In this work, a lattice Boltzmann equation (LBE) is developed to convection-diffusion flows with Neumann boundary condition in complex geometry. The physical fluid domain together with the physical boundary is extended to a large domain similar to the fictitious domain method, and the original convection-diffusion equation (CDE) is reformulated for the large domain, where the Neumann boundary condition is naturally incorporated to CDE without separated explicit treatment. Based on this extended CDE for the large domain, the LBE solver is designed accordingly. Several classical simulations of pure thermal diffusion/natural convection between two concentrated cylinders, natural convection flow around a circular cylinder with constant heat flux in square cavity, and mixed convection flow in a square lid-driven cavity with a circular cylinder are carried out to validate the present method. Numerical results show that the predictions by present LBE agree well with theoretical or other results.

A volumetric lattice Boltzmann (LB) method is developed for the particle-resolved direct numerical simulation of thermal particulate flows with conjugate heat transfer. This method is devised as a single-domain approach by applying the volumetric interpretation of the LB equation and introducing a solid fraction field to represent the particle. The volumetric LB scheme is employed to enforce the nonslip velocity condition in the solid domain, and a specialized momentum exchange scheme is proposed to calculate the hydrodynamic force and torque acting on the particle. To uniformly solve the temperature field over the entire domain with high numerical fidelity, an energy conservation equation is first derived by reformulating the convection term into a source term. A corresponding LB equation is then devised to automatically achieve the conjugate heat transfer condition and correctly handle the differences in thermophysical properties. Theoretical analysis of this LB equation is also performed to derive the constraints to preserve the numerical fidelity even near the solid-fluid interface. Numerical tests are first performed to validate the present volumetric LB method in various aspects. Then the sedimentation of a cold particle with conjugate heat transfer in a long channel is investigated. It is found that the sedimentation process can be divided into the accelerating, decelerating, and equilibrium stages. As a further application to dense particulate flows, the sedimentation of 2048 cold particles with conjugate heat transfer in a square cavity is simulated. The particulate Rayleigh-Bénard convection is successfully captured in this particle-resolved simulation.

We examine the deformation of homogeneous spherical fluid vesicles along their equator by a circular rigid ring. We consider deformations preserving the axial and equatorial mirror symmetries of the vesicles. The configurations of the vesicle are determined employing the spontaneous curvature model subject to the constraints imposed by the ring as well as of having constant area or volume. We determine two expressions of the force exerted by the ring, one involving a discontinuity in the derivative of the curvature of the membrane across the ring, and another one in terms of the global quantities of the vesicle. For small enough values of the spontaneous curvature there is only one sequence of configurations for either fixed area or volume. The behavior of constricted vesicles is similar for both constraints: they follow a transition from prolate to dumbbell shapes, which culminates in two quasispherical vesicles connected by a small catenoidlike neck. We analyze the geometry and the force of the small neck employing a perturbative analysis about the catenoid. A stretched vesicle initially adopts an oblate shape for either constraint. If the area is fixed the vesicle increasingly flattens until it attains a disklike shape, which we examine using an asymptotic analysis. If the volume is fixed, the poles approach until they touch and the vesicle adopts a discocyte shape. When the spontaneous curvature of the vesicle is close to the mean curvature of the constricted quasispherical vesicles, the sequences of configurations of both constraints develop bifurcations, and some of the configurations corresponding to one of their branches have the lowest energy.

