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The evolution of dynamic DNA nanostructures has propelled DNA nanotechnology into a robust and versatile field, offering groundbreaking applications in nanoscale communication, drug delivery, and molecular computing. Yet, the full potential of this technology awaits further enhancement through optimization of kinetic properties governing conformational changes. In this work, we introduce a mean-field theory to characterize the kinetic behavior of a dynamic DNA origami hinge where each arm bears complementary single-stranded DNA overhangs of different lengths, which can latch the hinge at a closed conformation. This device is currently being investigated for multiple applications, being of particular interest the development of DNA-based rapid diagnostic tests for coronavirus. Drawing from classical statistical mechanics theories, we derive analytical expressions for the mean binding time of these overhangs within a constant hinge. This analysis is then extended to flexible hinges, where the angle diffuses within a predetermined energy landscape. We validate our model by comparing it with experimental measurements of the closing rates of DNA nanocalipers with different energy landscapes and overhang lengths, demonstrating excellent agreement and suggesting fast angular relaxation relative to binding. These findings offer insights that can guide the optimization of devices for specific state lifetimes. Moreover, the framework introduced here lays the groundwork for further advancements in modeling the kinetics of dynamic DNA nanostructures. [ABSTRACT FROM AUTHOR]

We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates. [ABSTRACT FROM AUTHOR]

The potential energy landscape (PEL) formalism is a tool within statistical mechanics that has been used in the past to calculate the equation of states (EOS) of classical rigid model liquids at low temperatures, where computer simulations may be challenging. In this work, we use classical molecular dynamics (MD) simulations and the PEL formalism to calculate the EOS of the flexible q-TIP4P/F water model. This model exhibits a liquid–liquid critical point (LLCP) in the supercooled regime, at (Pc = 150 MPa, Tc = 190 K, and ρc = 1.04 g/cm3) [using the reaction field technique]. The PEL-EOS of q-TIP4P/F water and the corresponding location of the LLCP are in very good agreement with the MD simulations. We show that the PEL of q-TIP4P/F water is Gaussian, which allows us to calculate the configurational entropy of the system, Sconf. The Sconf of q-TIP4P/F water is surprisingly similar to that reported previously for rigid water models, suggesting that intramolecular flexibility does not necessarily add roughness to the PEL. We also show that the Adam–Gibbs relation, which relates the diffusion coefficient D with Sconf, holds for the flexible q-TIP4P/F water model. Overall, our results indicate that the PEL formalism can be used to study molecular systems that include molecular flexibility, the common case in standard force fields. This is not trivial since the introduction of large bending/stretching mode frequencies is problematic in classical statistical mechanics. For example, as shown previously, we find that such high frequencies lead to unphysical (negative) entropy for q-TIP4P/F water when using classical statistical mechanics (yet, the PEL formalism can be applied successfully). [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]

Crystal growth is a complex process with far-reaching implications for high-performance materials across various fields. Recent advancements in structural analysis methods such as polyhedral template matching, which allows semiconductor-specific analysis, coupled with simulation technology, have enabled the comprehensive study of crystallization dynamics in semiconductors. However, the exploration of polycrystalline semiconductors created with minimal external intervention of the crystallization processes is relatively uncharted in comparison with metals. In this study, we employ molecular dynamics to simulate the growth of polycrystalline CdTe/CdS with the assumptions of classical mechanics, a Stillinger–Weber potential, an amorphous substrate, and common vapor growth conditions to allow the polycrystalline structures to evolve naturally. Post-simulation, we identify and analyze impactful structures and events, comparing them to theory and experiment to gain insight into various modes of crystallization dynamics. Two research questions guided the study: (1) How realistic are assumption-less simulated polycrystalline semiconductor structures? (2) To what extent can the approach provide insight into crystallization? The simulations, performed with minimal external control, yield polycrystalline structures mirroring experimental findings. The analysis reveals key crystallization insights, such as the role of amorphous atoms in the transition from nucleation to grain growth and the transformative impact of single events, such as dislocations, on crystallization dynamics. The method paves the way for reproducing and analyzing realistic polycrystalline semiconductor structures with minimal simulation assumptions across various growth modes. [ABSTRACT FROM AUTHOR]

