We numerically investigate the nonequilibrium behaviors of classic particles with competing interactions confined in a two-dimensional logarithmic trap. We reveal a quench-induced surprising dynamics exhibiting rich dynamic patterns depending upon confinement strength and trap size, which is attributed to the time-dependent competition between interparticle repulsions and attractions under a circular confinement. Moreover, in the collectively diffusive motions of the particles, we find that the emergence of dynamic structure transformation coincides with a diffusive mode transition from superdiffusion to subdiffusion. These findings are likely useful in understanding the pattern selection and evolution in various chemical and biological systems in addition to modulated systems, and add a new route to tailoring the morphology of pattern-forming systems.

This paper proposes a model of the laser-driven electron acceleration that occurs when a high-intensity laser interacts with a nanoplate target. It shows that quasistatic electric ${\mathbf{E}}_{\mathrm{qs}}$ and magnetic ${\mathbf{B}}_{\mathrm{qs}}$ fields can be formed when the laser, polarized normal to the nanoplates, extracts electrons from the nanoplates. Considering the physical natures of ${\mathbf{E}}_{\mathrm{qs}}$ and ${\mathbf{B}}_{\mathrm{qs}}$, the amplitude of ${\mathbf{E}}_{\mathrm{qs}}$ is relatively larger than ${\mathbf{B}}_{\mathrm{qs}}$. Such a residual between static electric and magnetic field is shown to be crucial for the electron acceleration beyond the ponderomotive scaling, as it can cause onset of stochastic electron motion. The analysis demonstrates that the maximum electron energy in units of ponderomotive scaling depends on a single universal parameter, which is composed of laser amplitude, spacing between nanoplates, and electron initial conditions. The analytical results are confirmed by a series of two-dimensional particle-in-cell simulations using epoch code.

The penetration of a supersonic particle at the interface is studied in a binary complex plasma. Inspired by the experiments performed in the PK-3 Plus Laboratory on board the International Space Station, Langevin dynamics simulations were carried out. A Mach cone structure forms in the lateral wave behind the supersonic extra particle, where the kink of the cone flanks is observed at the interface. The propagation of the pulse-like perturbation along the interface is demonstrated by the evolution of the radial and axial velocity of the small particles in the vicinity of the interface. The decay of the pulse strength is determined by the friction, where the propagation distance can reach several interparticle distances for small damping rate. The dependence of the dynamics of the background particles in the vicinity of the interface on the penetration direction implies that the disparity of the mobility may be the cause of various interfacial effects.

Restricted Boltzmann machines (RBMs) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the representation power of RBMs to provide an exact decomposition of many-body contact interactions into one-body operators coupled to discrete auxiliary fields. This construction generalizes the well known Hirsch's transform used for the Hubbard model to more complicated theories such as pionless effective field theory in nuclear physics, which we analyze in detail. We also discuss possible applications of our mapping for quantum annealing applications and conclude with some implications for RBM parameter optimization through machine learning.

We investigate and compare the accuracy and efficiency of different numerical approaches to model the dynamics of finite-size particles using the lattice Boltzmann method (LBM). This includes the standard bounce-back (BB) and the equilibrium interpolation (EI) schemes. To accurately compare the different implementations, we first introduce a boundary condition to approximate the flow properties of an unbounded fluid in a finite simulation domain, taking into account the perturbation induced by a moving particle. We show that this boundary treatment is efficient in suppressing detrimental effects on the dynamics of spherical and ellipsoidal particles arising from the finite size of the simulation domain. We then investigate the performances of the BB and EI schemes in modeling the dynamics of a spherical particle settling under Stokes conditions, which can now be reproduced with great accuracy thanks to the treatment of the exterior boundary. We find that the EI scheme outperforms the BB scheme in providing a better accuracy scaling with respect to the resolution of the settling particle, while suppressing finite-size effects due to the particle discretization on the lattice grid. Additionally, in order to further increase the capability of the algorithm in modeling particles of sizes comparable to the lattice spacing, we propose an improvement to the EI scheme, the complete equilibrium interpolation (CEI). This approach allows us to accurately capture the boundaries of the particle also when located between two fluid nodes. We evaluate the CEI performance in solving the dynamics of an under-resolved particle under analogous Stokes conditions and also for the case of a rotating ellipsoid in a shear flow. Finally, we show that EI and CEI are able to recover the correct flow solutions also at small, but finite, Reynolds number. Adopting the CEI scheme it is not only possible to detect particles with zero lattice occupation, but also to increase up to one order of magnitude the accuracy of the dynamics of particles with a size comparable to the lattice spacing with respect to the BB and the EI schemes.

