Periodic Boundary Research Articles

Simple model for the fracture of a polymer chain: Single-bond potential of mean force and tension-based rate constants for chain rupture.

A linear chain of N particles connected by Morse bonds with periodic boundaries in a Brownian bath is considered as a model for polymer fracture. The potential of mean force (pomf) with respect to the length of a bond and its energy and entropic components are computed via Langevin Dynamics simulations at various chain elongations λ > 1. A narrow range of λ values is identified over which equilibrium is established between an intact (i) and a fractured (f) state over a pomf barrier. While the barrier and (f) regions of the pomf are well described by a well-known (N - 1)-bond adiabatic approximation, the shape of the (i) region departs from it, exhibiting a bimodal character. A new, 1-bond adiabatic approximation is proposed to explain this. The lower envelope of the two adiabatic approximations provides an excellent description of the pomf. The relationship between (f) states for individual bonds and for the entire chain is elucidated. A new approach, based on analysis of equilibrium tension autocorrelation functions, is developed to extract rate constants for the fracture and reformation of the chain in dependence of λ. Results from it agree with tension relaxation during nonequilibrium simulations initiated at equispaced configurations of the particles. Rate constants for chain fracture conform to a Boltzmann-Arrhenius-Zhurkov dependence on the tension averaged over the intact state of the chain, the activation length being higher than estimated from pomf extrema. These findings constitute a step toward a predictive multiscale simulation scheme for fracture in polymeric materials.

Experimental study on enhancing pedestrian efficiency and crowd safety with regular sound under open boundaries

Abstract We empirically investigated the impact of regular sound on planar pedestrian movement in open boundary environments, a rarely studied topic. Participants walked to regular sound with different tempos (70 BPM vs. 100 BPM) and types (monotone vs. periodic ‘tick-tack’ rhythm). We found that regular sounds at 100 BPM, close to the normal walking pace, improve pedestrian efficiency. They reduce passing time by 8.41% and increase average flow by 9.50%. This efficiency enhancement is lower compared to single-file experiment with periodic boundaries, where reaching a high-density jammed phase is easier. Additionally, this efficiency enhancement from sound is reduced by unstable step synchronization under open boundaries and turning behavior. Regular sound significantly improves crowd safety in turning areas, where congestion levels (Cls) and crowd danger (Cd) are highest. Cls decrease by 8.27% with the 100 BPM monotone, and Cd decreases by 19.1% with the 100 BPM periodic rhythm. Operationally, regular sounds at 100 BPM can be used to guide pedestrian flow smoothly and effectively in crowd management.

Research on compressor cascade flow field modeling method based on finite volume flux-informed neural network

For compressor cascade flow field modeling, there exists strong velocity shear in the leading edge separation flow, boundary layer, and wake, which leads to increased modeling errors. To improve the accuracy of the flow field modeling method, this paper introduces the concept of numerical flux from the finite volume method into the loss function to implement Euler equation physics-informed learning, and a finite volume flux-informed neural network (FVFI-net) is constructed. Selecting a high-load, large-turning-angle compressor cascade as the study object, a comparative analysis is conducted on the advantages and disadvantages of purely data-driven, weak physical constraint, and finite volume flux-informed methods in compressor cascade flow field modeling. The study found that compared to purely data-driven and weak physical constraint methods, FVFI-net can reduce the average error of aerodynamic parameters in the flow field by approximately 45.6% and 29.5%, respectively, at a 0° angle of attack. For the flow separation problem occurring at the suction side leading edge and the blade wake area caused by a 5° angle of attack, FVFI-net can effectively reduce modeling errors near the leading edge, in the wake region, and near the periodic boundaries, thus reducing the average error of the aerodynamic parameters of the flow field by about 49.2%and 31.3%, respectively, compared to pure data-driven and weak physical constraint methods.

Electrostatic Waves and Electron Holes in Simulations of Low-Mach Quasi-perpendicular Shocks

Collisionless low-Mach-number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave–particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic (v sh ≈ (5500–22000) km s−1) low-Mach-number shocks, with a specific focus on studying electrostatic waves in the shock ramp and precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counterstreaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that the EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities (v sh ≈ 300 km s−1), the ESW wavelength is reduced to one-tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations.

