Rayleigh-Taylor (RT) instabilities are prevalent in many physical regimes ranging from astrophysical to laboratory plasmas and have primarily been studied using fluid models, the majority of which have been ideal fluid models. This work presents a five-dimensional (two spatial dimensions, three velocity space dimensions) simulation using the continuum-kinetic model to study the effect of the collisional mean free path and transport on the instability growth. The continuum-kinetic model provides noise-free access to the full particle distribution function permitting a detailed investigation of the role of kinetic physics in hydrodynamic phenomena such as the RT instability. For long mean free path, there is no RT instability growth, but as collisionality increases, particles relax towards the Maxwellian velocity distribution, and the kinetic simulations reproduce the fluid simulation results. An important and novel contribution of this work is in the intermediate collisional cases that are not accessible with traditional fluid models and require kinetic modeling. Simulations of intermediate collisional cases show that the RT instability evolution is significantly altered compared to the highly collisional fluidlike cases. Specifically, the growth rate of the intermediate collisionality RT instability is lower than the high collisionality case while also producing a significantly more diffused interface. The higher moments of the distribution function play a more significant role relative to inertial terms for intermediate collisionality during the evolution of the RT instability interface. Particle energy flux is calculated from moments of the distribution and shows that transport is significantly altered in the intermediate collisional case and deviates much more so from the high collisionality limit of the fluid regime.

The laser wakefield acceleration of monoenergetic multi-GeV electron beams in the bubble regime is investigated via particle-in-cell simulations considering laser guiding of sub-petawatt pulses by an optimized plasma waveguide. The density profile of the plasma has a transverse transition from a low value for the laser guiding central channel to an optimal higher value for the surrounding plasma. Multidimensional particle-in-cell simulations in the nonlinear bubble regime show that when the spot size of the Gaussian laser pulse is matched to the diameter of the low-density laser-guiding plasma channel, electron self-injection can be transversely provided from the surrounding high-density plasma mitigating the need for a minimum electron density of the low-density channel to trigger the self-injection. Accordingly, the pump depletion and electron dephasing lengths can be increased by reducing the electron density of the axial channel, and the electron bunch can be accelerated to considerably longer distances. As a result, the energy gain of the trapped electrons, injected from the surrounding high-density region, can be efficiently enhanced. Under such conditions, a completely localized electron bunch with considerably decreased energy spread $(<2\%)$ and enhanced peak energy $\left(\sim 2.5\mathrm{GeV}\right)$ is accelerated over a length of $\sim 6\mathrm{mm}$ by a sub-petawatt laser pulse $\left(\sim 86\mathrm{TW}\right)$.

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine learning method where the optimization process of the network depends solely on the predicted functions without using any ground truth data. The model learns solutions that satisfy, up to an arbitrarily small error, Hamilton's equations and, therefore, conserve the Hamiltonian invariants. The choice of an appropriate activation function drastically improves the predictability of the network. Moreover, an error analysis is derived and states that the numerical errors depend on the overall network performance. The Hamiltonian network is then employed to solve the equations for the nonlinear oscillator and the chaotic Hénon-Heiles dynamical system. In both systems, a symplectic Euler integrator requires two orders more evaluation points than the Hamiltonian network to achieve the same order of the numerical error in the predicted phase space trajectories.

We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that mean square displacement relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading order contribution to the probability density function (PDF) of a Gaussian propagator under resetting exhibits a cusp independent of the specific details of the reset time distribution. For subdiffusion we derive the PDF in Laplace space for arbitrary resetting protocol. Resetting at constant rate allows evaluation of the PDF in terms of $H$ function. We analyze the steady state and derive the rate function governing the relaxation behavior. For a subdiffusive process the steady state could exist even if the distribution of reset times possesses only finite mean.

