Classical Mechanical Model Research Articles

The retarding effect of glacier degradation on the Earth’s rotation

IntroductionThe massive loss of global glacier mass caused by climate problems has caused concern, while the Earth’s rotation as the most significant form of motion has also been subtly affected. However, the quantitative effects of massive glaciers losing mass on Earth’s rotation have not been revealed.MethodsHerein, the knowledge of moment of inertia and suitable rotational inertia models in classical mechanics is initially utilized to assess the effect of quantitative glaciers losing mass on Earth's rotation.ResultsAfter specific calculations, the putative 200 billion tons of glaciers losing mass bring on an increase of 1.4099×10-4s in Earth’s rotation time in 365 days.DiscussionThis work examines the connection between glaciers losing mass and Earth’s rotation from classical mechanics, thus providing the way for investigations of relationship between climate changes and Earth.

Zhukovsky-Volterra top and quantisation ideals

In this letter, we revisit the quantisation problem for a fundamental model of classical mechanics—the Zhukovsky-Volterra top. We have discovered a four-parametric pencil of compatible Poisson brackets, comprising two quadratic and two linear Poisson brackets. Using the quantisation ideal method, we have identified two distinct quantisations of the Zhukovsky-Volterra top. The first type corresponds to the universal enveloping algebras of so(3), leading to Lie-Poisson brackets in the classical limit. The second type can be regarded as a quantisation of the four-parametric inhomogeneous quadratic Poisson pencil. We discuss the relationships between the quantisations obtained in our paper, Sklyanin's quantisation of the Euler top, and Levin-Olshanetsky-Zotov's quantisation of the Zhukovsky-Volterra top.

Multi-time-step coupling of peridynamics and classical continuum mechanics for dynamic brittle fracture

Peridynamics (PD), as a nonlocal theory, is well-suited for solving problems with discontinuities, such as cracks. However, the nonlocal effect of peridynamics makes it computationally expensive for dynamic fracture problems in large-scale engineering applications. As an alternative, this study proposes a multi-time-step (MTS) coupling model of PD and classical continuum mechanics (CCM) based on the Arlequin framework. Peridynamics is applied to the fracture domain of the structure, while continuum mechanics is applied to the rest of the structure. The MTS method enables the peridynamic model to be solved at a small time step and the continuum mechanical model is solved at a larger time step. Consequently, higher computational efficiency is achieved for the fracture domain of the structure while ensuring computational accuracy, and this coupling method can be easily applied to large-scale engineering fracture problems.

Strength-induced Peridynamic model for the dynamic failure of porous materials

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.

Classical and Quantum Mechanical Models of Many-Particle Systems

The workshop focused on the collective behavior of many-particle systems in various application fields: physics (gas dynamics, plasmas, quantum mechanics), mathematical biology (cell mobility, evolution of trait-structured species), and social sciences (wealth distribution). This includes famous models such as the Boltzmann equation of gas dynamics, Vlasov equation for plasmas, Fokker–Planck equations, Smoluchowski and related equations, Keller–Segel system of chemotaxis.

Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage

Demonstrating quantum advantage requires experimental implementation of a computational task that is hard to achieve using state-of-the-art classical systems. One approach is to perform sampling from a probability distribution associated with a certain class of highly entangled many-body wave functions. It has been suggested that such a quantum advantage can be certified with the (XEB). We critically examine this notion. First, we consider a “benign” setting, where an honest implementation of a noisy quantum circuit is assumed, and characterize the conditions under which the XEB approximates the of quantum dynamics. Second, we assume an “adversarial” setting, where all possible classical algorithms are considered for comparisons, and show that achieving relatively high XEB values does not imply faithful simulation of quantum dynamics. Specifically, we present an efficient classical algorithm that achieves high XEB values, namely 5–12% of those obtained in the state-of-the-art experiments, within just a few seconds using a single GPU machine. This is made possible by identifying and exploiting several vulnerabilities of the XEB, which allows us to achieve high XEB values without simulating a full quantum circuit. Remarkably, our algorithm features with the system size than a noisy quantum device for commonly studied random circuit ensembles in various architecture. We quantitatively explain the success of our algorithm and the limitations of the XEB by using a theoretical framework, in which the dynamics of the average XEB and fidelity are mapped to classical statistical mechanics models. Using this framework, we illustrate the relation between the XEB and the fidelity for quantum circuits in various architectures, with different choices of gate sets, and in the presence of noise. Taken together, our results demonstrate that XEB’s utility as a proxy for fidelity hinges on several conditions, which should be independently checked in the benign setting, but cannot be assumed in the general adversarial setting. Therefore, the XEB on its own has a limited utility as a benchmark for quantum advantage. We briefly discuss potential ways to overcome these limitations. Published by the American Physical Society 2024