Investigation on the width-to-depth ratio effect on turbulent flows in a sharp meandering channel with periodic boundaries using large eddy simulations

Investigation on the width-to-depth ratio effect on turbulent flows in a sharp meandering channel with periodic boundaries using large eddy simulations

Stability analysis of a stochastic port-Hamiltonian car-following model

Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model class is a generalisation of classical car-following approaches, including the optimal velocity model of Bando et al (1995 Phys. Rev. E 51 1035), the full velocity difference model of Jiang et al (2001 Phys. Rev. E 64 017101), and recent stochastic following models based on the Ornstein–Uhlenbeck process. In contrast to traditional models where the interaction is totally asymmetric (i.e. depending only on the speed and distance to the predecessor), the port-Hamiltonian car-following model also depends on the distance to the follower. We determine the exact stability condition of the finite system with N vehicles and periodic boundaries. The stable system is ergodic with a unique Gaussian invariant measure. Other properties of the model are studied using numerical simulation. It turns out that the Hamiltonian component improves the flow stability and reduces the total energy in the system. Furthermore, it prevents the problematic formation of stop-and-go waves with oscillatory dynamics, even in the presence of stochastic perturbations.

Contribution to micromechanical modeling of the shear wave propagation in a sand deposit

The object of study is the vertical wave propagation in a sand deposit. This paper is aimed at analyzing the vertical wave propagation in a sand deposit through micromechanical modeling that inherently takes account of intergranular slips during deformation. Such a problem, which is part of the general framework of wave propagation in the soil, has long been analyzed using continuum models based on approximate behavior laws. For this purpose, a 2D Discrete Element Method (DEM) model is developed. The DEM model is based on molecular dynamics with the use of circular shaped elements. The intergranular normal forces at contacts are calculated through a linear viscoelastic law while the tangential forces are calculated through a perfectly plastic viscoelastic model. A model of rolling friction is incorporated in order to account for the damping of the grains rolling motion. Different boundary conditions of the profile have been implemented; a bedrock at the base, a free surface at the top and periodic boundaries in the horizontal direction. The sand deposit is subjected to a harmonic excitation at the base. Using this model, the fundamental and resonance frequencies of the deposit are first determined. The former is determined from the low-amplitude free vibration and the latter by performing a variable-frequency excitation test. It is noted that there is a significant gap between the two frequencies, this gap could be attributed to the degradation of the soil shear modulus in the vicinity of the resonance. Such degradation is well proven in classical soil dynamics. The effects of deposit height and confinement on resonance frequency and free-surface dynamic amplification factor are then investigated. The obtained results highlighted that the resonance frequency is inversely proportional to the deposit’s thickness whereas the dynamic amplification factor Rd increases with the deposit’s thickness. In the other hand, when the confinement increases the deposit becomes stiffer, which results in reducing the amplification. Such result is in accordance with theoretical knowledge which states that the most rigid profiles such as rocks do not amplify seismic movement.

Software Infrastructure for Next-Generation QM/MM-ΔMLP Force Fields.

We present software infrastructure for the design and testing of new quantum mechanical/molecular mechanical and machine-learning potential (QM/MM-ΔMLP) force fields for a wide range of applications. The software integrates Amber's molecular dynamics simulation capabilities with fast, approximate quantum models in the xtb package and machine-learning potential corrections in DeePMD-kit. The xtb package implements the recently developed density-functional tight-binding QM models with multipolar electrostatics and density-dependent dispersion (GFN2-xTB), and the interface with Amber enables their use in periodic boundary QM/MM simulations with linear-scaling QM/MM particle-mesh Ewald electrostatics. The accuracy of the semiempirical models is enhanced by including machine-learning correction potentials (ΔMLPs) enabled through an interface with the DeePMD-kit software. The goal of this paper is to present and validate the implementation of this software infrastructure in molecular dynamics and free energy simulations. The utility of the new infrastructure is demonstrated in proof-of-concept example applications. The software elements presented here are open source and freely available. Their interface provides a powerful enabling technology for the design of new QM/MM-ΔMLP models for studying a wide range of problems, including biomolecular reactivity and protein-ligand binding.

