Numerical and analytical methods at both micro- and mesoscales are used to study how the electrical resistivity and the high-frequency tortuosity of solid foam are modified by the presence of membranes that partially or totally close the cell windows connecting neighbor pores. Finite-element-method simulations are performed on two pores connected by a single-holed membrane and on well-ordered Kelvin foam. For two pores connected by a single-holed membrane, we show that the equation for pore access resistance obtained by Sahu and Zwolak [Phys. Rev. E 98, 012404 (2018)] can predict, after a few modifications, the electrical resistivity at the membrane scale for a large range of membrane apertures. Considering these analytical results, we build a pore-network model by using two kinds of conductances at the pore scale: interpore conductance and intrapore conductance. Local interpore resistances govern foam electrical conductivity at small membrane aperture size, but when the membrane aperture has the same order of magnitude as the pore size, the intrapore resistances are no longer negligible. An important success of this pore-network model is that it can be used to study the effects of percolation on the foam electrical conductivity by using pore-network simulations on larger samples containing a few thousand pores and having different proportions of closed membrane randomly distributed over the sample. The tortuosity is found to be drastically larger than one in foam containing membranes with small apertures or a significant fraction of closed membranes.

A high-order implicit multidimensional particle-in-cell (PIC) method is developed for simulating plasmas at solid densities. The space-time arrangement is based on Yee and a leapfrog algorithm for electromagnetic fields and particle advancement. The field solver algorithm completely eliminates numerical instabilities found in explicit PIC methods with relaxed time step and grid resolution. Moreover, this algorithm eliminates the numerical cooling found in the standard implicit PIC methods by using a pseudo-electric-field method. The particle pusher algorithm combines the standard Boris particle pusher with the Newton-Krylov iteration method. This algorithm increases the precision accuracy by several orders of magnitude when compared with the standard Boris particle pusher and also significantly decreases the iteration time when compared with the pure Newton-Krylov method. The code is tested with several benchmarks, including Weibel instability, and relativistic laser plasma interactions at both low and solid densities.

A particle-in-cell (PIC) simulation code is used to investigate the transport and energy deposition of an intense proton beam in solid-state material. This code is able to simulate close particle interactions by using a Monte Carlo binary collision model. Such a model takes into account all related interactions between the incident protons and material particles, e.g., proton-nucleus, proton–bound-electron, and proton–free-electron collisions. This code also includes a Monte Carlo model for the collisional ionization and electron-ion recombination as well as the depression of the ionization potential by shielding of surrounding particles. Moreover, for intense proton beams, in order to include collective electromagnetic effects, significantly speed up the simulation, and simultaneously avoid numerical instabilities, an approach that combines the PIC method with a reduced model of high-density plasma based on Ohm's law is used. Simulation results indicate that the collective electromagnetic effects have a significant influence on the transport and energy deposition of proton beams. The Ohmic electric field would increase the stopping power and leads to a shortened range of proton beams in solid. The magnetic field would localize the energy deposition by collimating proton beams, which would otherwise be deflected by the collisions with nuclei.

Optimal transport (OT) has become a discipline by itself that offers solutions to a wide range of theoretical problems in probability and mathematics. Despite its appealing theoretical properties, solving the OT problem involves the resolution of a linear program whose computational cost can quickly become prohibitive whenever the size of the problem exceeds a few hundred points. The recent introduction of entropy regularization, however, has led to the development of fast algorithms for solving an approximate OT problem. The successes of those algorithms have resulted in a popularization of the applications of OT in several applied fields such as imaging sciences and machine learning, and in data sciences in general. Problems remain, however, as to the numerical convergence of those regularized approximations towards the actual OT solution. In addition, the physical meaning of this regularization is unclear. In this paper, we propose an approach to solving the discrete OT problem using techniques adapted from statistical physics. Our first contribution is to fully describe this formalism, including all the proofs of its main claims. In particular we derive a strongly concave effective free energy function that captures the constraints of the optimal transport problem at a finite temperature. Its maximum defines a pseudo distance between the two set of weighted points that are compared, which satisfies the triangular inequalities. The temperature dependent OT pseudo distance decreases monotonically to the standard OT distance, providing a robust framework for temperature annealing. Our second contribution is to show that the implementation of this formalism has the same properties as the regularized OT algorithms in time complexity, making it a competitive approach to solving the OT problem. We illustrate applications of the framework to the problem of protein fold recognition based on sequence information only.