Energies of Mechanical Fractional-Order Elements: Causal Concept and Kernel Effects

The energies of the classical Maxwell mechanical model of viscoelastic behavior have been studied as a template with a variety of relaxation kernels in light of a causal formulation of the force–displacement relationship. The starting point uses the Lorenzo–Hartley model with the time-fractional Riemann–Liouville derivative. This approach has been reformulated based on critical analysis, allowing for the application of a variety of relaxation (memory) functions mainly based on the Mittag-Leffler family, in order to meet the need for broader modeling of viscoelastic behavior. The examples provided include cases of the types of forces used by Lorenzo and Hartley as well as a new family of force approximations such as a general power-law ramp, polynomials, and the Prony series.

Sedimentation-Based Separation and Purification of Solid Industrial Waste: A Case Study of Phosphogpusym.

The continuous accumulation of solid industry waste, such as phosphogypsum, has emerged as a global environmental hazard and a significant obstacle to achieving a green and sustainable industry. To convert this industry waste to reusable resources, the development and implementation of simple and cost-efficient purification techniques is crucial. A sedimentation-based separation approach was developed to achieve this objective. Through a sedimentation process, a suspension of phosphogypsum particles is transformed into three distinct phases: a supernatant liquid, a concentrated slurry, and a solid precipitate. These phases primarily consist of soluble salts, a mixture of oxides and organic matter, and calcium phosphate dihydrates mixed with calcium phosphate, respectively. Through a sedimentation process, calcium sulfate dihydrate concentration can be significantly enhanced from 87.45 to 91.60% and further improved to 95.72% by repeating the sedimentation process three times. The various components obtained from this process can be effectively reused as mineral resources, soil amendment, and industry gypsum. The sedimentation process is expounded upon using both the classical mechanics model and Stokes' law. To foster a seamless industrial application, we have also designed a continuous settling skittle and a trail setup for industrial treatment of phosphogpysum. This innovative technique holds immense promise for its broader application, especially within but not limited to the phosphoric acid industry.

Integrable Quantum Circuits from the Star-Triangle Relation

The star-triangle relation plays an important role in the realm of exactly solvable models, offering exact results for classical two-dimensional statistical mechanical models. In this article, we construct integrable quantum circuits using the star-triangle relation. Our construction relies on families of mutually commuting two-parameter transfer matrices for statistical mechanical models solved by the star-triangle relation, and differs from previously known constructions based on Yang-Baxter integrable vertex models. At special value of the spectral parameter, the transfer matrices are mapped into integrable quantum circuits, for which infinite families of local conserved charges can be derived. We demonstrate the construction by giving two examples of circuits acting on a chain of Q−state qudits: Q-state Potts circuits, whose integrability has been conjectured recently by Lotkov et al., and ZQ circuits, which are novel to our knowledge. In the first example, we present for Q=3 a connection to the Zamolodchikov-Fateev 19-vertex model.

Element‐based coupling modeling of peridynamics and classical continuum mechanics for dynamic brittle fracture

AbstractIn this work, the hybrid peridynamic and classical continuum mechanical model based on the element‐type numerical discretization is used to study the dynamic fracture problem of brittle materials. The weak form of the motion equation for the hybrid model is derived by applying Hamilton's principle. An element‐based spatial discretization scheme is set up using the peridynamics‐based finite element method (PeriFEM) (Han and Li). The ‐convergence and m‐convergence of the hybrid model are analyzed to verify the numerical convergence and the mesh dependency. The influence of the area of the peridynamic model subdomain and the hybrid model subdomain on the calculation efficiency and accuracy is discussed. And the relationship between the crack propagation speed and the crack branching phenomenon is also investigated. Good agreements are obtained by comparing the crack path and the crack speed profile predicted by the hybrid model with those in the literature. Numerical results verify the ability and efficiency of the hybrid model for dynamic fracture problem.

