Charged particle dynamics under the influence of electromagnetic fields is a challenging spatiotemporal problem. Many high-performance physics-based simulators for predicting behavior in a charged particle beam are computationally expensive, limiting their utility for solving inverse problems online. The problem of estimating upstream six-dimensional (6D) phase space given downstream measurements of charged particles in an accelerator is an inverse problem of growing importance. This paper introduces a reverse latent evolution model designed for the temporal inversion of forward beam dynamics. In this two-step self-supervised deep learning framework, we utilize a conditional variational autoencoder (CVAE) to project 6D phase space projections of a charged particle beam into a lower-dimensional latent distribution. Subsequently, we autoregressively learn the inverse temporal dynamics in the latent space using a long short-term memory (LSTM) network. The coupled CVAE-LSTM framework can predict 6D phase space projections across all upstream accelerating sections based on single or multiple downstream phase space measurements as inputs. The proposed model also captures the aleatoric uncertainty of the high-dimensional input data within the latent space. This uncertainty, which reflects potential uncertain measurements at a given module, is propagated through the LSTM network to estimate uncertainty bounds for all upstream predictions, demonstrating the robustness of the LSTM network to random perturbations in the input.

In natural environments, cells move in the presence of multiple physical and chemical guidance cues. Using a model system for such guided cell migration, Dictyostelium discoideum (Dicty), we investigate how chemical and physical signals compete in guiding the motion of cell groups. In Dicty cells, chemical signals can lead to collective streaming behavior, in which cells follow one another head-to-tail and aggregate into clusters of $\sim {10}^5$ cells. We use experiments and numerical simulations to show that streaming and aggregation can be suppressed by the addition of a physical guidance cue of comparable strength to the chemical signals, parallel nanoridges. The bidirectional character of physical guidance by ridges is a determining factor in the suppression of streaming and aggregation. Thus, combining multiple types of guidance cues is a powerful approach to trigger or explain a broad range of collective cell behaviors.

When energy polydispersity is introduced into the Lennard-Jones (LJ) system, there is little effect on structure and dynamics [T. S. Ingebrigtsen and J. C. Dyre, J. Phys. Chem. B 127, 2837 (2023)]. For instance, at a given state point both the radial distribution function and the mean-square displacement as a function of time are virtually unaffected by even large energy polydispersity, which is in stark contrast to what happens when size polydispersity is introduced. We here argue—and validate by simulations of up to 30% polydispersity—that this almost invariance of structure and dynamics reflects an approximate invariance of the constant-potential-energy surface. Because $NVU$ dynamics defined as geodesic motion at constant potential energy is equivalent to Newtonian dynamics in the thermodynamic limit, the approximate invariance of the constant-potential-energy surface implies virtually the same physics of energy polydisperse LJ systems as of the standard single-component version. In contrast, the constant-potential-energy surface is significantly affected by introducing size polydispersity.

The prevailing method for addressing strong-coupling thermodynamics typically involves open quantum systems coupled to infinite baths in equilibrium through the Hamiltonian of mean force (HMF). However, its applicability to finite baths remains limited. In this work, we transcend this limit by considering the impacts of system-bath coupling which is not only on the system but also on the finite bath feedback. When the bath and system sizes are comparable, they act as each other's effective 'bath'. We introduce a parameter $\alpha$ within $[0,1]$, where $\alpha$ and $1-\alpha$ act as weighting factors to distribute the system-bath coupling between the system and the bath. Our approach innovatively incorporates the effect of coupling on the respective effective 'bath' into both the system and bath in the statistical factor form. We generalize the HMF and propose quantum Hamiltonians of mean forces to handle the distributed coupling of the system to finite baths. The additional parameter $\alpha$ is determined by minimizing the joint free energy density and is a new thermodynamic quantity representing the finite bath's influence. Examining the damped quantum harmonic oscillator with a finite bath, we find that $\alpha$ affects both states, leading to a complex phase diagram with unique phenomena at critical temperatures $T_L$ and $T_R$, including valleys, peaks, negative values, and discontinuities in entropy and specific heat. Notably, these anomalies disappear when $\alpha \to 1$, both at high temperatures and in the thermodynamic limit, indicating the negligible influence of coupling on the bath states and reverting to the HMF. Thus, studying finite-sized baths holds substantial significance in small quantum systems.