Coexistence of Defect Morphologies in Three-Dimensional Active Nematics.

We establish how active stress globally affects the morphology of disclination lines of a three-dimensional active nematic liquid crystal under chaotic flow. Thanks to a defect detection algorithm based on the local nematic orientation, we show that activity selects a crossover length scale in between the size of small defect loops and that of long and tangled defect lines of fractal dimension 2. This length scale crossover is consistent with the scaling of the average separation between defects as a function of activity. Moreover, on the basis of numerical simulation in a 3D periodic geometry, we show the presence of a network of regular defect loops, contractible onto the 3-torus, always coexisting with wrapping defect lines. While the length of regular defects scales linearly with the emerging active length scale, it verifies an inverse quadratic dependence for wrapping defects. The shorter the active length scale, the more the defect lines wrap around the periodic boundaries, resulting in extremely long and buckled structures.

GLOBAL SOLVABILITY OF AN INVERSE PROBLEM FOR A MOORE-GIBSON-THOMPSON EQUATION WITH PERIODIC BOUNDARY AND INTEGRAL OVERDETERMINATION CONDITIONS

This article studies the inverse problem of determining the pressure and convolution kernel in an integro-differential Moore-Gibson-Thompson equation with initial, periodic boundary and integral overdetermination conditions on the rectangular domain. By Fourier method this problem is reduced to an equivalent integral equation and on based of Banach’s f ixed point argument in a suitably chosen function space, the local solvability of the problem is proven. Then, the found solutions are continued throughout the entire domain of definition of the unknowns.

Efficient numerical calculation of Lyapunov-exponents and stability assessment for quasi-periodic motions in nonlinear systems

Investigating the stability of stationary motions is a highly relevant aspect when characterizing dynamical systems. For equilibria and periodic motions, well established theories and approaches exist to assess their stability: in both cases stability may be assessed using eigenvalue analyses of small perturbations. When it comes to quasi-periodic motions, such eigenvalue analyses are not applicable, since these motions can not be parameterized on finite time intervals. However, quasi-periodic motions can be densely embedded on finite invariant manifolds with periodic boundaries. In this contribution, a new approach is presented, which exploits this embedding in order to derive a sequence of finite mappings. Based on these mappings, the spectrum of 1st order Lyapunov-exponents is efficiently calculated. If the linearization of the problem is regular in the sense of Lyapunov, these exponents may be used to assess stability of the investigated solution. Beyond the numerical calculation of Lyapunov-exponents, an approach is presented which allows to check Lyapunov-regularity numerically. Together, both methods allow for an efficient numerical stability assessment of quasi-periodic motions. To demonstrate, verify and validate the developed approach, it is applied to quasi-periodic motions of two coupled van-der-Pol oscillators as well as a quasi-periodically forced Duffing equation. Additionally, a “step-by-step application instruction” is provided to increase comprehensibility and to discuss the required implementation steps in an applied context.

The influence of boundary conditions on the distribution of energetic electrons during collisionless magnetic reconnection

We conducted 2-D particle-in-cell simulations to investigate the impact of boundary conditions on the evolution of magnetic reconnection. The results demonstrate that the boundary conditions are crucial to this evolution. Specifically, in the cases of traditional periodic boundary (PB) and fully-opened boundary (OB) conditions, the evolutions are quite similar before the system achieves the fastest reconnection rate. However, differences emerge between the two cases afterward. In the PB case, the reconnection electric field experiences a rapid decline and even becomes negative, indicating a reversal of the reconnection process. In contrast, the system maintains a fast reconnection stage in the OB case. Suprathermal electrons are generated near the separatrix and in the exhaust region of both simulation cases. In the electron density depletion layer and the dipolarization front region, a larger proportion of suprathermal electrons are produced in the OB case. Medium-energy electrons are mainly located in the vicinity of the X-line and downstream of the reconnection site in both cases. However, in the OB case, they can also be generated in the electron holes along the separatrix. Before the reverse reconnection stage, no high-energy electrons are present in the PB case. In contrast, about 20% of the electrons in the thin and elongated electron current layer are high-energy in the OB case.