Experimental observations unambiguously reveal quasi-frictionless water flow through nanometer-scale carbon nanotubes (CNTs). Classical fluid mechanics is deemed unfit to describe this enhanced flow, and recent investigations indicated that quantum mechanics is required to interpret the extremely weak water–CNT friction. In fact, by quantum scattering, water can only release discrete energy upon excitation of electronic and phononic modes in the CNT. Here, we analyze in detail how a traveling water molecule couples to both plasmon and phonon excitations within a sub-nanometer, periodic CNT. We find that the water molecule needs to exceed a minimum speed threshold of ∼50 m/s in order to scatter against CNT electronic and vibrational modes. Below this threshold, scattering is suppressed, as in standard superfluidity mechanisms. The scattering rates, relevant for faster water molecules, are also estimated. [ABSTRACT FROM AUTHOR]

In light of the planar inverse problem of Newtonian Dynamics, we study the monoparametric family of regular orbits f (r , θ) = c in polar coordinates (where c is the parameter varying along the family of orbits), which are generated by planar potentials V = V (r , θ) . The corresponding family of orbits can be uniquely represented by the "slope function" γ = f θ f r . By using the basic partial differential equation of the planar inverse problem, which combines families of orbits and potentials, we apply a new methodology in order to find specific potentials, e.g., V = A (r) + B (θ) or V = H (γ) and one-dimensional potentials, e.g., V = A (r) or V = G (θ) . In order to determine such potentials, differential conditions on the family of orbits f (r , θ) = c are imposed. If these conditions are fulfilled, then we can find a potential of the above form analytically. For the given families of curves, such as ellipses, parabolas, Bernoulli's lemniscates, etc., we find potentials that produce them. We present suitable examples for all cases and refer to the case of straight lines. [ABSTRACT FROM AUTHOR]

In this note, I present two variations of the principle of stationary action in order to provide alternative ways for students to think about the action that they may find more intuitive than the traditional approach. These methods involve Lagrange multiplier techniques and are, therefore, best suited for students who are encountering the stationary action principle for a second or third time, perhaps in an advanced undergraduate mathematical methods course or a graduate classical mechanics course. Editor's Note: Students of advanced dynamics encounter the principle of stationary action, wherein the time-integral of the Lagrangian L = T - U is extremized; T and U are the kinetic and potential energies of a system. At first glance, extremizing the difference between T and U may seem strange; the usual justification is that it works in the sense of being equivalent to Newton's second law. In this paper, the author offers two alternative approaches to the least-action principle: extremizing the time-averaged kinetic energy or the product of the time-averaged kinetic and potential energies. The stationary paths are established, and it is shown how these include the customary energy-conserving paths and how they can be isolated. The motivation is to offer instructors options for ''deriving'' the principle of stationary action. Appropriate for upper/graduate-level dynamics students. [ABSTRACT FROM AUTHOR]

Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points. It would seem that few methods can be useful in such diverse applications. However, we here present a flexible modeling tool for the limit of theories, soft inductive limits, constituting a generalization of inductive limits of Banach spaces. In this context, general criteria for the convergence of dynamics will be formulated, and these criteria will be shown to apply in the situations mentioned and more. [ABSTRACT FROM AUTHOR]

AbstractThe static and dynamic pull-in characteristics of electrostatically and piezo-electrically actuated microbeam are investigated. The static pull-in voltage is evaluated using analytical methods based on MCST, CCMT and validated through the use of FE based COMSOL multiphysics tools. The dynamic pull-in voltage obtained from numerical technique and verified with existing literature, lower than the static pull-in voltage. The piezoelectric patch has a significant influence on the pull-in voltage and an effect on the aspect ratio. Moreover, the pull-in band and instability zone of the microbeam with weak and hard forcing function have been investigated using multiple scale method. [ABSTRACT FROM AUTHOR]

Quantum mechanics emerged a century ago. It abandoned the deterministic worldview that underlies classical mechanics for a more general theoretical system. It is now believed that everything should be described by quantum mechanics. Furthermore, in our efforts to rethink the theoretical system for information processing based on the classical worldview within the framework of quantum mechanics, it has become clear that even information processing tasks that were previously considered intractable can now be performed within the framework of quantum mechanics. For this issue, we interviewed NTT Distinguished Researcher Koji Azuma, a leader in the field of quantum network research at NTT, about his current research and his mindset as a researcher. [ABSTRACT FROM AUTHOR]