Diffusion of a Brownian particle along a stochastic harmonic oscillator chain is investigated. In contrast to the usually discussed Brownian motion driven by Gaussian white noise, the particle at high temperatures performs long Lévy flights. At high temperatures $T$ the diffusion coefficient scales as $D\sim T^{2+\alpha }$, where the parameter $\alpha$ determine the average damping force $\propto 1/\left(T^{\alpha }P\right)$ on the particle at large momentum $P$ and at high temperature. The exponent $\alpha$ depends on the particle-chain interaction and chain properties. It is shown that the mean time ${\overline{t}}_f$ necessary to perform a flight of $l$ lattice constant scales with $l$ as ${\overline{t}}_f\propto l^{2/3}$ at high temperatures and flight lengths. Last, the flight length probability distribution is found to decay as $1/l^{\beta }$ with the exponent $\beta =4/3$ being universal, i.e., independent of the model parameters.

Lattice Monte Carlo (LMC) simulations are widely used to investigate diffusion-controlled problems such as drug-release systems. The presence of an inhomogeneous diffusivity environment raises subtle questions about the interpretation of stochastic dynamics in the overdamped limit, an issue sometimes referred to as the “Ito-Stratonovich-isothermal dilemma.” We propose a LMC formalism that includes the different stochastic interpretations in order to model the diffusion of particles in a space-dependent diffusivity landscape. Using as an example a simple inhomogeneous one-dimensional system with a diffusivity interface and different boundary conditions, we demonstrate that we can properly reproduce the steady state and dynamic properties of these systems and that these properties do depend on the choice of calculus. In particular, we argue that the version of the LMC algorithm that uses Ito calculus, which is commonly used to model drug delivery systems, should be replaced by the isothermal version for most applications. Our LMC methodology provides an efficient alternative to Langevin simulations for a wide class of space-dependent diffusion problems.

For heat engines (including refrigerators) the separation of total entropy production in reversible parts $\mathrm{\Delta }S$ and irreversible contributions has proved to be very useful. The $\mathrm{\Delta }S$ are entropies for ideal lossless processes at the hot- and cold side and are important system parameters. For Carnot-like heat engines performing finite-time cycles, the concern was raised in a preceding paper that the $\mathrm{\Delta }S$ are not always independent from irreversibilities, if initial and final working fluid temperatures $T_f\left(t\right)$ differ in the isothermal transitions. It turns out that the $\mathrm{\Delta }S$ are unchanged and independent, if $T_f$ $\left(t\right)$ evolution is optimized for entropy minimization and apparent inconsistencies are cleared up. If nonisentropic transitions in the adiabatic cycle branches are taken into account, the difference of cold- and hot-side entropy reversibilities is equal to the entropy production in the adiabats. Maximization of cooling power is studied for various irreversible entropy models. The concepts are extended to noncyclic steady-state engines. Power maximization and efficiency calculations are performed exactly analytically. This serves as prerequisite for the hitherto unsolved problem of an accurate definition of reversible and irreversible entropy parts in thermoelectric (TE) converters in the case of inhomogeneous three-dimensional material distributions. It is revealed that for nonconstant Seebeck coefficients, additional terms to the Joule heat arise that destroy positive generator performance in the limit of heat conductance $k\to 0$, in contrast to the traditional constant material properties model. Thus, the concept of improving TE materials by reducing $k$ is in question and an adapted figure of merit $Z$ is presented to deal with the situation.

Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalization gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimized given a specific realization of the remaining weights. We show how these results—combined with ideas from statistical learning theory—provide a stringent asymptotic upper bound on the generalization gap of fully trained DNN as a function of the size of the dataset $P$. In particular, in the limit of large $P$ and $N_{\text{out}}$ (where $N_{\text{out}}$ is the size of the last layer) and $N_{\text{out}}\ll P$, the generalization gap approaches zero faster than $2N_{\text{out}}/P$, for any choice of both architecture and teacher function. Notably, this result greatly improves existing bounds from statistical learning theory. We test our predictions on a broad range of architectures, from toy fully connected neural networks with few hidden layers to state-of-the-art deep convolutional neural networks.