Coherent Vibrational Dynamics of Au144(SC8H9)60 Nanoclusters.

The coherent vibrational dynamics of Au144(SC8H9)60, obtained from femtosecond time-resolved transient absorption spectroscopy, are described. Two acoustic modes were identified and assigned, including 2.0 THz breathing and 0.7 THz quadrupolar vibrations. These assignments are consistent with predictions using classical mechanics models, indicating that bulk models accurately describe the vibrational properties of Au144(SC8H9)60. Coherent phonon signals were persistent for up to 3 ps, indicating energy dissipation by the nanocluster was the primary dephasing channel. The initial excitation phases of the breathing and quadrupolar modes were π-phase-shifted, reflecting differences in the displacive nuclear motion of the vibrations. The combined agreement of the vibrational frequencies, relative phases, and decoherence times supported predictions based on classical models. The vibrational frequencies were insensitive to silver substitution for gold but did show increased inhomogeneous damping of the coherent phonons. The ability to predict the vibrational properties of metal nanoclusters can have an impact on nanoresonator and mass sensing technologies.

Microscopic double-chain sawtooth model and macroscopic four-parameter fractional-order derivative viscoelastic model based on magnetorheological elastomers

In order to restore the distribution of ferromagnetic particles in magneto-rheological elastomers to the greatest extent, the magnetotropic effect of magneto-rheological elastomers is more accurately represented, and the dynamic mechanical properties of magneto-rheological elastomers are more accurately reflected. In this paper, based on the dipole theory, a new microscopic model of magnetorheological elastomer, the double chain sawtooth model, is proposed based on the chain model and the main chain adsorption model, and a macroscopic viscoelastic mechanical model of magnetorheological elastomer, the four-parameter fractional order derivative improvement model, is proposed based on the classical macroscopic mechanical parametric model and the fractional order derivative model. A microscopic model of magnetorheological elastomer was combined with a macroscopic model to describe its mechanical properties. Isotropic and anisotropic magnetorheological elastomers with different mass fractions and different silicone oil contents were prepared using silicone rubber as the matrix and carbonyl iron powder as the filling phase, and dynamic shear tests were conducted to verify the validity of the model.

Research on the dynamic evolution law of fissures in shallow-buried and short-distance coal seam mining in Lijiahao Coal Mine

Aiming at the problem of spontaneous combustion of coal relics caused by the overburden fracture network penetrating the upper and lower coal seams in the process of shallow-buried and short-distance coal seam mining, the 31114 working face of Lijiahao coal mine was used as the research background to study the characteristics of overburden transport and fracture development in shallow-buried and short-distance coal seam mining by using physical similar simulation test; the fractal dimension and image processing techniques were used to quantify the overburden fractures; the classical mechanical models of "solid support beam" and "masonry beam" were combined to analyze the causes of fracture dynamic evolution. The results show that: (1) Before the key seam fracture, the stress in the upper rock seam only changes in a small amount, and the stress in the lower rock seam evolves similarly to the single coal seam mining; when the key seam fracture is broken, the stress in the upper and lower rock seams will change by jumps. (2) The fractal dimension of the fissures rised from 1.4 to 1.5, the total area of fissures is increased from 16,638 pixels to 17,707 pixels, and the total length is increased from 2217 to 3071 pixels; after the main key layer of the overlying rock is broken, the fractal dimension of the fissures is reduced from 1.56 to 1.5, and the total area of fissures is reduced from 31,451 pixels to 29,089 pixels, the total length has increased from 5657 to 6619 pixels. (3) Before the key layer between the coal seams is broken, it will be suspended to form a "fixed beam". After the first break, the broken rock above it will settle synchronously until the rock blocks form a hinged structure and then collapse. After the fall stops, the key layer periodically breaks to form a "masonry beam" structure, and the overlying stratum settles synchronously.

Fragmentation dynamics of tetrachloromethane molecule induced by highly charged Ar7+-ion impact.

