In this paper, we develop a large $N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_{\text{ex}}\left(x\right)$, and repel each other via a class of pairwise interaction potentials $V_{\text{int}}\left(r\right)$ (where $r$ is distance between a pair of particles) such that $V_{\text{int}}\sim {\left|r\right|}^{-k}$ when $r\to 0$. We consider the case where every particle is interacting with $d$ (finite-range parameter) number of particles to its left and right. Due to the intricate interplay between external confinement, pairwise repulsion, and entropy, the density exhibits markedly distinct behavior in three regimes $k>0, k\to 0$, and $k<0$. From this field theory, we compute analytically the average density profile for large $N$ in these regimes. We show that the contribution from interaction dominates the collective behavior for $k>0$ and the entropy contribution dominates for $k<0$, and both contribute equivalently in the $k\to 0$ limit (finite-range log-gas). Given the fact that this family of systems is of broad relevance, our analytical findings are of paramount importance. These results are in excellent agreement with brute-force Monte Carlo simulations.

We consider Brownian motion under resetting in higher dimensions for the case when the return of the particle to the origin occurs at a constant speed. We investigate the behavior of the probability density function (PDF) and of the mean-squared displacement (MSD) in this process. We study two different resetting protocols: exponentially distributed time intervals between the resetting events (Poissonian resetting) and resetting at fixed time intervals (deterministic resetting). We moreover discuss a general problem of the invariance of the PDF with respect to the return speed, as observed in the one-dimensional system for Poissonian resetting, and show that this one-dimensional situation is the only one in which such an invariance can be found. However, the invariance of the MSD can still be observed in higher dimensions.

We use the Gurevich-Pitaevskii approach based on the Whitham averaging method for studying the formation of dispersive shock waves in an intense light pulse propagating through a saturable nonlinear medium. Although the Whitham modulation equations cannot be diagonalized in this case, the main characteristics of the dispersive shock can be derived by means of an analysis of the properties of these equations at the boundaries of the shock. Our approach generalizes a previous analysis of steplike initial intensity distributions to a more realistic type of initial light pulse and makes it possible to determine, in a setting of experimental interest, the value of measurable quantities such as the wave-breaking time or the position and light intensity of the shock edges.

We present a complete theory of the scattering of a particle in a Yukawa potential when the screening length is much larger than the classical impact parameter for ${90}^{\circ }$ deflection and than the de Broglie length. The classical limit, the quantum limit, and the intermediate case are investigated, enabling an accurate determination of the argument of the Coulomb logarithm in the general case. The connection with previously published results is made.

Dynamics of a particle diffusing in a confinement can be seen a sequence of bulk-diffusion-mediated hops on the confinement surface. Here, we investigate the surface hopping propagator that describes the position of the diffusing particle after a prescribed number of encounters with that surface. This quantity plays the central role in diffusion-influenced reactions and determines their most common characteristics such as the propagator, the first-passage time distribution, and the reaction rate. We derive explicit formulas for the surface hopping propagator and related quantities for several Euclidean domains: half-space, circular annuli, circular cylinders, and spherical shells. These results provide the theoretical ground for studying diffusion-mediated surface phenomena. The behavior of the surface hopping propagator is investigated for both “immortal” and “mortal” particles.

Thermodynamic uncertainty relations (TURs) set fundamental bounds on the fluctuation and dissipation of stochastic systems. Here, we examine these bounds, in experiment and theory, by exploring the entire phase space of a cyclic information engine operating in a nonequilibrium steady state. Close to its maximal efficiency, we find that the engine violates the original TUR. This experimental demonstration of TUR violation agrees with recently proposed softer bounds: The engine satisfies two generalized TUR bounds derived from the detailed fluctuation theorem with feedback control and another bound linking fluctuation and dissipation to mutual information and Renyi divergence. We examine how the interplay of work fluctuation and dissipation shapes the information conversion efficiency of the engine, and find that dissipation is minimal at a finite noise level, where the original TUR is violated.

Near the melting transition the bending elastic constant $\kappa$, an emergent property of double-stranded DNA (dsDNA), is shown not to follow the rodlike scaling for small-length $N$. The reduction in $\kappa$ with temperature is determined by the denatured bubbles for a continuous transition, e.g., when the two strands are Gaussian, but by the broken bonds near the open end in a Y-like configuration for a first-order transition as for strands with excluded volume interactions. In the latter case, a lever rule is operational, implying a phase coexistence although dsDNA is known to be a single phase.

We propose a model of antibiotic diffusion through a bacterial biofilm when diffusion and/or absorption barriers develop in the biofilm. The idea of this model is: We deduce details of the diffusion process in a medium in which direct experimental study is difficult, based on probing diffusion in external regions. Since a biofilm has a gel-like consistency, we suppose that subdiffusion of particles in the biofilm may occur. To describe this process we use a fractional subdiffusion-absorption equation with an adjustable anomalous diffusion exponent. The boundary conditions at the boundaries of the biofilm are derived by means of a particle random walk model on a discrete lattice leading to an expression involving a fractional time derivative. We show that the temporal evolution of the total amount of substance that has diffused through the biofilm explicitly depends on whether there is antibiotic absorption in the biofilm. This fact is used to experimentally check for antibiotic absorption in the biofilm and if subdiffusion and absorption parameters of the biofilm change over time. We propose a four-stage model of antibiotic diffusion in biofilm based on the following physical characteristics: whether there is absorption of the antibiotic in the biofilm and whether all biofilm parameters remain unchanged over time. The biological interpretation of the stages, in particular their relation with the bacterial defense mechanisms, is discussed. Theoretical results are compared with empirical results of ciprofloxacin diffusion through Pseudomonas aeruginosa biofilm, and ciprofloxacin and gentamicin diffusion through Proteus mirabilis biofilm.