We argue that it is adherence to the axiom of counterfactual definiteness and not to that of locality and realism that results in Bell inequality violations. Furthermore, this axiom is not supported in classical mechanics because of deeper implications that arise from the principle of stationary action. This means that the Bell inequality fails classically, effectively removing the classical-quantum boundary–a conclusion prophesized by Bell himself. An implication here is that a local hidden variable theory, in the configuration space of classical mechanics, may not be ruled out. Basing our idea on Jacobi's "initial variable" framework, we propose that a classical path of stationary action that recedes into the infinite past and stretches into an infinite future implies a reality that lacks counterfactual definiteness. We then corroborate this with recent experimental results, through which it could be understood that our world could be such a reality. [ABSTRACT FROM AUTHOR]

The freeze–thaw (FT) cycle will lead to rock damage and cause hidden danger to the safety of rock engineering. In order to explore the FT damage characteristics of rocks in cold regions, 0, 20, 30, 40 and 50 FT cycle tests and uniaxial compression tests were carried out on intact and single-fracture cyan specimens with crack inclination angle β of 0°, 45° and 90°, respectively, to study the FT damage problems of rocks from the aspects of physical, mechanical and energy characteristics. The results show that the FT damage of cyan sandstone specimens is mainly dominated by the mechanical action of water–ice phase transition, resulting in relatively little influence on the saturation weight. The porosity of the cyan sandstone specimen increases gradually with the increase of FT cycle, and it has an exponential function relationship with the peak strength, Hoek–Brown model parameter s and energy storage limit, which also implies their variation with the increase of FT cycle. Based on Lemaitre's strain equivalent hypothesis and energy dissipation principle, FT-stress damage models of intact and fractured rocks are established. It is found that the initial damage and critical damage are positively correlated with the number of FT cycles and negatively correlated with crack inclination angle. With initial damage as the characteristic parameter, a critical damage model for rocks subjected to FT cycles is proposed based on the test data and data obtained from existing references. In addition, a normalized degradation equation for the peak strength and energy storage limit of FT-damaged rocks under uniaxial compression is proposed based on classical damage mechanics and critical damage model, and its applicability is verified by test data and relevant data from references. In general, the results of this study can provide a reference for the study of FT damage of rocks in cold regions, and be conducive to clarifying the relationship between FT damage of rocks and the deterioration of mechanical properties and energy storage capacity. Highlights: The change of peak strength, apparent stiffness, Hoek Brown model parameter were discussed. The energy accumulation effect, energy storage limit, peak dissipated energy and energy dissipation effect were analyzed. A freeze–thaw-stress damage model for intact and fractured rocks was established, the concepts of initial and critical damage were introduced. The critical damage model of FT damaged rocks was obtained and discussed. The normalized degradation equations of peak strength and energy storage limit of FT damaged rocks are proposed. [ABSTRACT FROM AUTHOR]

Understanding degrees of freedom in classical mechanics is fundamental to characterizing physical systems. Counting them is usually easy, especially if we can assign them a clear meaning. However, the precise definition of a degree of freedom is not usually presented in first-year physics courses since it requires mathematical knowledge only learned in more advanced courses. In this paper, we use a pedagogical approach motivated by simple but non-trivial mechanical examples to define degrees of freedom and configuration spaces. We highlight the role that topology plays in understanding these ideas. Editor's Note Landau and Lifshitz defined a degree of freedom as "the number of independent quantities which must be specified in order to define uniquely the position of any system." Undergraduate physics students may find this concept obvious when a system is simple, such as a particle free to move in three dimensions, but struggle with the concept when faced with a more complex system, especially one with constraints. This paper shows how to present the concept of "degrees of freedom" in a mathematically rigorous but accessible way using examples like the coupled double pendulum. [ABSTRACT FROM AUTHOR]

