The present paper analyzes the typical unified lattice Boltzmann (LB) models for different convection-diffusion (CD) problems in multiphase systems. The CD problems in multiphase systems can be roughly classified into three groups: CD problems with a continuous scalar value and a continuous flux, a discontinuous scalar value and a continuous flux, a continuous scalar value and a discontinuous flux. The characteristics of the corresponding unified LB models for the three kinds of CD problems are analyzed and the equivalence between the LB models based on different perspectives or numerical schemes is revealed. Finally, a comprehensive multiphase LB model (CMLBM) capable of solving different isotropic and anisotropic CD problems in multiphase systems is proposed. Four typical CD problems in multiphase systems are calculated to validate the CMLBM; the results show that it performs well against the typical isotropic and anisotropic CD problems in multiphase systems.

The unique nanometer-sized helical structure in $\mathrm{Sm}{C}_{\alpha }^{*}$ may sometimes evolve continuously to the micrometer-sized one in $\mathrm{Sm}{C}^{*}$; conceivably ferroelectric $\mathrm{Sm}{C}_{\alpha }^{*}$ is to be unwound by an applied electric field. By drawing electric-field-induced birefringence contours in the field-temperature phase diagram and by studying the superlattice structure of the field-induced subphase with resonant x-ray scattering, we established that an applied field unexpectedly stabilizes the well-known antiferroelectric four-layer biaxial subphase as well as the other prototypal ferrielectric three-layer one in the $\mathrm{Sm}{C}_{\alpha }^{*}$ temperature range; the effective long-range interlayer interaction due to the discrete flexoelectric effect actually plays an important role in stabilizing not only the biaxial subphases but also the optically uniaxial $\mathrm{Sm}{C}_{\alpha }^{*}$ subphase, contrary to the notion that the competition between the direct interactions of the nearest-neighbor layers and those of the next-nearest-neighbor layers should be required for the nanometer-sized helical structure.

We explicitly consider the spatial profile of the light field in the study of exciton transport through a one-dimensional molecular aggregate in the cavity. When the scale of the aggregate is comparable with the cavity wavelength, the resultant exciton-photon coupling strength varies with the position of each monomer. Such effect is explicitly included in a quantum master equation describing the dynamics of the excitonic, photonic, and vibrational modes. By investigating the steady-state exciton currents, we show that the strong and spatially varying exciton-photon coupling dominates the exciton transport and significantly enhances the transport efficiency. With suitable intermonomer distance, the delocalized polaronic mode generates more occupation on the acceptor monomer than the bridge monomers and thus makes it a more efficient channel for exciton transfer. The effects of localized vibrations are also investigated, and the vibration-assisted exciton transport is demonstrated with strong exciton-vibration coupling. Our results show that the vibrational modes are not as significant as the spatially varying exciton-photon couplings in affecting the exciton transport.

The friction coefficient of molecular solutes depends on the solute, on the solvent, and on the solute-solvent interactions, but is typically assumed to not depend on an externally applied force that acts on the solute. In this paper we compute the friction memory function from molecular dynamics simulations and show that the friction coefficients of harmonically confined methane, water, ${\mathrm{Na}}^{+}$, an artificial ${\mathrm{Na}}^{-}$ ion, and glycerol in water in fact increase with confinement strength. The results show that the friction increase with confinement strength is a fundamental effect that occurs for hydrophobic, hydrophilic, as well as charged molecules. We demonstrate that a parameter-free extraction of the running integral over the memory function yields the most robust results when compared to methods based on parametrization or Fourier transforms. In all systems, this friction increase is accompanied by a slowdown of the solvent dynamics in the first hydration shell of the solutes. By simulations of a confined glycerol molecule in water-glycerol mixtures, we furthermore demonstrate that the friction dependence on the confining potential is magnified in more viscous solvents, which suggests that this effect plays an important role for larger molecules in highly viscous solutions like polymer melts, in line with dynamic scaling arguments.

Stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems that experience strong fluctuations. The definitions of work and heat and the microscopically reversible condition are two key concepts in the current framework of stochastic thermodynamics. Herein, we apply stochastic thermodynamics to small systems with odd controlling parameters and find that the definition of heat and the microscopically reversible condition are incompatible. Such a contradiction also leads to a revision to the fluctuation theorems and nonequilibrium work relations. By introducing adjoint dynamics, we find that the total entropy production can be separated into three parts, with two of them satisfying the integral fluctuation theorem. Revising the definitions of work and heat and the microscopically reversible condition allows us to derive two sets of modified nonequilibrium work relations, including the Jarzynski equality, the detailed Crooks work relation, and the integral Crooks work relation. We consider the strategy of shortcuts to isothermality as an example and give a more sophisticated explanation for the Jarzynski-like equality derived from shortcuts to isothermality.