The ion impact multiple ionization and subsequent dissociation of CCl4 is studied using a beam of Ar7+ ion having the energy of about 1MeV in a linear time- of-flight mass spectrometer, coupled with a position-sensitive detector. The complete, as well as incomplete Coulomb explosion pathways, for CCl4 2+ and CCl4 3+ ions are identified and studied. The kinetic energy release distributions of channels, kinetic energies, and momentum distributions of fragmented ions, as well as neutrals, are also calculated. Possible modes of fragmentation pathways, i.e., concerted and/or sequential, for all the identified channels are studied using Newton diagrams, Dalitz plots, and kinetic energy distributions. The dynamical information and fragmentation pathways were analyzed with the Dalitz plot and Newton diagram for the three-body dissociation channel. The nature of the fragmentation process is further investigated with simulated Dalitz plots and Newton diagrams using the simple classical mechanical model.

Coacervation and adhesion mechanism of PEI/TA hydrogel revealed by molecular dynamics simulations.

Coacervate-derived polyethyleneimine (PEI)/thioctic acid (TA) hydrogels can efficiently repel interfacial water and achieve robust underwater adhesion on diverse substrates, thus representing a promising material for a wide range of biomedical uses such as wound dressings, hemostatic agents, drug carriers, and tissue repair. Understanding the cohesion and adhesion dynamics in this coacervate-to-hydrogel strategy is critical for the development of underwater bioadhesive. However, these mechanisms remain obscure due to the difficulty of obtaining the atomic details. In this work, we first applied quantum calculations and classical mechanics models to obtain accurate force field parameters for PEI and TA. Based on the refined force field, we employed microsecond-long all-atom molecular dynamics (MD) simulations to investigate the coacervation of PEI/TA complex and its adhesion on glass and polypropylene. Our simulations revealed that the phase transition in PEI/TA coacervation was jointly achieved by two types of aggregation, i.e., TA-TA aggregation through hydrophobic associations and PEI-TA aggregation driven by electrostatic interactions. In addition, MD simulations further depicted the distinct adhesion modes of PEI/TA on the two substrates. TA assembled on top of the hydrophobic polypropylene substrate, replacing the interfacial water, whereas PEI amines penetrated the interfacial water to directly bind to the silanols of the hydrophilic glass substrate. The tight adhesion of PEI/TA hydrogel was then quantified by the diffusion coefficient of molecular moieties, which reflected the extremely low mobility of the bound moieties. These findings deepen our understanding of the formation and adhesion of PEI/TA hydrogel at the atomic level and provide guidance for the future design of advanced bioadhesive for potential clinical applications.

Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with U(1) symmetry

We study a ($1+1$)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements, both of which conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling behaviors akin to Tomonaga-Luttinger-liquid theory for equilibrium critical quantum systems with $U(1)$ symmetry, such as logarithmic scaling of bipartite charge fluctuation, power-law decay of charge correlation functions, and logarithmic scaling of charge-resolved entanglement whose coefficient becomes a universal quadratic function in a flux parameter. These critical features, however, do not persist below the transition, in contrast to a recent prediction based on replica field theory and mapping to a classical statistical mechanical model.

Simulation of polymeric mixed ionic and electronic conductors with a combined classical and quantum mechanical model.

In organic polymeric materials with mixed ionic and electronic conduction (OMIEC), the excess charge in doped polymers is very mobile and the dynamics of the polymer chain cannot be accurately described with a model including only fixed point charges. Ions and polymer are comparatively slower and a methodology to capture the correlated motions of excess charge and ions is currently unavailable. Considering a prototypical interface encountered in this type of materials, we constructed a scheme based on the combination of MD and QM/MM to evaluate the classical dynamics of polymer, water and ions, while allowing the excess charge of the polymer chains to rearrange following the external electrostatic potential. We find that the location of the excess charge varies substantially between chains. The excess charge changes across multiple timescales as a result of fast structural fluctuations and slow rearrangement of the polymeric chains. Our results indicate that such effects are likely important to describe the phenomenology of OMIEC, but additional features should be added to the model to enable the study of processes such as electrochemical doping.