This study aims to examine the effectiveness of Conceptual Problem Solving-based learning in improving student conceptual understanding of Newtonian mechanics. The quasi-experimental method with a nonrandomized control group pretest-posttest design was used to compare students conceptual in the experimental and control class. The subjects in this study were 69 first-year students of the Physics Education study program at one of the state universities in Yogyakarta. Force Concept inventories are used to assess students conceptual understanding of Newtonian mechanics. The findings revealed that there was significant difference in the increase in students conceptual understanding between the experimental and control groups. The increase in conceptual mismatch in experimental class students using CPS learning was higher (N-gain = 0.33) compared to control class students using direct instruction learning (N-gain = 0.11), although both groups experienced an increase. This study provides a real picture that the CPS technique can be used as a more successful strategy to improve the quality of physics learning, especially in improving knowledge of basic topics that are often difficult for students to understand, one of which is Newton's Law. [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 study the impact of nonextensive entropy on the thermodynamics of various black hole configurations, utilizing both Tsallis and Kaniadakis statistical frameworks. Additionally, we explore the stability of these black holes using the framework of nonextensivity. Our analysis reveals that the nonextensive Kaniadakis entropy does not result in any stability for the black holes. In contrast, the nonextensive Tsallis entropy ensures the stability of various black hole configurations. [ABSTRACT FROM AUTHOR]

Quantum and classical mechanics are fundamentally different theories, but the correspondence principle states that quantum particles behave classically in the appropriate limit. For high-energy periodic quantum systems, the emergence of the classical description should be understood in a distributional sense, i.e., the quantum probability density approaches the classical distribution when the former is coarse-grained. Following a simple reformulation of this limit in the Fourier space, in this paper, we investigate the macroscopic behavior of freely falling quantum particles. To illustrate how the method works and to fix some ideas, we first successfully apply it to the case of a particle in a box. Next, we show that, for a particle bouncing under the gravity field, in the limit of a high quantum number, the leading term of the quantum distribution corresponds to the exact classical distribution plus sub-leading corrections, which we interpret as quantum corrections at the macroscopic level. [ABSTRACT FROM AUTHOR]

Recent efforts to conceptually design a technologically meaningful electromagnetic retarded engine indicated that this can only be done using the immense charge and current densities which exist in the atomic scale. However, this scale cannot be described by Newtonian physics, and only a quantum description will suffice to describe the dynamics of an electron on this scale properly. Here we study the retarded field quantum engine and highlight the differences between the quantum and the classical retarded engines. It is emphasized that the constituents of the retarded engine studied in the current paper do not move in relativistic speeds, hence they are analyzed using un-relativistic classical mechanics and un-relativistic quantum mechanics (Schrödinger's equations). The retardation effect is due to the finite propagation speed of the field and not the relativistic motion of the particles. [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]

The given text discusses different approaches to finding equations of motion for physical systems, such as the Newtonian, Lagrangian, and Hamiltonian approaches. It presents a supplementary tool using the total differential of the mechanical energy function to obtain equations of motion for certain systems. The text also explores the relationship between this approach and Hamilton's equations of motion. Additionally, the text provides concise and factual information about different types of motion and their corresponding equations, making it a useful resource for library patrons conducting research on these topics. [Extracted from the article]

This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid, is to interpret the phase space function Q —a transform of the better known Wigner function—as a proper probability distribution, roughly analogous to the probability distribution ρ in classical statistical mechanics. Here I motivate the Q-based interpretation, investigate whether it is empirically adequate, and outline some of its key conceptual features. I argue that the Q-based interpretation is attractive in that it promises having no measurement problem, is conceptually parsimonious, and has the potential to apply elegantly to relativistic and field-theoretic contexts. [ABSTRACT FROM AUTHOR]