Through an explicit construction, we assign to any infinite temperature autocorrelation function $C\left(t\right)$ a set of functions ${\alpha }^n\left(t\right)$. The construction of ${\alpha }^n\left(t\right)$ from $C\left(t\right)$ requires the first $2n$ temporal derivatives of $C\left(t\right)$ at times 0 and $t$. Our focus is on ${\alpha }^n\left(t\right)$ that (almost) monotonously decrease; we call these “arrows of time functions” (AOTFs). For autocorrelation functions of few-body observables we numerically observe the following: An AOTF featuring a low $n$ may always be found unless the system is in or close to a nonchaotic regime with respect to a variation of some system parameter. All ${\alpha }^n\left(t\right)$ put upper bounds to the respective autocorrelation functions, i.e., ${\alpha }^n\left(t\right)\ge C^2\left(t\right)$. Thus the implication of the existence of an AOTF is comparable to that of the H theorem, as it indicates a directed approach to equilibrium. We furthermore argue that our numerical finding may to some extent be traced back to the operator growth hypothesis. This argument is laid out in the framework of the so-called recursion method.

The spread of disinformation (maliciously spread false information) in online social networks has become an important problem in today's society. Disinformation's spread is facilitated by the fact that individuals often accept false information based on cognitive biases which predispose them to believe information that they have heard repeatedly or that aligns with their beliefs. Moreover, disinformation often spreads in direct competition with corresponding true information. To model these phenomena, we develop a model for two competing beliefs spreading on a social network, where individuals have an internal opinion that models their cognitive biases and modulates their likelihood of adopting one of the competing beliefs. By numerical simulations of an agent-based model and a mean-field description of the dynamics, we study how the long-term dynamics of the spreading process depend on the initial conditions for the number of spreaders and the initial opinion of the population. We find that the addition of cognitive biases enriches the transient dynamics of the spreading process, facilitating behavior such as the revival of a dying belief and the overturning of an initially widespread opinion. Finally, we study how external recruitment of spreaders can lead to the eventual dominance of one of the two beliefs.

We calibrate a Kuramoto-model-inspired representation of peer-to-peer collaboration using data on the maximum team size where coordination breaks down. The Kuramoto model is modified, normalizing the coupling by the degree of input and output nodes, reflecting dispersion of cognitive resources in both absorbing incoming- and tracking outgoing-information. We find a critical point, with loss of synchronization as the number of nodes grows and analytically determine this point and calibrate the coupling with the known maximum team size. We test that against the known “span of control” for a leader/supervisor organization. Our results suggest larger maximum team sizes than early management science proposes, but are consistent with studies that focus only the relationship between supervisor and subordinates, excluding other internal interactions in the team.

We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evolution of (suitably defined) mean fields coupled to marginally stable, fast fluctuation fields. By exploiting this scale separation, an efficient hybrid fast-eigenvalue/slow-initial-value solution algorithm can be developed in which the amplitude of the fast fluctuations is slaved to the slowly evolving mean fields to ensure marginal stability—and temporal scale separation—is maintained. For 2D systems, the fluctuation eigenfunctions are labeled by their Fourier wave numbers characterizing spatial variability in that extended spatial direction, and the marginal mode(s) must coincide with the fastest-growing mode(s) over all admissible Fourier wave numbers. Here we derive an ordinary differential equation governing the slow evolution of the wave number of the fastest-growing fluctuation mode that simultaneously must be slaved to the mean dynamics to ensure the mode has zero growth rate. We illustrate the procedure in the context of a 2D model partial differential equation that shares certain attributes with the equations governing strongly stratified shear flows and other strongly constrained forms of geophysical turbulence in extreme parameter regimes. The slaved evolution follows one or more marginal stability manifolds, which constitute select state-space structures that are not invariant under the full flow dynamics yet capture quasicoherent structures in physical space in a manner analogous to invariant solutions identified in, e.g., transitionally turbulent shear flows. Accordingly, we propose that marginal stability manifolds are central organizing structures in a dynamical systems description of certain classes of multiscale flows in which scale separation justifies a QL approximation of the dynamics.

In this work, we introduce a neural network algorithm designed to automatically identify similarity relations from data. By uncovering these similarity relations, our network approximates the underlying physical laws that relate dimensionless quantities to their dimensionless variables and coefficients. Additionally, we develop a linear algebra framework, accompanied by code, to derive the symmetry groups associated with these similarity relations. While our approach is general, we illustrate its application through examples in fluid mechanics, including laminar Newtonian and non-Newtonian flows in smooth pipes, as well as turbulent flows in both smooth and rough pipes. Such examples are chosen to highlight the framework's capability to handle both simple and intricate cases, and further validate its effectiveness in discovering underlying physical laws from data.