Thermal transitions in a one-dimensional, finite-size Ising model

We revisit the one-dimensional ferromagnetic Ising spin chain with a finite number of spins and periodic boundaries, deriving analytically and verifying numerically its various stationary and dynamical properties at different temperatures. In particular, we determine the probability distributions of magnetization, the number of domain walls, and the corresponding residence times for different chain lengths and magnetic fields. While we study finite systems at thermal equilibrium, we identify several temperatures similar to the critical temperatures for first-order phase transitions in the thermodynamic limit. We illustrate the utility of our results by their application to structural transitions in biopolymers having non-trivial intermediate equilibrium states.

Unveiling mechanisms in Cu2O-catalyzed electroreduction of CO2 through theoretical resolution using periodic boundary and saturation cluster models

The imperative need to reduce atmospheric CO2 to mitigate global warming and advance sustainable energy systems has driven extensive research. Copper oxide (Cu2O) has emerged as a promising catalyst for electroreduction of CO2, yet its catalytic mechanism remains debated. This study employs a theoretical approach to delve into the intricate details of CO2 electroreduction catalyzed by Cu2O. Utilizing both periodic boundary and saturation cluster models, we explore various reaction pathways, successfully identifying key transition states and intermediates with each model. A comprehensive analysis and comparison of results from both models are conducted. To enhance understanding, we develop a method simulating the impact of an electric field, employed to probe the ongoing reaction. Additionally, we consider the solid–liquid interface by introducing solvent molecules and buffer ions into our analysis. This comprehensive theoretical investigation aims to elucidate the mechanism governing the electroreduction of CO2 catalyzed by Cu2O and analogous semiconductor oxides, providing valuable insights into this critical process.

The collective dynamics of a stochastic Port-Hamiltonian self-driven agent model in one dimension

This paper studies the collective motion of self-driven agents in a one-dimensional space with periodic boundaries, using a stochastic Port-Hamiltonian system (PHS) with symmetric nearest-neighbor interactions and additive Brownian noise as an external input. In the case of a quadratic potential the PHS is an Ornstein-Uhlenbeck process for which we explicitly determine the distribution for any time t ≥ 0 and in the limit t → ∞. In particular, we characterize the collective motion by showing that the agents’ positions tend to build exactly one cluster. This is confirmed in simulations that show rapid and coordinated motion among agents, driven by noise, despite the absence of a preferred direction of motion in the model. Remarkably, the theoretical properties observed in the Ornstein-Uhlenbeck process also emerge in simulations of the nonlinear model incorporating a general interaction potential.

A Numerical Analysis of Conformal Energy Selective Surface Array with Synthetic Functions Expansion

Energy selective surface (ESS) is a special kind of metasurface with great potential in high-power microwave protection. In this paper, the electromagnetic (EM) properties of an ESS array are analyzed with synthetic functions expansion (SFX) method. A cylindrical conformal ESS array based on an I-shape element is designed for demonstration. The Bistatic RCS as well as electric field distribution of the ESS array is calculated with SFX and traditional full-wave numerical methods. The results show that SFX exhibits great advantages in memory cost while maintaining the same level of accuracy and efficiency with the multi-layer fast multipole method (MLFMM). Besides, the EM performance of the designed ESS is calculated with an array with finite elements and unit cell with periodic boundaries, respectively. The results show a good agreement. The proposed method can also be applied to the analysis of other kinds of metasurfaces whose elements share similar geometries with periodic or quasi-periodic arrangement. Especially for large-scale arrays, this method could well overcome the difficulty of balancing accuracy, efficiency, and resource consumption.

A Novel Shrink–Expand–Shrink Method for Modeling Composites with Ultrahigh Volume Fractions of Pre-Graded and Gradient-Distributed Particles

An advanced shrink–expand–shrink method is proposed in this paper for efficiently modeling concrete-like particle-reinforced composites with ultrahigh volume fraction of aggregates. The gradation of the aggregates can be pre-given and the aggregate spatial distribution can be nonuniform. By this method, the shrunk aggregates are first generated in the model space, and then expanded to jostle each other, afterwards they are shrunk again to normal size to obtain the final mesostructure models. Any high volume fractions of particles even more than 90% can be easily achieved by adjusting the shrinkage level during this process. Besides, a gradient distribution algorithm is established to conform to the aggregate segregation during the actual pouring process, and the corresponding periodic boundaries can also be generated to quickly create large specimens. Finally, the compression processes of polymer concrete with different aggregate packing densities are calculated via a finite element method. The shrink–expand–shrink method and the corresponding numerical models have memorable importance in the performance analysis and material design of particle-reinforced composites.