A possible way to increase the operating speed and field capacity of a cultivator-fertiliser is to modify its configuration scheme. According to our hypothesis, placing the fertiliser hopper directly on the tractor frame could reduce the traction resistance of the cultivator-fertiliser and consequently increase its operating speed and field capacity. Validating this hypothesis requires a comparative evaluation of the existing configuration schemes for cultivator-fertilisers. However, there are currently no such comprehensive studies available. This research aims to develop a mathematical model for conducting a comparative theoretical evaluation of various configuration schemes for cultivator-fertilisers. The development of this model incorporated principles from classical and agricultural mechanics. We developed a mathematical model and conducted a theoretical evaluation of existing configuration schemes for cultivator-fertilisers, such as mounting the hopper on a separate trailed chassis, mounting the hopper and tillage working bodies on one frame, and mounting the hopper directly on the tractor frame. The working width of the cultivator-fertiliser was constant and amounted to 6.2 m. The effective engine power of the tractor was taken to be 220 × 103 W. It was found that placing the fertiliser hopper on the tractor frame maximises the field capacity to 3.9 ha∙h−1. The increase in field capacity was 8.9–16.0%. In this case, the fertiliser hopper volume should be 1.89 m3 and travel speed 8.45 km∙h−1. [ABSTRACT FROM AUTHOR]

The phenomenon of peripheral rock instability is more common in crushed bedrock roadways, and the fundamental reason for this lies in the significantly different characteristics of its peripheral rock stress field. Taking the newly dug belt inclined shaft of PingDingShan TianAn Coal Co., Ltd. No. 6 Mine as the engineering background, a mechanical model of a broken perimeter rock roadway was established by using classical rock mechanics theory. Stress distribution around the roadway of the broken perimeter rock medium was systematically analyzed, and radial and tangential stress formulas of the broken perimeter rock were deduced. Through the formula calculation, it was deduced that there was a stress drop in the intact surrounding rock outside the disturbed zone, and the radial stress of the intact surrounding rock in its deep part was relatively increased, while the tangential stress was relatively decreased. The existence of crushed surrounding rock increased the minimum principal stress and decreased the maximum principal stress of the unfractured surrounding rock, which proves that a well-maintained disturbed zone can play a lining role. Thus, a "U-shaped steel + inverted arch + bottom arch linkage beam + floor bolt compensation" support program was proposed. This joint support program easily forms a closed support structure, which is more effective in controlling the deformation of tunnel perimeter rock. The support structure can effectively resist the deformation of the surrounding rock and enhance bottom drum resistance. Through numerical simulation, it was concluded that the horizontal displacement of the two gangs was reduced by 70%, and the displacement of the top and bottom plates was reduced by 77% after optimization of the support, which effectively controlled the stability of the broken surrounding rock. [ABSTRACT FROM AUTHOR]

Uncovering the mechanisms of physics is driving a new paradigm in artificial intelligence (AI) discovery. Today, physics has enabled us to understand the AI paradigm in a wide range of matter, energy, and space-time scales through data, knowledge, priors, and laws. At the same time, the AI paradigm also draws on and introduces the knowledge and laws of physics to promote its own development. Then this new paradigm of using physical science to inspire AI is the physical science of artificial intelligence (PhysicsScience4AI, PS4AI). Although AI has become the driving force for development in various fields, there is still a “black box” phenomenon that is difficult to explain in the field of AI deep learning. This article will briefly review the connection between relevant physics disciplines (classical mechanics, electromagnetism, statistical physics, quantum mechanics) and AI. It will focus on discussing the mechanisms of physics disciplines and how they inspire the AI deep learning paradigm, and briefly introduce some related work on how AI solves physics problems. PS4AI is a new research field. At the end of the article, we summarize the challenges facing the new physics-inspired AI paradigm and look forward to the next generation of artificial intelligence technology. This article aims to provide a brief review of research related to physics-inspired AI deep algorithms and to stimulate future research and exploration by elucidating recent advances in physics. [ABSTRACT FROM AUTHOR]

The pathways and timescales of vibrational energy flow in nitromethane are investigated in both gas and condensed phases using classical molecular mechanics, with a particular focus on relaxation in liquid water. We monitor the flow of excess energy deposited in vibrational modes of nitromethane into the surrounding solvent. A marked energy flux anisotropy is found when nitromethane is immersed in liquid water, with a preferential flow to those water molecules in contact to the nitro group. The factors that permit such anisotropic energy relaxation are discussed, along with the potential implications on the molecule's non-equilibrium dynamics. In addition, the energy flux analysis allows us to identify the solvent motions responsible for the uptake of solute energy, confirming the crucial role of water librations. Finally, we also show that no anisotropic vibrational energy relaxation occurs when nitromethane is surrounded by argon gas. [ABSTRACT FROM AUTHOR]