The activation of a gene is a complex biochemical process and could involve small steps, creating a memory between individual events. However, the effect of this molecular memory was often neglected in previous work. How the molecular memory affects gene expression remains not fully explored. We analyze a stochastic model of bursty gene expression, where the waiting time from inactivation to activation is assumed to follow a nonexponential (in fact, Erlang) distribution. We derive the analytical expression for the gene-product distribution, which explicitly traces the effect of molecule memory. Interestingly, we find that the effect of molecular memory is equivalent to the introduction of feedback. In addition, we analytically show that the stationary distribution is always super-Poissonian, independent of the detail of the waiting-time distribution, and there is the optimal step size that minimizes the Fano factor for any given mean burst size and is a decreasing function of the mean burst size. These analytical results indicate that molecular memory is an unneglectable factor affecting gene expression.

Phase reduction is a powerful technique that makes possible to describe the dynamics of a weakly perturbed limit-cycle oscillator in terms of its phase. For ensembles of oscillators, a classical example of phase reduction is the derivation of the Kuramoto model from the mean-field complex Ginzburg-Landau equation (MF-CGLE). Still, the Kuramoto model is a first-order phase approximation that displays either full synchronization or incoherence, but none of the nontrivial dynamics of the MF-CGLE. This fact calls for an expansion beyond the first order in the coupling constant. We develop an isochron-based scheme to obtain the second-order phase approximation, which reproduces the weak-coupling dynamics of the MF-CGLE. The practicality of our method is evidenced by extending the calculation up to third order. Each new term of the power-series expansion contributes with additional higher-order multibody (i.e., nonpairwise) interactions. This points to intricate multibody phase interactions as the source of pure collective chaos in the MF-CGLE at moderate coupling.

In recent years, there has been a proliferation of online gambling sites, which has made gambling more accessible with a consequent rise in related problems, such as addiction. Hence, the analysis of the gambling behavior at both the individual and the aggregate levels has become the object of several investigations. In this paper, resorting to classical methods of the kinetic theory, we describe the behavior of a multiagent system of gamblers participating in lottery-type games on a virtual-item gambling market. The comparison with previous, often empirical, results highlights the ability of the kinetic approach to explain how the simple microscopic rules of a gambling-type game produce complex collective trends, which might be difficult to interpret precisely by looking only at the available data.

We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit nonlinear velocity-alignment interactions with neighbors within their field of view. The stochasticity in the dynamics is spatially heterogeneous and arises implicitly from the nature of the interparticle interactions. We observe long-time spatial cohesion in the emergent flocking dynamics, despite the absence of attractive forces that explicitly depend on the relative positions of particles. The wide array of flocking patterns exhibited by this model are characterized by identifying spatially distinct clusters and computing their corresponding angular momenta.

In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field ${\varphi }^4$ model with a ${\mathbb{Z}}_2$ symmetry. Our purpose is discovering, if any, the relation between the second-order ${\mathbb{Z}}_2$-symmetry-breaking phase transition and the geometric entities mentioned above. The mean-field interaction allows us to solve analytically either the thermodynamic in the canonical ensemble or the topology by means of Morse theory. We have analyzed the results in the light of two theorems on sufficiency conditions for symmetry-breaking phase transitions recently proven. This study is part of a research line based on the general framework of geometric-topological approach to Hamiltonian chaos and critical phenomena.

A characteristic of chaotic scattering is the excess of elastic over inelastic scattering processes quantified by the elastic enhancement factor $F_M(T,\gamma )$, which depends on the number of open channels $M$, the average transmission coefficient $T$, and internal absorption $\gamma$. Using a microwave cavity with the shape of a chaotic quarter-bow-tie billiard, we study the elastic enhancement factor experimentally as a function of the openness, which is defined as the ratio of the Heisenberg time and the Weisskopf (dwell) time and is directly related to $M$ and the size of internal absorption. In the experiments $2\le M\le 9$ open channels with an average transmission coefficient $0.34<T<0.98$ and moderate internal absorption strength in the range of $\gamma =0.9–2.8$ are achieved. The experimental results for the enhancement factor are shown to agree well with random matrix theory predictions. Furthermore, in order to corroborate the wave-chaotic features of the microwave system, the spectral fluctuation properties are studied for $M=2$ channels. Agreement with those exhibited by typical, fully chaotic systems is illustrated, which is exemplary for the nearest-neighbor spacing distribution and the average power spectrum. Here we take into account the incompleteness of the sequence of resonance frequencies ascribed to the small yet nonvanishing internal absorption.