Studies on the Performance of Equal Strength Cantilever Beam-Based FBG Acceleration Sensors

Based on the principle of FBG sensing and classical mechanics model of acceleration,the fundamental frequency and acceleration sensitivity coefficient of the fiber Bragg grating (FBG) acceleration sensor are theoretically analyzed in this study. An equal strength cantilever beam-based FBG acceleration sensor was designed based on the vibration frequency of conventional bridges and carried out experimental research. The results show that the fundamental frequency of the sensor increases when the cantilever beam thickness increases, while the sensitivity coefficient decreases. However, when the block mass increased, the fundamental frequency decreased in contrast to an elevated sensitivity coefficient. The experimental findings were found to be in line with the theoretical hypothesis. The sensors had good signal response performance and anti-transverse interference performance. In order to solve the problem of low sensitivity coefficient of sensor, the sensor was optimized and tested following the plane section assumption principle of classical mechanics. The result shows that the fundamental frequency of the optimized sensor remains unchanged, the sensitivity coefficient is increased by 2.6 times. The research provided an FBG acceleration sensor with suitable fundamental frequency, high sensitivity and other excellent performance for bridge monitoring.

Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge

There has been much recent progress on exotic surface critical behavior, yet the classical-quantum correspondence of special and extraordinary-log criticality remains largely unclear. Employing worm Monte Carlo simulations, we explore the surface criticality at an emergent superfluid-Mott insulator critical point in the Villain representation, which is believed to connect classical and quantum O(2) critical systems. We observe a special transition with the thermal and magnetic renormalization exponents $y_t=0.58(1)$ and $y_h=1.690(1)$ respectively, which are close to recent estimates from models with discrete spin variables. The existence of extraordinary-log universality is evidenced by the critical exponent $\hat{q}=0.58(2)$ from two-point correlation and the renormalization-group parameter $\alpha=0.28(1)$ from superfluid stiffness, which obey the scaling relation of extraordinary-log critical theory and recover the logarithmic finite-size scaling of critical superfluid stiffness in open-edge quantum Bose-Hubbard model. Our results bridge recent observations of surface critical behavior in the classical statistical mechanical models [Parisen Toldin, Phys. Rev. Lett. 126, 135701 (2021); Hu $et$ $al.$, $ibid.$ 127, 120603 (2021); Parisen Toldin $et$ $al.$, $ibid.$ 128, 215701 (2022)] and the open-edge quantum Bose-Hubbard model [Sun $et$ $al.$, Phys. Rev. B 106, 224502 (2022)].

JAX-ReaxFF: A Gradient-Based Framework for Fast Optimization of Reactive Force Fields.

The reactive force field (ReaxFF) model bridges the gap between traditional classical models and quantum mechanical (QM) models by incorporating dynamic bonding and polarizability. To achieve realistic simulations using ReaxFF, model parameters must be optimized against high fidelity training data which typically come from QM calculations. Existing parameter optimization methods for ReaxFF consist of black box techniques using genetic algorithms or Monte Carlo methods. Due to the stochastic behavior of these methods, the optimization process oftentimes requires millions of error evaluations for complex parameter fitting tasks, thereby significantly hampering the rapid development of high quality parameter sets. Rapid optimization of the parameters is essential for developing and refining Reax force fields because producing a force field which exhibits empirical accuracy in terms of dynamics typically requires multiple refinements to the training data as well as to the parameters under optimization. In this work, we present JAX-ReaxFF, a novel software tool that leverages modern machine learning infrastructure to enable fast optimization of ReaxFF parameters. By calculating gradients of the loss function using the JAX library, JAX-ReaxFF utilizes highly effective local optimization methods that are initiated from multiple guesses in the high dimensional optimization space to obtain high quality results. Leveraging the architectural portability of the JAX framework, JAX-ReaxFF can execute efficiently on multicore CPUs, graphics processing units (GPUs), or even tensor processing units (TPUs). As a result of using the gradient information and modern hardware accelerators, we are able to decrease ReaxFF parameter optimization time from days to mere minutes. Furthermore, the JAX-ReaxFF framework can also serve as a sandbox environment for domain scientists to explore customizing the ReaxFF functional form for more accurate modeling.