Bacteria meticulously regulate their intracellular ion concentrations and create ionic concentration gradients across the bacterial membrane. These ionic concentration gradients provide free energy for many cellular processes and are maintained by transmembrane transport. Given the physical dimensions of a bacterium and the stochasticity in transmembrane transport, intracellular ion concentrations and hence the charge state of a bacterium are bound to fluctuate. Here we investigate the charge noise of hundreds of nonmotile bacteria by combining electrical measurement techniques from condensed matter physics with microfluidics. In our experiments, bacteria in a microchannel generate charge density fluctuations in the embedding electrolyte due to random influx and efflux of ions. Detected as electrical resistance noise, these charge density fluctuations display a power spectral density proportional to $1/f^2$ for frequencies $0.05\mathrm{Hz}\le f\le 1\mathrm{Hz}$. Fits to a simple noise model suggest that the steady-state charge of a bacterium fluctuates by $\pm 1.30\times {10}^{6}e(e\approx 1.60\times {10}^{-19}\mathrm{C})$, indicating that bacterial ion homeostasis is highly dynamic and dominated by strong charge noise. The rms charge noise can then be used to estimate the fluctuations in the membrane potential; however, the estimates are unreliable due to our limited understanding of the intracellular concentration gradients.

Vertex models, such as those used to describe cellular tissue, have an energy controlled by deviations of each cell area and perimeter from target values. The constrained nonlinear relation between area and perimeter leads to new mechanical response. Here we provide a mean-field treatment of a highly simplified model: a uniform network of regular polygons with no topological rearrangements. Since all polygons deform in the same way, we only need to analyze the ground states and the response to deformations of a single polygon (cell). The model exhibits the known transition between a fluid/compatible state, where the cell can accommodate both target area and perimeter, and a rigid/incompatible state. We calculate and measure the mechanical resistance to various deformation protocols and discover that at the onset of rigidity, where a single zero-energy ground state exists, linear elasticity fails to describe the mechanical response to even infinitesimal deformations. In particular, we identify a breakdown of reciprocity expressed via different moduli for compressive and tensile loads, implying nonanalyticity of the energy functional. We give a pictorial representation in configuration space that reveals that the complex elastic response of the vertex model arises from the presence of two distinct sets of reference states (associated with target area and target perimeter). Our results on the critically compatible tissue provide a new route for the design of mechanical metamaterials that violate or extend classical elasticity.

By means of the direct simulation Monte Carlo method, the effect of rarefaction on the heat fluxes and the hydrodynamics of a granular gas bounded by thermal walls is investigated. The heat flux is found to evolve nonmonotonically with the particle inelasticity due to the competition between the particle inelasticity and rarefaction. The former enhances the heat flux, and the latter reduces the heat flux. As the particles become more inelastic, the onset of the heat flux diminishment due to rarefaction is found to be signaled by a temperature gradient collapse. The same temperature gradient convergence, which precedes the rarefied-reduced heat flux, is also found as the applied temperature gradient is increased.

We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid turbulence and estimate the scale at which they become important. As anticipated by Betchov in a prescient series of works more than six decades ago, this scale is about equal to the Kolmogorov length, even though that is several orders of magnitude above the mean free path. This result implies that the deterministic version of the incompressible Navier-Stokes equation is inadequate to describe the dissipation range of turbulence in molecular fluids. Within this range, the fluctuating hydrodynamics equation of Landau and Lifschitz is more appropriate. In particular, our analysis implies that both the exponentially decaying energy spectrum and the far-dissipation-range intermittency predicted by Kraichnan for deterministic Navier-Stokes will be generally replaced by Gaussian thermal equipartition at scales just below the Kolmogorov length. Stochastic shell model simulations at high Reynolds numbers verify our theoretical predictions and reveal furthermore that inertial-range intermittency can propagate deep into the dissipation range, leading to large fluctuations in the equipartition length scale. We explain the failure of previous scaling arguments for the validity of deterministic Navier-Stokes equations at any Reynolds number and we provide a mathematical interpretation and physical justification of the fluctuating Navier-Stokes equation as an “effective field theory” valid below some high-wave-number cutoff $\mathrm{\Lambda }$, rather than as a continuum stochastic partial differential equation. At Reynolds number around a million, comparable to that in Earth's atmospheric boundary layer, the strongest turbulent excitations observed in our simulation penetrate down to a length scale of about eight microns, still two orders of magnitude greater than the mean free path of air. However, for longer observation times or for higher Reynolds numbers, more extreme turbulent events could lead to a local breakdown of fluctuating hydrodynamics.