The dynamic properties of an interfacial flow between heavy and light incompressible fluids that are initially Rayleigh-Taylor unstable and are subjected to an external acceleration field oriented in opposition to the density gradient are studied. Rayleigh-Taylor instability occurs in nature with a constant acceleration driven by gravity. However, there are some engineering applications, such as high-energy-density processes observed in inertial and magnetic confined fusion capsules where the acceleration field is not constant. In those applications, Rayleigh-Taylor instability is known to evolve under time-varying acceleration profiles, a phenomenon also observed in supernova formation. Here, we perform implicit large-eddy simulations of density stratification under time-dependent acceleration profiles. Most earlier studies of Rayleigh-Taylor instability under variable acceleration have used a sequence of step functions to simulate acceleration reversals (accel-decel-accel). For the current study, we use a sinusoidal profile, which allows a smoother transition between acceleration and deceleration, and represents smooth transitions that occur in engineering and astrophysical applications. For various imposed acceleration profiles, we compare spatially averaged statistics of the evolving flow against a straightforward and widely utilized scaling, the double integral of acceleration. It will be shown here that this scaling allows distinction between the mean behaviors due to the stepwise and the smooth acceleration profiles and, importantly, that the flow tends to move towards self-similar evolution quicker when the acceleration profile is smoother.

The magnetohydrodynamic (MHD) instability in the HL-2A tokamak has been comprehensively studied, including ideal MHD ballooning and kink modes, as well as the operational $\beta$ limit imposed jointly by them. It shows an internal ballooning mode appearing in the plasma with parabolic pressure and current density profiles exhibited in the case with a higher $\beta$ ($\beta$ is the ratio of thermal to magnetic pressures). The joint effects of the safety factor and $\beta$, as well as the structural features of various $n$ (toroidal mode number) kink modes were investigated. The combination of the axial and edge safety factors, ($q_0,q_a$), leads to a corresponding equilibrium, and its stability is determined by both the safety factors and $\beta$. Multiple $n$ kink branches can coexist in the plasma. At a higher $\beta$ value (${\beta }_p=2$) for the case $q_0=0.95$, $n=1,2,3$ and 4 kinks are generally internal modes, dominated by the $\left(m\right[=n],n)$ branch. Here $m$ is the poloidal mode number. When $q_0=1.05$ and $q_0=1.3$, the $n>1$ kink mode is generally an external mode. The larger $q_0$ is compared to one, the more unstable the system becomes, and the more complex the mode structure changes with $n$. The $\beta$ limit imposed by the kink modes in the HL-2A limiter discharge is close to that of the ballooning mode, and the maximum normalized $\beta$, ${\beta }_N$, is both ${\beta }_N^c\approx 2.0$, whereas the kink $\beta$ limit in the divertor discharge (${\beta }_N^c=2.5$) is much higher than the ballooning $\beta$ limit (${\beta }_N^c\approx 1.9$). This indicates that the introduction of a divertor configuration in HL-2A is effective in increasing the kink $\beta$ limit rather than the ballooning $\beta$ limit. The maximum $\beta$ that can be achieved by the HL-2A divertor discharge is affected by the internal ballooning modes and is somewhat lower than the kink $\beta$ limit, except for the high-performance discharge.

A gradient of a single salt in a solution generates an electric field but not a current. Recent theoretical work by one of us [P. B. Warren, Phys. Rev. Lett. 124, 248004 (2020)] showed that the Nernst-Planck equations imply that crossed gradients of two or more different salts generate ion currents. These currents in solution have associated nonlocal electric fields. Particle motion driven by these nonlocal fields has recently been observed in experiment by Williams et al. [Phys. Rev. Fluids 9, 014201 (2024)], a phenomenon which was dubbed action-at-a-distance diffusiophoresis. Here we use a magnetostatic analogy to show that in the far-field limit, these nonlocal currents and electric fields both have the functional form of the magnetic field of a magnetic dipole, decaying as $r^{-d}$ in $d=2$ and $d=3$ dimensions. These long-ranged electric fields are generated entirely within solutions and have potential practical applications since they can drive both electrophoretic motion of particles and electro-osmotic flows. The magnetostatic analogy also allows us to import tools and ideas from classical electromagnetism into the study of multicomponent salt solutions.

Geometry and topology play a fundamental role in determining pattern formation on 2D surfaces in condensed matter physics. For example, local positive Gaussian curvature of a 2D surface attracts positive topological defects in a liquid crystal phase confined to the curved surface while repelling negative topological defects. Although the cone geometry is flat on the flanks, the concentrated Gaussian curvature at the cone apex geometrically frustrates liquid crystal orientational fields arbitrarily far away. The apex acts as an unquantized pseudodefect interacting with the topological defects on the flank. By exploiting the conformal mapping methods of Vafa et al. [Phys. Rev. E 106, 024704 (2022)], we explore a simple theoretical framework to understand the ground states of liquid crystals with $p$-fold rotational symmetry on cones and uncover important finite-size effects for the ground states with boundary conditions that confine both plus and minus defects to the cone flanks. By combining the theory and simulations, we present results for liquid crystal ground states on cones with antitwist boundary conditions at the cone base, which enforce a total topological charge of $-1$. We find that additional quantized negative defects are created on the flank as the cone apex becomes sharper via a defect unbinding process, such that an equivalent number of quantized positive defects become trapped at the apex, thus partially screening the apex charge, whose magnitude is a continuous function of cone angle.

