim is to find three-dimensional potentials with symmetrical properties, i.e., V (x , y , z) = P (x , y) + Q (z) , or, V (x , y , z) = P (x 2 + y 2) + Q (z) and V (x , y , z) = P (x , y) Q (z) , where P and Q are arbitrary C 2 -functions, which are characterized as semi-separable and they produce a pre-assigned two-parametric family of orbits f (x , y , z) = c 1 , g (x , y , z) = c 2 ( c 1 , c 2 = const) in 3D space. There exist two linear PDEs which are the basic equations of the Inverse Problem of Newtonian Dynamics and are satisfied by these potentials. Pertinent examples are presented for all the cases. Two-dimensional potentials are also included into our study. Families of straight lines is a special category of curves in 3D space and are examined separately. [ABSTRACT FROM AUTHOR]

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 spacetime: this is the principle of minimal group representation, which allows us to consistently and simultaneously obtain a natural description of spacetime's 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 M p (n) , the double covering of S L (2 C) 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 (the 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 that divides the Hilbert space into even and odd states that are mutually orthogonal. They carry spin weight of 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) spacetime for n → ∞ . (vii) There emerges a relation between the eigenvalue α of our coherent-state metric solution and the black-hole area (entropy) as A b h / 4 l p 2 = α , relating the phase space of the metric found, g a b , and the black hole area, A b h , through the Planck length l p 2 and the eigenvalue α of the coherent states. As a consequence of the lowest level of the quantum-discrete-spacetime spectrum—e.g., the ground state associated to n = 0 and its characteristic length—there exists a minimum entropy related to the black-hole history. [ABSTRACT FROM AUTHOR]