Ten different thermodynamic properties of the noble gas argon in the liquid and supercritical regions were obtained from semiclassical Monte Carlo simulations in the isothermal-isobaric ensemble using ab initio potentials for the two-body and nonadditive three-body interactions. Our results for the density and speed of sound agree with the most accurate experimental data for argon almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This demonstrates the high predictive but yet unexploited power of ab initio potentials in the field of molecular modeling and simulation for thermodynamic properties of fluids.

In this paper, we construct quantum analogs starting from classical stochastic processes, by replacing random “which path” decisions with superpositions of all paths. This procedure typically leads to nonunitary quantum evolution, where coherences are continuously generated and destroyed. In spite of their transient nature, these coherences can change the scaling behavior of classical observables. Using the zero temperature Glauber dynamics in a linear Ising spin chain, we find quantum analogs with different domain growth exponents. In some cases, this exponent is even smaller than for the original classical process, which means that coherence can play an important role to speed up the relaxation process.

It is usually expected that time delays cause oscillations in dynamical systems—there might appear cycles around stationary points. Here we study random walks with asymmetric time delays. In our models, the probability of a walker to move to the right or to the left depends on the difference between two state-dependent fitness functions evaluated at two different times. We observe a different behavior—a dependence of the mean position of the walker on time delays. Moreover, the effect of time delays is reversed when one shifts (in a symmetric way) fitness functions. This is a joint effect of both stochasticity and time delays present in the system. The position of a random walker may be interpreted as a frequency of a given strategy in discrete replicator dynamics of evolutionary games. Then our results show that the effect of asymmetric time delays on the equilibrium structure of a population depends not only on time delays, but also on details of the fitness functions.

We outline an approach to calculating the quantum mechanical propagator in the presence of geometrically nontrivial Dirichlet boundary conditions. The method is based on a generalization of an integral transform of the propagator studied in previous work (the so-called “hit function”) and a convergent sequence of Padé approximants that exposes the limit of perfectly reflecting boundaries. In this paper the generalized hit function is defined as a many-point propagator, and we describe its relation to the sum over trajectories in the Feynman path integral. We then show how it can be used to calculate the Feynman propagator. We calculate analytically all such hit functions in $D=1$ and $D=3$ dimensions, giving recursion relations between them in the same or different dimensions and apply the results to the simple cases of propagation in the presence of perfectly conducting planar and spherical plates. We use these results to conjecture a general analytical formula for the propagator when Dirichlet boundary conditions are present in a given geometry, also explaining how it can be extended for application for more general, nonlocalized potentials. Our work has resonance with previous results obtained by Grosche in the study of path integrals in the presence of delta potentials. We indicate the eventual application in a relativistic context to determining Casimir energies using this technique.

Medical resources are crucial in mitigating epidemics, especially during pandemics such as the ongoing COVID-19. Thereby, reasonable resource deployment inevitably plays a significant role in suppressing the epidemic under limited resources. When an epidemic breaks out, people can produce resources for self-protection or donate resources to help others for treatment. That is, the exchange of resources also affects the transmission between individuals, thus, altering the epidemic dynamics. To understand factors on resource deployment and the interplay between resource and transmission we construct a metapopulation network model with resource allocation. Our results indicate actively or promptly donating resources is not helpful to suppress the epidemic under both homogeneous population distribution and heterogeneous population distribution. Besides, strengthening the speed of resources production can significantly increase the recovery rate so that they reduce the final outbreak size. These results may provide policy guidance toward epidemic containment.