In this paper, we introduce a general framework for coinfection as cooperative susceptible-infected-removed (SIR) dynamics. We first solve the SIR model analytically for two symmetric cooperative contagions [L. Chen et al., Europhys. Lett. 104, 50001 (2013)] and then generalize and solve the model exactly in the symmetric scenarios for three and more cooperative contagions. We calculate the transition points and order parameters, i.e., the total number of infected hosts. We show that the behavior of the system does not change qualitatively with the inclusion of more diseases. We also show analytically that there is a saddle-node-like bifurcation for two cooperative SIR dynamics and that the transition is hybrid. Moreover, we investigate where the symmetric solution is stable for initial fluctuations. We finally explore sets of parameters which give rise to asymmetric cases, namely, the asymmetric cases of primary and secondary infection rates of one pathogen with respect to another. This setting can lead to fewer infected hosts, a higher epidemic threshold, and also continuous transitions. These results open the road to a better understanding of disease ecology.

Particle dispersions provide a promising tool for the engineering of functional materials that exploit self-assembly of complex structures. Dispersion made from magnetic colloidal particles is a great choice; they are biocompatible and remotely controllable among many other advantages. However, their dominating dipolar interaction typically limits structural complexity to linear arrangements. This paper shows how a magnetostatic equilibrium state with noncollinear arrangement of the magnetic moments, as reported for ferromagnetic Janus particles, enables the controlled self-organization of diverse structures in two dimensions via constant and low-frequency external magnetic fields. Branched clusters of staggered chains, compact clusters, linear chains, and dispersed single particles can be formed and interconverted reversibly in a controlled way. The structural diversity is a consequence of both the inhomogeneity and the spatial extension of the magnetization distribution inside the particles. We draw this conclusion from calculations based on a model of spheres with multiple shifted dipoles. The results demonstrate that fundamentally new possibilities for responsive magnetic materials can arise from interactions between particles with a spatially extended, anisotropic magnetization distribution.

For dry granular materials falling through a circular exit at the bottom of a silo, no continuous flow can be sustained when the diameter $D$ of the exit is less than five times the characteristic size of the grains. If the bottom of the silo rotates horizontally with respect to the wall of the silo, finite flow rate can be sustained even at small $D$. We investigate the effect of bottom rotation to the flow rate of monodisperse plastic beads of $d=6\mathrm{mm}$ diameter from a cylindrical silo of 19 cm inner diameter. We find that the flow rate $W$ follows Beverloo law down to $D=1.3d$ and that $W$ increases with the rotation speed $\omega$ in the small exit regime. If the exit is at an off-center distance $R$ from the axis of the silo, $W$ increases with the rate of area swept by the exit. On the other hand, when the exit diameter is large, $W$ decreases with increasing $\omega$ at small $\omega$ but increases with $\omega$ at large $\omega$. Such nonmonotonic dependence of flow rate on rotation speed may be explained as a gradual change from funnel flow to mass flow due to the shear at the bottom of the silo.

Wind dispersal of seeds is an essential mechanism for plants to proliferate and to invade new territories. In this paper we present a methodology used in our recent work [Rabault, Fauli, and Carlson, Phys. Rev. Lett. 122, 024501 (2019)] that combines 3D printing, a minimal theoretical model, and experiments to determine how the curvature along the length of the wings of autorotating seeds, fruits, and other diaspores provides them with an optimal wind dispersion potential, i.e., minimal terminal descent velocity. Experiments are performed on 3D-printed double-winged synthetic fruits for a wide range of wing fold angles (obtained from normalized curvature along the wing length), base wing angles, and wing loadings to determine how these affect the flight. Our experimental and theoretical models find an optimal wing fold angle that minimizes the descent velocity, where the curved wings must be sufficiently long to have horizontal segments, but also sufficiently short to ensure that their tip segments are primarily aligned along the horizontal direction. The curved shape of the wings of double winged autorotating diaspores may be an important parameter that improves the fitness of these plants in an ecological strategy.

Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNNs) can efficiently characterize anomalous diffusion by determining the exponent from a single short trajectory, outperforming the standard estimation based on the MSD when the available data points are limited, as is often the case in experiments. Furthermore, the RNNs can handle more complex tasks where there are no standard approaches, such as determining the anomalous diffusion exponent from a trajectory sampled at irregular times, and estimating the switching time and anomalous diffusion exponents of an intermittent system that switches between different kinds of anomalous diffusion. We validate our method on experimental data obtained from subdiffusive colloids trapped in speckle light fields and superdiffusive microswimmers.

We study a quantum Stirling cycle which extracts work using quantized energy levels of a potential well. The work and the efficiency of the engine depend on the length of the potential well, and the Carnot efficiency is approached in a low temperature limiting case. We show that the lack of information about the position of the particle inside the potential well can be converted into useful work without resorting to any measurement. In the low temperature limit, we calculate the amount of work extractable from distinguishable particles, fermions, and bosons.

The optically injected semiconductor laser system has proven to be an excellent source of experimental nonlinear dynamics, particularly regarding the generation of excitable pulses. Typically for low-injection strengths, these pulses are the result of a small above-threshold perturbation of a stable steady state, the underlying physics is well described by the Adler phase equation, and each laser intensity pulse is accompanied by a $2\pi$ phase rotation. In this article, we show how, with a dual-state quantum dot laser, a variation of type I excitability is possible that cannot be described by the Adler model. The laser is operated so that emission is from the excited state only. The ground state can be activated and phase locked to the master laser via optical injection while the excited state is completely suppressed. Close to the phase-locking boundary, a region of ground-state emission dropouts correlated to excited-state pulses can be observed. We show that the phase of the ground state undergoes bounded rotations due to interactions with the excited state. We analyze the system both experimentally and numerically and find excellent agreement. Particular attention is devoted to the bifurcation conditions needed for an excitable pulse as well as its time evolution.

In this first paper of a series dedicated to the microphysics of unmagnetized, relativistic collisionless pair shocks, we discuss the physics of the Weibel-type transverse current filamentation instability that develops in the shock precursor, through the interaction of an ultrarelativistic suprathermal particle beam with the background plasma. We introduce in particular the notion of the “Weibel frame,” or scattering center frame, in which the microturbulence is of mostly magnetic nature. We calculate the properties of this frame, using first a kinetic formulation of the linear phase of the instability, relying on Maxwell-Jüttner distribution functions, then using a quasistatic model of the nonlinear stage of the instability. Both methods show that (i) the Weibel frame moves at subrelativistic velocities relative to the background plasma, therefore at relativistic velocities relative to the shock front; (ii) the velocity of the Weibel frame relative to the background plasma scales with ${\xi }_{\mathrm{b}}$, i.e., the pressure of the suprathermal particle beam in units of the momentum flux density incoming into the shock; and (iii) the Weibel frame moves slightly less fast than the background plasma relative to the shock front. Our theoretical results are found to be in satisfactory agreement with the measurements carried out in dedicated large-scale 2D3V particle-in-cell simulations.

The dynamic structure factor (DSF) of the Yukawa system is here obtained with highly converged molecular dynamics (MD) over the entire liquid phase. The data provide a rigorous test of theoretical models of ion-acoustic wave-dispersion relations, the intermediate scattering function, and the high-frequency response. We compare our MD results with seven diverse models, finding good agreement among those that enforce the three basic sum rules for dispersion properties, although one of the models has previously unreported spurious peaks. The MD simulations reveal that at intermediate frequencies $\omega$, the high-frequency response of the DSF follows a power law, going approximately as ${\omega }^{-p}$, where $p>0$, and $p$ shows nontrivial dependencies on the wave vector $q$ and the plasma parameters $\kappa$ and $\mathrm{\Gamma }$. In contrast, among the seven comparison models, the predicted high-frequency response is found to be independent of $\{q,\kappa ,\mathrm{\Gamma }\}$. This high-frequency power suggests a useful fitting form. In addition, these results expose limitations of several models and, moreover, suggest that some approaches are difficult or impossible to extend because of the lack of finite moments. We also find the double-plasmon resonance peak in our MD simulations that none of the theoretical models predicts.