Molecular motion in polymers is frozen below the glass transition temperature $T_g$ and changes of viscoelastic functions are most spectacular near $T_g$. Exceptional enhancement of molecular mobility and a decrease of polymer viscosity, by several orders of magnitude, down to the viscous flow regime, are observed way below $T_g$ by light absorption. Relaxation processes, which take decades to centuries in some high-$T_g$ polymers, are reduced to minute timescales by sub-$T_g$ light absorption. Here we develop a model for this intriguing albeit spectacular action of light on glass forming materials and we propose experiments to relate light absorption to materials properties. The model provides a solution to a long-lasting problem of how molecular mobility is enhanced in solid polymers by photoisomerization and provides a tool for a better understanding of the relationship between light absorption and material properties and developing photosensitive polymers for light to mechanical energy transduction.

Swimmers and self-propelled particles are physical models for the collective behavior and motility of a wide variety of living systems, such as bacteria colonies, bird flocks, and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behavior. Here we study colloids in a dc electric field. Our quasi-two-dimensional system of electrically driven particles exhibits a rich and exotic phase behavior exhibiting passive crystallites, motile crystallites, an active gas, and banding. Amongst these are two mesophases, reminiscent of systems with competing interactions. At low field strengths activity suppresses demixing, leading to motile crystallites. Meanwhile, at high field strengths, activity drives partial demixing to traveling bands. We parametrize a particulate simulation model which reproduces the experimentally observed phases.

Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning or twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and average coordination numbers as low as 0.53 and 2.5, respectively, when the particles experience high resistance to sliding, rolling, and twisting. Only when the particle model includes rolling and twisting friction were experimental volume fractions reproduced.

Design of slender artificial materials and morphogenesis of thin biological tissues typically involve stimulation of isolated regions (inclusions) in the growing body. These inclusions apply internal stresses on their surrounding areas that are ultimately relaxed by out-of-plane deformation (buckling). We utilize the Föppl-von Kármán model to analyze the interaction between two circular inclusions in an infinite plate that their centers are separated a distance of $2\ell$. In particular, we investigate a region in phase space where buckling occurs at a narrow transition layer of length ${\ell }_D$ around the radius of the inclusion, $R$ (${\ell }_D\ll R$). We show that the latter length scale defines two regions within the system, the close separation region, $\ell -R\sim {\ell }_D$, where the transition layers of the two inclusions approximately coalesce, and the far separation region, $\ell -R\gg {\ell }_D$. While the interaction energy decays exponentially in the latter region, $E_{\text{int}}\propto e^{-(\ell -R)/{\ell }_D}$, it presents nonmonotonic behavior in the former region. While this exponential decay is predicted by our analytical analysis and agrees with the numerical observations, the close separation region is treated only numerically. In particular, we utilize the numerical investigation to explore two different scenarios within the final configuration: The first where the two inclusions buckle in the same direction (up-up solution) and the second where the two inclusions buckle in opposite directions (up-down solution). We show that the up-down solution is always energetically favorable over the up-up solution. In addition, we point to a curious symmetry breaking within the up-down scenario; we show that this solution becomes asymmetric in the close separation region.

This paper reports on the molecular dynamics simulations of classical two-dimensional (2D) electric dipole systems. The properties of 2D systems with bare (nonscreened) and screened dipole-dipole interactions have been investigated. Based on the polygon construction method, we present simulation results on the phase transition, and we locate the melting and freezing points of 2D dipole systems in terms of a polygon disorder parameter, with the polygon disorder parameter being the sum of nontriangular polygon order parameters. It was found that the phase transition of the system occurs when the polygon disorder parameter has a value 0.165. This result was cross-checked by using both local and overall orientational order parameters. We also identified that the value of the average local orientational order parameter at the phase transition point is 0.67. These results are valid for the ordinary (bare) dipole-dipole interaction as well as the screened dipole-dipole interaction, and they are expected to be general for other 2D systems with repulsive pair interaction. We observed that both melting and freezing points shift to lower values of temperature due to screening. In the liquid state, the radial distribution function and polygon construction method show the loss of order in a structure as screening becomes more severe. Furthermore, the impact of screening on the system's collective excitation spectra and diffusive characteristics at liquid and solid states has been studied. Results show the decrease in the values of both longitudinal and transverse sound speeds and the emergence of anomalous superdiffusive motion in the liquid state due to screening.