We study dynamics in ensembles of identical excitable units with global repulsive interaction. Starting from active rotators with additional higher order Fourier modes in on-site dynamics, we observe, at sufficiently strong repulsive coupling, large-scale collective oscillations in which the elements form two separate clusters. Transitions from quiescence to clustered oscillations are caused by global bifurcations involving the unstable clustered steady states. For clusters of equal size, the scenarios evolve either through simultaneous formation of two heteroclinic trajectories or through two simultaneous saddle-node bifurcations on invariant circles. If the sizes of clusters differ, two global bifurcations are separated in the parameter space. Stability of clusters with respect to splitting perturbations depends on the kind of higher order corrections to on-site dynamics; we show that for periodic oscillations of two equal clusters the Watanabe-Strogatz integrability marks a change of stability. By extending our studies to ensembles of voltage-coupled Morris-Lecar neurons, we demonstrate that similar bifurcations and switches in stability occur also for more elaborate models in higher dimensions.

Bacterial quorum sensing is the communication that takes place between bacteria as they secrete certain molecules into the intercellular medium that later get absorbed by the secreting cells themselves and by others. Depending on cell density, this uptake has the potential to alter gene expression and thereby affect global properties of the community. We consider the case of multiple bacterial species coexisting, referring to each one of them as a genotype and adopting the usual denomination of the molecules they collectively secrete as public goods. A crucial problem in this setting is characterizing the coevolution of genotypes as some of them secrete public goods (and pay the associated metabolic costs) while others do not but may nevertheless benefit from the available public goods. We introduce a network model to describe genotype interaction and evolution when genotype fitness depends on the production and uptake of public goods. The model comprises a random graph to summarize the possible evolutionary pathways the genotypes may take as they interact genetically with one another, and a system of coupled differential equations to characterize the behavior of genotype abundance in time. We study some simple variations of the model analytically and more complex variations computationally. Our results point to a simple trade-off affecting the long-term survival of those genotypes that do produce public goods. This trade-off involves, on the producer side, the impact of producing and that of absorbing the public good. On the nonproducer side, it involves the impact of absorbing the public good as well, now compounded by the molecular compatibility between the producer and the nonproducer. Depending on how these factors turn out, producers may or may not survive.

We investigate dilation-induced surface deformations in a discontinuous shear thickening (DST) suspension to determine the relationship between dilation and stresses in DST. Video is taken at two observation points on the surface of the suspension in a rheometer while shear and normal stresses are measured. A roughened surface of the suspension is observed as particles poke through the liquid-air interface, an indication of dilation in a suspension. These surface roughening events are found to be intermittent and localized spatially. Shear and normal stresses also fluctuate between high- and low-stress states, and surface roughening is observed frequently in the high-stress state. On the other hand, a complete lack of surface roughening is observed when the stresses remain at low values for several seconds. Surface roughening is most prominent while the stresses grow from the low-stress state to the high-stress state, and the roughened surface tends to span the entire surface by the end of the stress growth period. Surface roughening is found only at stresses and shear rates in and above the shear thickening range. These observed relations between surface roughening and stresses confirm that dilation and stresses are coupled in the high-stress state of DST.

We suggest a geometrical mechanism for the ordering of slender filaments inside nonisotropic containers, using cortical microtubules in plant cells and the packing of viral genetic material inside capsids as concrete examples. We show analytically how the shape of the cell affects the ordering of phantom elastic rods that are not self-avoiding (i.e., self-crossing is allowed). We find that for oblate cells, the preferred orientation is along the equator, while for prolate spheroids with an aspect ratio close to 1, the orientation is along the principal (long axis). Surprisingly, at a high enough aspect ratio, a configurational phase transition occurs and the rods no longer point along the principal axis, but at an angle to it, due to high curvature at the poles. We discuss some of the possible effects of self-avoidance using energy considerations. These results are relevant to other packing problems as well, such as the spooling of filament in the industry or spider silk inside water droplets.

The head-on collision of compressional shocks in two-dimensional dusty plasmas is investigated using both molecular dynamical and Langevin simulations. Two compressional shocks are generated from the inward compressional boundaries in simulations. It is found that, during the collision of shocks, there is a generally existing time delay of shocks $\tau$, which diminishes monotonically with the increasing compressional speed of boundaries, corresponding to the time resolution of the studied system. Dispersive shock waves (DSWs) are generated around the shock front for some conditions. It is also found that the period of the DSW decreases monotonically with the inward compressional speed of boundaries, more substantially than the time delay of shocks $\tau$. When the inward compressional speed of boundaries increases further, the DSWs gradually vanish. We speculate that, for these high compressional speeds of boundaries, the period of the DSW might be reduced to a comparable timescale of the time delay of shocks $\tau$, i.e., the time resolution of our studied system, or even shorter, thus the DSW reasonably vanishes.