We study a persistent exclusion process with time-periodic external potential on a one-dimensional periodic lattice through numerical simulations. A set of run-and-tumble particles move on a lattice of length $L$ and tumbling probability $\gamma \ll 1$ and interact among each other via hard-core exclusion. The effect of the external potential has been modeled as a special site where the tumbling probability is 1. We call it a "defect" site and move its location along the ring lattice with speed $u$. In the case of $\gamma =0$ the system goes to a jammed state when there is no defect. But introduction of the moving defect creates a strongly phase-separated state where almost all active particles are present in a single large cluster, for small and moderate $u$. This striking effect is caused by the long-range velocity correlation of the active particles, induced by the moving defect. For large $u$, a single large cluster is no longer stable and breaks into multiple smaller clusters. For nonzero $\gamma$ a competition develops between the timescales associated with tumbling and defect motion. While the moving defect attempts to create long-range velocity order, bulk tumbling tends to randomize the velocity alignment. If $\gamma$ is comparable to $u/L$, then a relatively small number of tumbles take place during the time the moving defect travels through the entire system. In this case, the defect has enough time to restore the order in the system and our simulations show that the long-range order in velocity and density survive for $\gamma$ values in this range. As $\gamma$ increases further, long-range order is destroyed and the system develops multiple regions of high and low density. We characterize the density inhomogeneity in this case by measuring subsystem density fluctuations and present a heat map in the $\gamma \text{−}u$ plane showing the regions with most pronounced density inhomogeneities.

Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by the complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, while lacking conventional long-range order, as in liquids and glasses. In this work, we begin a program to quantify the structural properties of nonhyperuniform and hyperuniform networks. In particular, large two-dimensional (2D) Voronoi networks (graphs) containing approximately 10,000 nodes are created from a variety of different point configurations, including the antihyperuniform hyperplane intersection process (HIP), nonhyperuniform Poisson process, nonhyperuniform random sequential addition (RSA) saturated packing, and both non-stealthy and stealthy hyperuniform point processes. We carry out an extensive study of the Voronoi-cell area distribution of each of the networks by determining multiple metrics that characterize the distribution, including their average areas and corresponding variances as well as higher-order cumulants (i.e., skewness ${\gamma }_1$ and excess kurtosis ${\gamma }_2$). We show that the HIP distribution is far from Gaussian, as evidenced by a high skewness (${\gamma }_1=3.16$) and large positive excess kurtosis (${\gamma }_2=16.2$). The Poisson (with ${\gamma }_1=1.07$ and ${\gamma }_2=1.79$) and non-stealthy hyperuniform (with ${\gamma }_1=0.257$ and ${\gamma }_2=0.0217$) distributions are Gaussian-like distributions, since they exhibit a small but positive skewness and excess kurtosis. The RSA (with ${\gamma }_1=0.450$ and ${\gamma }_2=-0.0384$) and the highest stealthy hyperuniform distributions (with ${\gamma }_1=0.0272$ and ${\gamma }_2=-0.0626$) are also non-Gaussian because of their low skewness and negative excess kurtosis, which is diametrically opposite of the non-Gaussian behavior of the HIP. The fact that the cell-area distributions of large, finite-sized RSA and stealthy hyperuniform networks (e.g., with $N\approx 10,000$ nodes) are narrower, have larger peaks, and smaller tails than a Gaussian distribution implies that in the thermodynamic limit the distributions should exhibit compact support, consistent with previous theoretical considerations. Moreover, we compute the Voronoi-area correlation functions $C_{00}\left(r\right)$ for the networks, which describe the correlations between the area of two Voronoi cells separated by a given distance $r$ [M. A. Klatt and S. Torquato, Phys. Rev. E 90, 052120 (2014)]. We show that the correlation functions $C_{00}\left(r\right)$ qualitatively distinguish the antihyperuniform, nonhyperuniform, and hyperuniform Voronoi networks considered here. Specifically, the antihyperuniform HIP networks possess a slowly decaying $C_{00}\left(r\right)$ with large positive values, indicating large fluctuations of Voronoi cell areas across scales. While the nonhyperuniform Poisson and RSA network possess positive and fast decaying $C_{00}\left(r\right)$, we find strong anticorrelations in $C_{00}\left(r\right)$ (i.e., negative values) for the hyperuniform networks. The latter indicates that the large-scale area fluctuations are suppressed by accompanying large Voronoi cells with small cells (and vice versa) in the systems in order to achieve hyperuniformity. In summary, we have shown that cell-area distributions and pair correlation functions of Voronoi networks enable one to distinguish quantitatively antihyperuniform, standard nonhyperuniform, and hyperuniform networks from one another.