Newton's third law, action = reaction, is a foundational statement of classical mechanics. However, in natural and living systems, this law appears to be routinely violated for constituents interacting in a nonequilibrium environment. Here, we use computer simulations to explore the macroscopic phase behavior implications of breaking microscopic interaction reciprocity for a simple model system. We consider a binary mixture of attractive particles and introduce a parameter that is a continuous measure of the degree to which interaction reciprocity is broken. In the reciprocal limit, the species are indistinguishable, and the system phase separates into domains with distinct densities and identical compositions. Increasing nonreciprocity is found to drive the system to explore a rich assortment of phases, including phases with strong composition asymmetries and three-phase coexistence. Many of the states induced by these forces, including traveling crystals and liquids, have no equilibrium analogs. By mapping the complete phase diagram for this model system and characterizing these unique phases, our findings offer a concrete path forward toward understanding how nonreciprocity shapes the structures found in living systems and how this might be leveraged in the design of synthetic materials. [ABSTRACT FROM AUTHOR]

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]

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]

This review highlights the role of computational chemistry, specifically quantum and molecular mechanics, in the development of folate‐based anticancer drugs. Folate receptors (FRs) are overexpressed in cancerous cells, rendering these receptors a key focus in the design of targeted drug delivery systems. These computational tools are fundamental for analyzing drug–receptor interactions and overcoming the limitations of traditional drug development processes. A 10‐year literature survey demonstrated advancements in employing FRs for targeted cancer therapy. Key findings reveal that structural modifications to folate derivatives consistently enhance binding affinities and specificity toward FRα and FRβ. Computational methodologies predicted and analyzed molecular interactions, validated by experimental data. Functional groups play a crucial role in enhancing binding stability and interaction strength within FR binding pockets. Detailed structural insights into folate derivatives and antifolates interacting with FRs have identified critical residues involved in binding, aiding the design of targeted therapeutics. [ABSTRACT FROM AUTHOR]

People have long had a problem: the equations of motion that reflect the laws of physics are invariant under time inversion, while there always are irreversible processes for gases composed of microscopic particles. This article solves the problem. The point is that we should distinguish between the concepts of the equation of motion and concrete motion. We also need to distinguish between the concepts of time-inverse motion and reverse motion. The former is anticlockwise, which is a fictional motion, while the latter is clockwise. For the single-particle motions in classical mechanics and in quantum mechanics, we present mathematical expressions for time-inversion motion and reverse motion, respectively. We demonstrate that single-particle motion is irreversible. The definition of the reversibility of two-particle collisions is given. According to the definition, the two-particle collision as a microscopic motion process is irreversible. Consequently, for a gas consisting of a large number of particles colliding with each other, its movement should be irreversible, unless the condition of detailed balance is met. We provide a physical explanation for detailed balance, which does not concern the meaning of microscopic reversibility. The detailed balance means that after a pair of reciprocal collisions occur, the distribution function of the particles remains unchanged. Therefore, microscopic two-particle collision events are irreversible, but the statistical average of a large number of collision events makes it possible for the macroscopic process of a gas to be reversible. Conclusively, we clarify the microscopic mechanism of the irreversible process of gases. [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]

Impact peril for warm-blooded organisms produced by a sequence of ultra-wideband electromagnetic sub-nanosecond pulses, used in various scientific and technological applications, is assessed by calculation methods of radiophysics and classical mechanics. Threshold values of the sequence parameters whose long time excess can be perilous for human have been determined. [ABSTRACT FROM AUTHOR]