We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds $\mathrm{LiF}, {\mathrm{B}}_4\mathrm{C}, \mathrm{BN}, {\mathrm{CH}}_4, {\mathrm{CH}}_2, {\mathrm{C}}_2{\mathrm{H}}_3, \mathrm{CH}, {\mathrm{C}}_2\mathrm{H}, \mathrm{MgO}, \mathrm{and} {\mathrm{MgSiO}}_3$. For all these materials, we provide the pressure and internal energy over a density-temperature range from $\sim 0.5$ to 50 g ${\mathrm{cm}}^{-3}$ and from $\sim {10}^4$ to ${10}^9$ K, which are based on $\sim 5000$ different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of $\mathrm{L}$- and $\mathrm{K}$-shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of ${\mathrm{H}}_2\mathrm{O},$ ${\mathrm{H}}_2{\mathrm{O}}_2,$ ${\mathrm{Al}}_2{\mathrm{O}}_3, \mathrm{CO}, \mathrm{and} {\mathrm{CO}}_2$ to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.

Perfectly matched layer (PML) boundary conditions are constructed for the Dirac equation and general electromagnetic potentials. A PML extension is performed for the partial differential equation and two versions of a staggered-grid single-cone finite-difference scheme. For the latter, PML auxiliary functions are computed either within a Crank-Nicholson scheme or one derived from the formal continuum solution in integral form. Stability conditions are found to be more stringent than for the original scheme. Spectral properties under spatially uniform PML confirm damping of any out-propagating wave contributions. Numerical tests deal with static and time-dependent electromagnetic textures in the boundary regions for parameters characteristic for topological insulator surfaces. When compared to the alternative imaginary-potential method, PML offers vastly improved wave absorption owing to a more efficient suppression of back-reflection. Remarkably, this holds for time-dependent textures as well, making PML a useful approach for transient transport simulations of Dirac fermion systems.

We present a framework exploiting the cascade of phase transitions occurring during a simulated annealing of the expectation-maximization algorithm to cluster datasets with multiscale structures. Using the weighted local covariance, we can extract, a posteriori and without any prior knowledge, information on the number of clusters at different scales together with their size. We also study the linear stability of the iterative scheme to derive the threshold at which the first transition occurs and show how to approximate the next ones. Finally, we combine simulated annealing together with recent developments of regularized Gaussian mixture models to learn a principal graph from spatially structured datasets that can also exhibit many scales.

We study the classical and quantum ergodic lemon billiard introduced by Heller and Tomsovic in Phys. Today 46(7), 38 (1993), for the case $B=1/2$, which is a classically ergodic system (without a rigorous proof) exhibiting strong stickiness regions around a zero-measure bouncing ball modes. The structure of the classical stickiness regions is uncovered in the S-plots introduced by Lozej [Phys. Rev. E 101, 052204 (2020)]. A unique classical transport or diffusion time cannot be defined. As a consequence the quantum states are characterized by the following nonuniversal properties: (i) All eigenstates are chaotic but localized as exhibited in the Poincaré-Husimi (PH) functions. (ii) The entropy localization measure A (also the normalized inverse participation ratio) has a nonuniversal distribution, typically bimodal, thus deviating from the beta distribution, the latter one being characteristic of uniformly chaotic systems with no stickiness regions. (iii) The energy-level spacing distribution is Berry-Robnik-Brody (BRB), capturing two effects: the quantally divided phase space (because most of the PH functions are either the inner-ones or the outer-ones, dictated by the classical stickiness, with an effective parameter ${\mu }_1$ measuring the size of the inner region bordered by the sticky invariant object, namely, a cantorus), and the localization of PH functions characterized by the level repulsion (Brody) parameter $\beta$. (iv) In the energy range considered (between 20 000 states to 400 000 states above the ground state) the picture (the structure of the eigenstates and the statistics of the energy spectra) is not changing qualitatively, as $\beta$ fluctuates around 0.8, while ${\mu }_1$ decreases almost monotonically, with increasing energy.