Parameters affecting plug characteristics in dense phase pneumatic conveying of ellipsoidal particles

Even though particle shape tends to have a major influence on the bulk behaviour of a granular system, perfectly spherical particles are often used in numerical simulations. In this study, we examine the plug flow of ellipsoidal particles in dense phase horizontal pneumatic conveying within a rigid and cylindrical pipe with periodic boundaries in the axial direction. We use coupled Computational Fluid Dynamics (CFD) – Discrete Element Method (DEM) simulations to investigate the effect of particle shape on four plug characteristics: velocity, length, porosity, and particle exchange rate with the stationary bed. Both ellipsoidal and spherical particles are used, and the parameters varied are the particle size, aspect ratio, pressure gradient, particle–particle and particle–wall sliding and rolling friction coefficients, and coefficients of restitution. The steady state characteristics of plugs composed of spherical particles are distinctly different from those composed of ellipsoidal particles. Certain parameters, including the particle–wall rolling friction and restitution coefficients, have minimal impact on the steady state plug characteristics. The present study also suggests that introducing interparticle rolling friction for perfectly spherical particles can achieve the velocity and length appropriate for plugs composed of ellipsoidal particles, although differences in dynamics may persist. Overall, this comprehensive analysis offers valuable insights into plug flow behaviour with non-spherical particles, aiding in the efficient modelling and design of pneumatic conveying systems.

Perturbing fast neutrino flavor conversion

The flavor evolution of neutrinos in dense astrophysical sources, such as core-collapse supernovae or compact binary mergers, is non-linear due to the coherent forward scattering of neutrinos among themselves. Recent work in this context has been addressed to figure out whether flavor equipartition could be a generic flavor outcome of fast flavor conversion. We investigate the flavor conversion physics injecting random perturbations in the neutrino field in two simulation setups: 1. a spherically symmetric simulation shell without periodic boundaries, with angular distributions evolving dynamically thanks to non-forward scatterings of neutrinos with the background medium, and neutrino advection; 2. a periodic simulation shell, with angular distributions of neutrinos defined a priori and neutrino advection. We find that, independent of the exact initial flavor configuration and type of perturbations, flavor equipartition is generally achieved in the system with periodic boundaries; in this case, perturbations aid the diffusion of flavor structures to smaller and smaller scales. However, flavor equipartition is not a general outcome in the simulation shell without periodic boundaries, where the inhomogeneities induced perturbing the neutrino field affect the flavor evolution, but do not facilitate the diffusion of flavor waves. This work highlights the importance of the choice of the simulation boundary conditions in the exploration of fast flavor conversion physics.

Comparative Numerical Study of Conventional and Hydraulic Wells Turbine for Ocean-Wave Energy Conversion

The Wells turbine is an ocean wave energy converter that has been implemented in several countries around the world. The hysteresis phenomenon, which causes a torque reduction when the rotor acquires air flow acceleration, is one of the Wells turbine's drawbacks. One enhancement strategy is converting the conventional Wells turbine, which operates in air, into a hydraulic Wells turbine, which operates in ocean water. This method aims to obtain a higher density of working fluid, which can increase the momentum acting on the Wells turbine blades. This research compared the performance and hysteresis phenomenon of conventional and hydraulic Wells turbines. A CFD method based on Reynolds Averaged Navier-Stokes (RANS) and k-ω SST turbulence model is used in this study. Under transient conditions, 3D modeling with periodic boundaries is applied to model the hysteresis phenomenon. This study demonstrated that the hydraulic Wells turbine outperforms the conventional Wells turbine. According to the simulation result, the hydraulic turbine achieves a significant improvement in maximum torque, approximately 124% of the conventional air turbine torque. The concept of immersing the Wells turbine in ocean water improves its efficiency as well. Furthermore, unlike the conventional one, the hydraulic Wells turbine does not exhibit hysteresis.