In a large body of rock-physics research, seismic wave velocity dispersion and attenuation in fluid-saturated porous rock are studied by constructing analytical or numerical models for time- or frequency-dependent dynamic (effective, or viscoelastic) moduli. A key and broadly used model of such kind is the Zener's, or the standard linear solid (SLS). This model is qualitatively successful in explaining many field and laboratory observations and serves as the key element of many generalizations such as the Burgers model for plastic deformations or the generalized SLS explaining band-limited or near-constant seismic attenuation. However, as a physical model of fluid-saturated porous rock, the SLS has several major limitations: disregard of inertial effects, absence of secondary wave modes and lack of key physical parameters such as porosity and Skempton coefficients. Grainy and porous rock is an unconsolidated material in which the effective density is frequency-dependent, and its effects on wave velocities may exceed those of the dynamic modulus. To overcome these limitations of the empirical SLS, we propose a rigorous rheologic model based on classical continuum mechanics and called the extended SLS, or eSLS. This rheology explains the available attenuation and dispersion observations equally well, but it is also close to Biot's model, honours all poroelastic relations, includes inertial effects, and reveals several new physical properties of the material. Detailed comparison of the eSLS and Biot's models gives a physical-mechanism-based classification of wave-induced fluid flow (WIFF) phenomena. In this classification, the so-called 'global-scale' flows occur in Biot's type structures within the material, whereas the 'local-scale' WIFF occurs in eSLS-type structures. Combining Biot's and eSLS models gives a broad class of rheologies for linear anelastic phenomena within rock with a single type of porosity. The model can be readily generalized to multiple porosities and different types of internal variables, such as describing squirt flows, wetting or thermoelastic effects. Modelling is conducted with relatively little effort, using a single matrix equation similar to a mechanical form of the standard SLS. By combining the eSLS and Biot's models, observations of dynamic-modulus dispersion and attenuation can be inverted for macroscopic mechanical properties of porous materials. [ABSTRACT FROM AUTHOR]

Reduced mass value and vector are well known for the two-body problem, but the many-body reduced vector problem is not solved yet. The study of many-body problems and their applications (such as vibrational spectroscopy) is one of the more important physical problems. Vibrational spectroscopy provides a powerful tool to perceive the molecular structures and atom motions of molecules. The water molecule is a threebody system stretching vibration that has been previously quantized; their frequencies were defined and showed the infrared (IR) absorption spectrum based on Morse potential. In this work, the reduced mass of the many-body problem is being solved and then used to study the intensity of the stretching vibration modes and show the ratio is in agreement with experiments. The molecule was studied in classical and quantum mechanics to determine its absorption intensity as an example of a reduced mass problem. The results show molecular atomic motions and changes in dipole and reduced mass vector. A Morse-like model for bending was predicted based on the spectroscopic vibration frequency and intensity, defining the bending potential depth of 93.5 kJ/mol. [ABSTRACT FROM AUTHOR]

Background: In a previous work, the problem of identifying residual stresses through relaxation methods was demonstrated to be mathematically ill-posed. In practice, it means that the solution process is affected by a bias-variance tradeoff, where some theoretically uncomputable bias has to be introduced in order to obtain a solution with a manageable signal-to-noise ratio. Objective: As a consequence, an important question arises: how can the solution uncertainty be quantified if a part of it is inaccessible? Additional physical knowledge could—in theory—provide a characterization of bias, but this process is practically impossible with presently available techniques. Methods: A brief review of biases in established methods is provided, showing that ruling them out would require a piece of knowledge that is never available in practice. Then, the concept of average stresses over a distance is introduced, and it is shown that finding them generates a well-posed problem. A numerical example illustrates the theoretical discussion Results: Since finding average stresses is a well-posed problem, the bias-variance tradeoff disappears. The uncertainties of the results can be estimated with the usual methods, and exact confidence intervals can be obtained. Conclusions: On a broader scope, we argue that residual stresses and relaxation methods expose the limits of the concept of point-wise stress values, which instead works almost flawlessly when a natural unstressed state can be assumed, as in classical continuum mechanics (for instance, in the theory of elasticity). As a consequence, we are forced to focus on the effects of stress rather than on its point-wise evaluation. [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]

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]