Particle-in-cell and Monte Carlo collision (PIC-MCC) has been widely adopted as a simulation method for electric propulsion. However, neutral atoms move much more slowly than other species, which can cause a serious reduction in simulation speed. In this work, we investigate the view factor model in combination with the PIC-MCC method and propose a method for simulating three-dimensional neutral atoms. The accuracy of the PIC-MCC method can be significantly improved by updating the neutral distribution periodically. We compare the computational results with the fixed-neutral PIC-MCC model of the miniature ring-cusp discharge experiment at the University of California, Los Angeles (UCLA). The plasma distribution and potential distribution of the simulation match well with the UCLA experimental data. Compared with the fixed-neutral model, the view factor model increases the simulation time by only 33% while it improves the distribution accuracy of neutrals, plasma density, and electric potential, and reduces the simulation errors of discharge current and discharge power from 19.8% to 9.8%. The accuracy of PIC-MCC simulation has been improved at the expense of slightly increasing the computational time.

In this paper we study the phase diagram of the five-state Potts antiferromagnet on the bisected-hexagonal lattice. This question is important since Delfino and Tartaglia recently showed that a second-order transition in a five-state Potts antiferromagnet is allowed, and the bisected-hexagonal lattice had emerged as a candidate for such a transition on numerical grounds. By using high-precision Monte Carlo simulations and two complementary analysis methods, we conclude that there is a finite-temperature first-order transition point. This one separates a paramagnetic high-temperature phase, and a low-temperature phase where five phases coexist. This phase transition is very weak in the sense that its latent heat (per edge) is two orders of magnitude smaller than that of other well-known weak first-order phase transitions.

In this work, we show theoretically and numerically that a one-dimensional reaction-diffusion system, near the Turing bifurcation, produces different number of stripes when, in addition to random noise, the Fourier mode of a prepattern used to initialize the system changes. We also show that the Fourier modes that persist are inside the Eckhaus stability regions, while those outside this region follow a wave number selection process not predicted by the linear analysis. To test our results, we use the Brusselator reaction-diffusion system obtaining an excellent agreement between the weakly nonlinear predictions of the real Ginzburg-Landau equations and the numerical solutions near the bifurcation. Although the persistence of patterns is not relevant as a simple generating mechanism of self-organization, it is crucial to understand the formation of patterns that occurs in multiple stages. In this work, we discuss the relevance of our results on the robustness and diversity of solutions in multiple-steps mechanisms of biological pattern formation and auto-organization in growing domains.

Exploration of granular physics for three-dimensional geometries interacting with deformable media is crucial for further understanding of granular mechanics and vehicle-terrain dynamics. A modular screw propelled vehicle is, therefore, designed for testing the accuracy of a novel helical granular scaling law in predicting vehicle translational velocity and power. A dimensional analysis is performed on the vehicle and screw pontoons. Two additional pontoon pairs of increased size and mass are determined from dimensional scalars. The power and velocity of these larger pairs are predicted by the smaller pair using the scaling relationships. All three sets are subjected to ten trials of five angular velocities ranging from 13.7 to 75.0 revolutions per minute in a high interlock lunar regolith analog derived from mining tailings. Experimental agreement for prediction of power (3–9% error) and translational velocity (2–12% error) are observed. A similar set of geometries is subjected to multibody dynamics and discrete element method cosimulations of Earth and lunar gravity to verify a gravity-dependent subset of the scaling laws. These simulations show agreement (under 5% error for all sets) and support law validity for gravity between Earth and lunar magnitude. These results support further expansion of granular scaling models to enable prediction for vehicle-terrain dynamics for a variety of environments and geometries.

The mechanism of pressure-driven transport of simple liquid through a nanoporous graphene membrane has been analyzed using nonequilibrium molecular dynamics simulation. In this study, we investigate liquid dynamics properties such as local density, pressure variation, and local viscosity depending on the flow region. With movement of the specular reflection wall at the end of the front and back reservoirs, a pressure difference occurs mainly due to the change in the relative distance between the liquid molecules in the corresponding reservoir. The interfacial pressure difference strongly depends on the intermolecular force of the graphene membrane governed by the layered structure of the simple liquid and the applied flow velocity. The local viscosity was calculated for a nanochannel of simple liquid sheared by graphene walls. The liquid velocity adjacent to the pore edge was considered as the slip velocity, which provides updates in the Sampson flow equation. We observed that the entrance interfacial pressure and higher local viscosity in the vicinity of the graphene membrane, which are associated with the optimized definition of the wall-liquid boundary near the pore edge, play a critical role in the permeation of simple liquids through the nanoporous graphene membrane.

In a recent paper by Fronczak et al. [Phys. Rev. E 101, 022111 (2020)], a simple spin model has been studied in full detail via microcanonical approaches. The authors stress that the range of microcanonical temperature ${\beta }_m>1$ is unattainable in this model and the system undergoes a phase transition when the external parameter $a=1$ in the microcanonical ensemble. The purpose of this comment is to state that the treatment of the microcanonical entropy in the commented paper is inappropriate since the fact that ergodicity is broken in the microcanonical dynamics is ignored by the authors. The phase transition in the microcanonical ensemble, considered in the commented paper, could occur only with a nonlocal dynamics which is often difficult to justify physically.