Since 1970, the Rössler system has remained as a considerably simpler and minimal-dimensional chaos serving system. Unveiling the dynamics of a system of two coupled chaotic oscillators that lead to the emergence of extreme events in the system is an engrossing and crucial scientific research area. Our present study focuses on the emergence of extreme events in a system of diffusively and bidirectionally two coupled Rössler oscillators and unraveling the mechanism behind the genesis of extreme events. We find the appearance of extreme events in three different observables: average velocity, synchronization error, and one transverse directional variable to the synchronization manifold. The emergence of extreme events in average velocity variables happens due to the occasional in-phase synchronization. The on-off intermittency plays a crucial role in the genesis of extreme events in the synchronization error dynamics and in the transverse directional variable to the synchronization manifold. The bubble transition of the chaotic attractor due to the on-off intermittency is illustrated for the transverse directional variable. We use generalized extreme value theory to study the statistics of extremes. The extreme events data sets concerning the average velocity variable follow a generalized extreme value distribution. The inter-event intervals of the extreme events in the average velocity variable spread well exponentially. The upshot of the interplay between the coupling strength and the frequency mismatch between the oscillators in the genesis of extreme events in the coupled system is depicted numerically.

The main properties of the transient evolution and steady-state generation of fiber lasers with polarization domains of radiation in the laser resonator are investigated based on the constructed Lyapunov functional. The direction of the transient evolution is determined without restrictions on the parameters of the lasing model used and the initial conditions of the transient process. The obtained results are in good agreement with experimental data on the formation of laser radiation polarization domains and domain walls separating these domains from each other.

The study of structures involving vortices in one component and bright solitary waves in another has a time-honored history in two-component atomic Bose-Einstein condensates. In the present work, we revisit this topic, extending considerations well past the near-integrable regime of nearly equal scattering lengths. Instead, we focus on stationary states and spectral stability of such structures for large values of the intercomponent interaction coefficient. We find that the state can manifest dynamical instabilities for suitable parameter values. We also explore a phenomenological, yet quantitatively accurate upon suitable tuning, particle model which, also in line with earlier works, offers the potential of accurately following the associated stability and dynamical features. Finally, we probe the dynamics of the unstable vortex-bright structure, observing an unprecedented, to our knowledge, instability scenario in which the oscillatory instability leads to a patch of vorticity that harbors and eventually ejects multiple vortex-bright structures.

When a millimetric body is placed atop a vibrating liquid bath, the relative motion between the object and the interface generates outward-propagating waves with an associated momentum flux. Prior work has shown that isolated chiral objects, referred to as spinners, can thus rotate steadily in response to their self-generated wavefield. Here, we consider the case of two cochiral spinners held at a fixed spacing from one another but otherwise free to interact hydrodynamically through their shared fluid substrate. Two identical spinners are able to synchronize their rotation, with their equilibrium phase difference sensitive to their spacing and initial conditions, and even cease to rotate when the coupling becomes sufficiently strong. Nonidentical spinners can also find synchrony provided their intrinsic differences are not too disparate. A hydrodynamic wave model of the spinner interaction is proposed, recovering all salient features of the experiment. In all cases, the spatially periodic nature of the capillary wave coupling is directly reflected in the emergent equilibrium behaviors.

We present GenEFT, an effective theory framework for shedding light on the statics and dynamics of neural network generalization, and illustrate it with graph learning examples. We first investigate the generalization phase transition as data size increases, comparing experimental results with information-theory-based approximations. We then introduce an effective theory for the dynamics of representation learning, where latent-space representations are modeled as interacting particles (“repons”), and find that it explains our experimentally observed phase transition between generalization and overfitting as encoder and decoder learning rates are scanned. This highlights the potential of physics-inspired effective theories for bridging the gap between theoretical predictions and practice in machine learning.