We use the Parsons-Lee modification of Onsager's second virial theory within the restricted orientation (Zwanzig) approximation to analyze the phase behavior of hard cylindrical rods confined in narrow pores. Depending on the wall-to-wall separation we predict a number of distinctly different surface-generated nematic phases, including a biaxial planar nematic with variable number of layers, a monolayer homeotropic, and a hybrid T-type structure (a planar layer combined with a homeotropic one). For narrow pores, we find evidence of two types of second-order uniaxial-biaxial transitions depending on the aspect ratio of the particles. More specifically, we observe a continuous crossover from $n$ to $n+1$ layers, each with a distinct planar anchoring symmetry as well as first-order transitions from planar to homeotropic surface anchoring. Contrary to the previously studied case of parallelepipeds we find that the surface anchoring transition from planar to homeotropic symmetry occurs at much lower overall rod packing fractions. This renders the observation of homeotropic capillary nematics much more realistic in experimental systems of strongly confined anisotropic colloids. Unlike confined parallelepipeds, cylindrical rods gradually increase the number of the nematic planar layers (without any phase transitions). However, a weakly first-order transition was observed between two planar structures with $n$ and $n+1$ layers in wide pores and longer rods. In addition, the cylindrical rods exhibit a first-order transition from the homeotropic structure to the uniaxial (or biaxial) T phase that has not been observed in confined hard parallelepipeds. We further demonstrate a reentrant uniaxial-biaxial-uniaxial-biaxial phase sequence for confined cylinders at small aspect ratio. Our results also clearly demonstrate that stable T-type surface ordering is a subtle capillary effect that only becomes manifest in sufficiently narrow pores away from the two-dimensional bulk limit.

A detailed parametric study on the linear stability analysis of a three-dimensional thin liquid film flowing down a uniformly heated slippery inclined plane is carried out for disturbances of arbitrary wavenumbers, where the liquid film satisfies Newton's law of cooling at the film surface. A coupled system of boundary value problems is formulated in terms of the amplitudes of perturbation normal velocity and perturbation temperature, respectively. Analytical solution of the boundary value problems demonstrates the existence of three dominant modes, the so-called H mode, S mode, and P mode, where the S mode and P mode emerge due to the thermocapillary effect. It is found that the onset of instabilities for the H mode, S mode, and P mode reduces in the presence of wall slip and leads to a destabilizing influence. Numerical solution based on the Chebyshev spectral collocation method unveils that the finite wavenumber H-mode instability can be stabilized, but the S-mode instability and the finite wavenumber P-mode instability can be destabilized by increasing the value of the Marangoni number. On the other hand, the Biot number shows a dual role in the H-mode and S-mode instabilities. But the P-mode instability can be made stable with the increasing value of the Biot number and the decreasing values of the Marangoni number and the Prandtl number. Furthermore, the H-mode and S-mode instabilities become weaker, but the P-mode instability becomes stronger, with the increasing value of the spanwise wavenumber. In addition, the shear mode emerges in the numerical simulation when the Reynolds number is large, which can be destabilized slightly with the increasing value of the Marangoni number; however, it can be stabilized with the increasing value of the slip length and introducing the spanwise wavenumber to the infinitesimal perturbation.

This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights alter with time through a rate-based adaptive mechanism inspired by the Hebbian learning rule. These simultaneously evolving disparate adaptive coupling weights lead to a phenomenon in that the in-phase synchronization is completely obliterated; instead, the antiphase synchronization is originated. In addition, the onsets of antiphase synchronization and desynchronization are manageable through both dyadic and triadic learning rates. The theoretical validation of these numerical assessments is delineated thoroughly by employing Ott-Antonsen dimensionality reduction. The framework and results of the Letter would help understand the underlying synchronization behavior of a range of real-world systems, such as the brain functions and social systems where interactions evolve with time.