We study the Poisson geometrical formulation of quantum mechanics for finite dimensional mixed and pure states. Equivalently, we show that quantum mechanics can be understood in the language of classical mechanics. We review the symplectic structure of the Hilbert space and identify its canonical coordinates. We extend the geometric picture to the space of density matrices D N + . We find it is not symplectic but admits a linear s u (N) Poisson structure. We identify Casimir surfaces of D N + and show that the space of pure states P N ≡ C P N − 1 is one of its symplectic submanifolds which is an intersection of primitive Casimirs. We identify generic symplectic submanifolds of D N + and calculate their dimensions. We find that D N + is singularly foliated by the symplectic leaves of varying dimensions, also known as coadjoint orbits. We also find an ascending chain of Poisson submanifolds D N M ⊂ D N M + 1 for 1 ≤ M ≤ N − 1. Each such Poisson submanifold D N M is obtained by tracing out the C M states from the bipartite system C N × C M and is an intersection of N − M primitive Casimirs of D N + . Their Poisson structure is induced from the symplectic structure of the bipartite system. We also show their foliations. Finally, we study the positive semi-definite geometry of the symplectic submanifold E N M consisting of the mixed states with maximum entropy in D N M . [ABSTRACT FROM AUTHOR]

Determining the causality in electromagnetism is more difficult than determining the causality in classical mechanics. Newton's second law and the laws of Faraday and of Ampere are very different in character. Whereas Newton's second law holds for a point in space, the laws of Faraday and of Ampere hold for a region in space. The ultimate aim of this article is to delve into the correct mechanism of propagation of electromagnetic waves. And, in this article, we investigate the wrong reasoning of other authors. It is concluded that an electric field neither generates nor induces a magnetic field and a magnetic field neither generates nor induces an electric field. [ABSTRACT FROM AUTHOR]

To harvest the full potential of the peridynamic approach, the state‐of‐the‐art material models should be usable without redeveloping or reimplementing them from classical continuum mechanics theory. User materials (UMAT) in finite element codes allow the researchers or engineers to apply their own material routines. Simple interfaces are specified to allow the utilization of material behaviors in software. In order to use these already existing and often validated models with Peridynamics, a UMAT interface is presented. It allows the simplified use of already existing material routines in the peridynamic framework Peridigm. The interface is based on the finite element (FE) software Abaqus UMAT definition and allows the integration of Fortran routines directly into Peridigm. In addition, the same material model implementations are applicable in finite element applications as well as peridynamic simulations. In the presentation, the interface is presented and various material models are utilized and compared between Peridynamics and FE methods. The effect of the horizon and nonlocal boundaries are analyzed and discussed. [ABSTRACT FROM AUTHOR]

When the elastic‐brittle cracked body is subjected to compressive‐shear loading, not only does the phenomenon of wing crack initiation and propagation occur, but there is also a notable incidence of secondary crack initiation and propagation due to shear stress. Moreover, the shear fracture toughness (KIIc) predicted by the fracture criterion in the framework of classical fracture mechanics is usually smaller than the tensile fracture toughness (KIc), which is inconsistent with the actual observations. Therefore, this research firstly establishes a mechanical model of an elastic‐brittle cracked body under biaxial compression considering three kinds of crack parameters and materials' mechanical properties. Then, the stress field characteristics at the crack tip are analyzed. Next, a compression‐shear mixed fracture criterion is proposed. Finally, the effects of the lateral pressure coefficient (λ), critical plastic zone size (rc), friction coefficient (f), and deformation parameters of the crack surface on the failure modes at the crack tip are investigated. Highlights: A distinction is made between the failure and loading modes of the cracked rock mass.The stress field at the crack tip under compression and shear conditions is analyzed.A compression‐shear fracture criterion related to KIc and KIIc of materials is proposed.Conditions for the occurrence of shear failure at the crack tip are discussed. [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]

A combinatorial approach has been applied to the allowable permutations of quantum electronic configurations under the constraints of Hund's rule for established ground state configurations toward an under-approximation of electronic structure entropy. Combined with a previously reported over-approximation, the approximations are used in conjunction in an attempt to bracket the upper and lower entropy limits for multiconfigurational ground state electronic structure entropy and compared to known standard molar entropies for the elements. This formality has been used for the application of a classical statistical mechanics methodology to be applied to the discrete sets of quantum mechanical states of Pu in order to calculate orbital occupancies in Pu's multiconfigurational ground state. Without consideration of the relative energies of various possible electronic configurations contributing to the multiconfigurational ground state, the calculations are performed under a general energy degeneracy assumption weighted to the number of permutations for specific configurations. The number of configurations assumed to significantly contribute is gradually constrained in order to approach a low-order approximation of orbital occupancies in Pu that are then compared to experimental and other calculated results from the literature. [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]