With advances in laser technology reaching the multipetawatt era, the expanding experimental prospects for high-order harmonic generation from solid targets prompt more rigorous particle-in-cell (PIC) simulation campaigns for elucidating the generation mechanisms. However, accurately representing a broad range of high frequencies in multidimensional simulations remains challenging. The commonly employed finite difference time domain (FDTD) method, the Yee stencil, introduces artificial numerical dispersion, inducing unphysical angular deviation of higher-order harmonics. This paper uses EPOCH and WarpX PIC codes to present a comprehensive analysis of numerical dispersion mitigation for two-dimensional (2D) simulations of high-order harmonic generation. Results conclude that carefully orienting high-frequency elements within the 2D simulated grid for the standard FDTD scheme can provide significant accuracy improvements at moderate resolution and computational power for cases with a distinct propagation direction for the electromagnetic radiation of interest. This study also evaluates higher-order pseudospectral analytical time-domain (PSATD) solvers, which eliminate angular deviations across all tested angles of incidence and promise to enhance scalability in exascale computing environments.

We investigate the electrostatic interactions between two charged anisotropic conductors using a combination of asymptotic and numerical methods. For widely separated particles, we employ the method of reflections to analyze the interactions. Although the formulation applies to conductors of arbitrary shapes, it is specifically implemented for spheroid-sphere systems to capture anisotropy effects in a simple configuration. In near-contact cases with axisymmetric configurations, the lubrication approximation is used to extend the analysis. Additionally, we develop a boundary integral method to study particle interactions at arbitrary separations, validating the results with asymptotic solutions for both near and far fields. We derive analytical expressions for the electrostatic force and torque on a spheroid due to another spheroid in the far-field regime. When combined with hydrodynamic effects, the electrostatic torque competes with the hydrodynamically favorable alignments of a pair of settling spheroids in certain regions while reinforcing them in others. Consequently, the inclusion of electrostatic effects may influence the instability observed in dilute suspensions of spheroids.

Synchronization forms the basis of many coordination phenomena in natural systems, enabling them to function cohesively and support their fundamental operations. However, there are scenarios where synchronization disrupts a system's proper functioning, necessitating mechanisms to control or suppress it. While several methods exist for controlling synchronization in nonspatially embedded oscillators, to the best of our knowledge, no such strategies have been developed for swarmalators (oscillators that simultaneously move in space and synchronize in time). In this work, we address this gap by introducing a control strategy based on Hamiltonian control theory to suppress synchronization in a system of swarmalators confined to a one-dimensional space. The numerical investigations we performed demonstrate that the proposed control strategy effectively suppresses synchronized dynamics within the swarmalator population. We studied the impact of the number of controlled swarmalators and the strength of the control term in its original form and a simplified one.

A two-dimensional model is designed for intercellular calcium (${\mathrm{Ca}}^{2+}$) waves in the presence of long-range (LR) paracrine coupling due to the action of extracellular messengers and ${\mathrm{Ca}}^{2+}$-activated degradation of inositol 1,4,5-triphosphate (${\mathrm{IP}}_3$) by a $3-kinase$. Using mean-field theory, a statistical variable is defined to detect the emergence of intercellular spiral waves of ${\mathrm{Ca}}^{2+}$. The latter are generated by the local heterogeneity caused by asymmetrical stimulation of the network. It is confirmed that spiral waves may develop when the synchronization degree is low. It is found that balanced LR coupling and ${\mathrm{IP}}_3$ degradation, under appropriate external hormonal stimulation, can effectively control the creation and propagation of spiral waves. A higher LR degree disrupts network synchronization, and only specific ranges of stimulation factor support spiral waves. Weak ${\mathrm{IP}}_3$ degradation and stronger LR degree disintegrate spiral symmetry with increased hormonal stimulation. Strong ${\mathrm{IP}}_3$ degradation has the opposite effect.