We revisit the question of wave-number selection in pattern-forming systems by studying the one-dimensional stabilized Kuramoto-Sivashinsky equation with additive noise. In earlier work, we found that a particular periodic state is more probable than all others at very long times, establishing the critical role of noise in the selection process. However, the detailed mechanism by which the noise picked out the selected wave number was not understood. Here, we address this issue by analyzing the noise-averaged time evolution of each unstable mode from the spatially homogeneous state, with and without noise. We find drastic differences between the nonlinear dynamics in the two cases. In particular, we find that noise opposes the growth of Eckhaus modes close to the critical wave number and boosts the growth of Eckhaus modes with wave numbers smaller than the critical wave number. We then hypothesize that the main factor responsible for this behavior is the excitation of long-wavelength $(q\to 0)$ modes by the noise. This hypothesis is confirmed by extensive numerical simulations. We also examine the significance of the magnitude of the noise.

Cells of the social amoeba Dictyostelium discoideum migrate to a source of periodic traveling waves of chemoattractant as part of a self-organized aggregation process. An important part of this process is cellular memory, which enables cells to respond to the front of the wave and ignore the downward gradient in the back of the wave. During this aggregation, the background concentration of the chemoattractant gradually rises. In our microfluidic experiments, we exogenously applied periodic waves of chemoattractant with various background levels. We find that increasing background does not make detection of the wave more difficult, as would be naively expected. Instead, we see that the chemotactic efficiency significantly increases for intermediate values of the background concentration but decreases to almost zero for large values in a switch-like manner. These results are consistent with a computational model that contains a bistable memory module, along with a nonadaptive component. Within this model, an intermediate background level helps preserve directed migration by keeping the memory activated, but when the background level is higher, the directional stimulus from the wave is no longer sufficient to activate the bistable memory, suppressing directed migration. These results suggest that raising levels of chemoattractant background may facilitate the self-organized aggregation in Dictyostelium colonies.

Multiple scattering of light by resonant vapor is characterized by Lévy-type superdiffusion with a single-step size distribution $p\left(x\right)\propto 1/x^{1+\alpha }$. We investigate Lévy flight of light in a hot rubidium vapor collisional-broadened by 50 torr of He gas. The frequent collisions produce Lorentzian absorptive and emissive profiles with $\alpha <1$ and a corresponding divergent mean step size. We extract the Lévy parameter $\alpha \approx 0.5$ in a multiple-scattering regime from radial profile of the transmission and from violation of the Ohm's law. The measured radial transmission profile and the total diffusive transmission curves are well reproduced by numerical simulations for Lorentzian line shapes.

We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small feedback vertex set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learns a variational distribution parametrized using neural networks to approximate the original Boltzmann distribution. The method is able to estimate free energy, compute observables, and generate unbiased samples via direct sampling without autocorrelation. Extensive experiments show that our approach is more accurate than existing approaches for sparse spin glasses. On random graphs and real-world networks, our approach significantly outperforms the standard methods for sparse systems, such as the belief-propagation algorithm; on structured sparse systems, such as two-dimensional lattices our approach is significantly faster and more accurate than recently proposed variational autoregressive networks using convolution neural networks.

Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network where intrinsic correlations in particle positions is controlled by the fractal iteration. Specifically, we calculate the critical packing fractions of site-diluted lattices of Sierpiński gaskets (SG's) with varying degrees of fractal iteration. Our results suggest that although the correlation length exponent and fractal dimension of the RP of these lattices are identical to that of the regular triangular lattice, the critical volume fraction is dramatically lower due to the fractal nature of the network. Furthermore, we develop a simplified model for an SG lattice based on the fragility analysis of a single SG. This simplified model provides an upper bound for the critical packing fractions of the full fractal lattice, and this upper bound is strictly obeyed by the disorder averaged RP threshold of the fractal lattices. Our results characterize rigidity in ultralow-density fractal networks.

The Hamiltonian mean-field model is investigated in the presence of a field. The self-consistent equations for the magnetization and the energy per particle are derived, and the field effect on the caloric curve is presented. The analytical geometric approach to Hamiltonian dynamics, under the hypothesis of quasi-isotropy, allows us to calculate the field effect on the energy-dependent microcanonical mean Ricci curvature and its fluctuations. Notably, the method proved suitable to identify that stable and metastable solutions of the Lyapunov exponent exhibit intriguing distinct curvature behavior very close to the critical point at extremely low field values. In addition, finite-size molecular dynamics (MD) simulations are used to observe the evolution of the magnetization and their components, including the stability properties of the solutions. Most importantly, comparison of finite-size MD calculations of the Lyapunov exponent and related properties with those via the geometric approach unveil the sensible dependence of these microcanonical quantities on energy, number of particles, and field, before a quasisaturation behavior at high fields. Finally, relaxation properties from out-of-equilibrium initial conditions are discussed in light of MD simulations.