It is well known that a pile of grains starts and stops flowing at different angles of repose. It is also known that such starting and stopping angles exhibit thickness-dependent behavior, with deeper layers beginning to flow more readily and arresting at lower angles than shallower materials. These considerations have motivated various rheological assumptions in granular constitutive laws. This paper demonstrates that such observations can instead be partly attributed to inertial effects. In particular, we examine the roles of two control parameters characterizing conventional chute flow experiments: the rate of inclination of the chute, and the threshold surface velocity associated with identification of the flow. Both of these parameters control the system's momentum at different instances. We perform two-dimensional discrete element simulations and also develop a one-dimensional analytic model based on the standard $\mu \left(I\right)$ rheology. Results indeed indicate a difference between the starting and stopping angles as well as a thickness dependency, despite the absence of any hysteresis or material length scale in the underlying rheological model. Higher threshold velocities are shown to produce higher angles at which flow begins. In addition, the starting (stopping) angle increases (decreases) with the applied inclination rate. For thick enough granular layers, no matter how small the rate is, critical angles are shown to deviate from the quasistatic limit. Therefore, inertial effects should not a priori be neglected. To finalize our argument, we show the effect of the inclination rate and the threshold velocity in a laboratory setup, using small-scale experiments of an inclined chute.

Biomolecular condensates play a central role in the spatial organization of living matter. Their formation is now well understood as a form of liquid-liquid phase separation that occurs very far from equilibrium. For instance, they can be modeled as active droplets, where the combination of molecular interactions and chemical reactions result in microphase separation. However, so far, models of chemically active droplets are spatially continuous and deterministic. Therefore, the relationship between the microscopic parameters of the models and some crucial properties of active droplets (such as their polydispersity, their shape anisotropy, or their typical lifetime) is yet to be established. In this work, we address this question computationally, using Brownian dynamics simulations of chemically active droplets: the building blocks are represented explicitly as particles that interact with attractive or repulsive interactions, depending on whether they are in a droplet-forming state or not. Thanks to this microscopic and stochastic view of the problem, we reveal how driving the system away from equilibrium in a controlled way determines the fluctuations and dynamics of active emulsions.

Granular flows in small-outlet hoppers exhibit several characteristic but poorly understood behaviors: temporary clogs (pauses) where flow stops before later spontaneously restarting, permanent clogs that last indefinitely, and non-Gaussian, nonmonotonic flow-rate statistics. These aspects have been studied independently, but a model of hopper flow that explains all three has not been formulated. Here, we introduce a phenomenological model that provides a unifying dynamical mechanism for all three behaviors: coupling between the flow rate and a hidden mode that controls the stability of clogs. In the theory, flow rate evolves according to Langevin dynamics with multiplicative noise and an absorbing state at zero flow, conditional on the hidden mode. The model fully reproduces the statistics of pause and clog events of a large ($>40000$ flows) experimental dataset, including nonexponentially distributed clogging times and non-Gaussian flow rate distribution, and explains the stretched-exponential growth of the average clogging time with outlet size. Further, we identify the physical nature of the hidden mode in microscopic configurational features, including size and smoothness of the static arch structure formed during pauses and clogs. Our work provides a unifying framework for several poorly understood clogging phenomena, and suggests numerous new paths toward further understanding of this complex system.

We present a self-consistent theory for sound propagation in a simple model of a disordered solid. The solid is modeled as a collection of randomly distributed particles connected by harmonic springs with strengths that depend on the interparticle distances, i.e., the Euclidean random matrix model of Mézard et al. [Nucl. Phys. B 559, 689 (1999)]. The derivation of the theory combines two exact projection operator steps and a factorization approximation. Within our approach, the square of the speed of sound is non-negative. We expect that an unjamming transition would manifest itself through the vanishing of the speed of sound.

We explore the fractional advection-diffusion equation and rare events associated with the ACTRW model. When waiting times have a finite mean but infinite variance, and the displacements follow a narrow distribution, the fractional operator is defined in terms of space rather than time. The far tail of the positional distribution is governed by rare events, which exhibit a different scaling compared to typical fluctuations. Additionally, we establish a strong relationship between the number of renewals and the positional distribution in the context of large deviations. Throughout the manuscript, the theoretical results are validated through simulations.