The nonequilibrium dynamics of stochastic systems are typically characterized by the joint probability distribution and its time evolution within configuration space or through trajectory ensembles. Within the framework of trajectory ensembles, processes occurring on exponentially rare spatio-temporal scales are of particular interest. Recent research has demonstrated that Doob dynamics is a highly effective method for sampling these rare trajectories. Most existing methods directly sample specific transition trajectories within the trajectory space. However, they fundamentally lack the capacity to resolve the time evolution of configuration-space probability distributions associated with these rare trajectories. In this study, we demonstrate how to construct Doob dynamics by approximating the leading eigenstate of the tilted generator using the variational autoregressive networks (VAN) ansatz. This approach enables us to sample the time-evolution information of the probability distribution associated with rare trajectories and to compute the large deviation statistics. We apply our methodology to two typical lattice models: the East and the Fredrickson-Andersen models, to sample large deviation statistics and probability distributions in one-dimensional and two-dimensional scenarios, respectively. Finally, we discuss the limitations of our method and propose potential solutions.

We study fractional Laplace motion (FLM) obtained from subordination of fractional Brownian motion (FBM) to a gamma process in the presence of an external drift that acts on the composite process or of an internal drift acting solely on the parental process. We derive the statistical properties of this FLM process and find that the external drift does not influence the mean-squared displacement, whereas the internal drift leads to normal diffusion, dominating at long times in the subdiffusive Hurst exponent regime. We also investigate the intricate properties of the probability density function (PDF), demonstrating that it possesses a central Gaussian region whose expansion in time is influenced by FBM's Hurst exponent. Outside of this region, the PDF follows a non-Gaussian pattern. The kurtosis of this FLM process converges toward the Gaussian limit at long times insensitive to the extreme non-Gaussian tails. Additionally, in the presence of the external drift, the PDF remains symmetric and centered at $x=vt$. In contrast, for the internal drift this symmetry is broken. The results of our computer simulations are fully consistent with the theoretical predictions. The FLM model is suitable for describing stochastic processes with a non-Gaussian PDF and long-ranged correlations of the motion.

The differentiation of hematopoietic stem cells has been investigated through extensive experimental studies, establishing a paradigm for stem cell differentiation studies. However, a systematic dynamical analysis of the intricate lineage progression in hematopoiesis has yet to be fully elucidated. In this paper, we construct a dynamical model which allows us to identify seven essential cell states throughout the hierarchical process of hematopoietic differentiation. Starting from common myeloid progenitors, the model tracks the progression through granulocyte-monocyte progenitors and megakaryocyte-erythrocyte progenitors, ultimately giving rise to the generation of monocytes, granulocytes, erythrocytes, and megakaryocytes. By performing systematic perturbations and statistical analyses, we uncover the core networks associated with these cell states and the mechanisms underlying cell fate transitions. For a system of ordinary differential equations describing a known gene regulatory network, by performing random searches within a high-dimensional parameter space, we can create a mapping between specific parameter configurations and diverse cell fates, thus providing profound insights into the intricate processes underlying cellular differentiation. The model presented here provides a comprehensive description of the underlying dynamics and gives deeper insights into the intricate mechanisms of cellular fate determination during the hierarchical cascade of hematopoietic differentiation.

Sperm bundling, swarming, and aggregation are observed in various species, suggesting that grouping enhances motility. In this study, we developed a numerical model of sperm computed by fluid-structure interactions between multiple flagella, showing that hydrodynamic interactions allow the sperm model to form polar orders, in which they swim alongside each other. The time required for order formation depends on the density $n$ and is scaled by $lnn/n$. A wave propagation model controlled by the time derivative of flagellar curvature was introduced to represent flagellar synchronization via hydrodynamic interactions. The polar state results in hydrodynamic flagellar synchronization due to relatively long contact time, which increases swimming speed and flagellar beat speed by approximately 10% compared with no synchronization. During coordinated locomotion, the mechanical power performed by cells is similar to that in isolated systems, but grouping lowers the viscous resistance per cell and increases swimming speed by a factor of 2 compared to solitary swimming under high-density physiological conditions. Thus swimming efficiency increases with density (under physiological conditions, two- to fivefold times higher than in isolated systems). These numerical results show that, in the ordered state, sperm swim faster while expending less energy, suggesting that ordered swimming aids long-distance swimming from an energy perspective.