With the rich dynamics studies of single-state processes, the two-state processes are attracting more interest, since they are widely observed in complex system and have effective applications in diverse fields, such as foraging behavior of animals. This paper builds the theoretical foundation of the process with two states: Lévy walk and Brownian motion, having been proved to be an efficient intermittent search process. The sojourn time distributions in two states are both assumed to be heavy-tailed with exponents ${\alpha }_{\pm }\in (0,2)$. The dynamical behaviors of this two-state process are obtained through analyzing the ensemble-averaged and time-averaged mean-squared displacements (MSDs) in weak and strong aging cases. It is discovered that the magnitude relationship of ${\alpha }_{\pm }$ decides the fraction of two states for long times, playing a crucial role in these MSDs. According to the generic expressions of MSDs, some inherent characteristics of the two-state process are detected. The effects of the fraction on these observables are presented in detail for six different cases. The key of getting these results is to calculate the velocity correlation function of the two-state process, the techniques of which can be generalized to other multistate processes.

We study the Ginibre ensemble of $N\times N$ complex random matrices and compute exactly, for any finite $N$, the full distribution as well as all the cumulants of the number $N_r$ of eigenvalues within a disk of radius $r$ centered at the origin. In the limit of large $N$, when the average density of eigenvalues becomes uniform over the unit disk, we show that for $0<r<1$ the fluctuations of $N_r$ around its mean value $\langle N_r\rangle \approx N{r}^2$ display three different regimes: (i) a typical Gaussian regime where the fluctuations are of order $O\left(N^{1/4}\right)$, (ii) an intermediate regime where $N_r-\langle N_r\rangle =O\left(\sqrt{N}\right)$, and (iii) a large deviation regime where $N_r-\langle N_r\rangle =O\left(N\right)$. This intermediate behavior (ii) had been overlooked in previous studies and we show here that it ensures a smooth matching between the typical and the large deviation regimes. In addition, we demonstrate that this intermediate regime controls all the (centered) cumulants of $N_r$, which are all of order $O\left(\sqrt{N}\right)$. We show that the intermediate deviation function that describes these intermediate fluctuations can be computed explicitly and we demonstrate that it is universal, i.e., it holds for a large class of complex random matrices. Our analytical results are corroborated by precise “importance sampling” Monte Carlo simulations.

Although classical and quantum heat engines work on entirely different fundamental principles, there is an underlying similarity. For instance, the form of efficiency at optimal performance may be similar for both types of engines. In this work, we study a three-level laser quantum heat engine operating at maximum ecological function (EF) which represents a compromise between the power output and the loss of power due to entropy production. We present numerical as well as analytic results for the global and local optimization of our laser engine in different operational regimes. Particularly, we observe that in low-temperature regimes, the three-level laser heat engine can be mapped to Feynman's ratchet and pawl model, a steady-state classical heat engine. Then we derive analytic expressions for efficiency under the assumptions of strong matter-field coupling and high bath temperatures. Upper and lower bounds on the efficiency exist in case of extreme asymmetric dissipation when the ratio of system-bath coupling constants at the hot and the cold contacts respectively approaches zero or infinity. These bounds have been established previously for various classical models of Carnot-like engines. Further, for weak (or intermediate) matter-field coupling in the high-temperature limit, we derive some new bounds on the efficiency of the engine. We conclude that while the engine produces at least 75% of the power output as compared with the maximum power conditions, the fractional loss of power is appreciably low in case of the engine operating at maximum EF, thus making this objective function relevant from an environmental point of view.

Integrable systems do not obey the strong eigenstate thermalization hypothesis (ETH), which has been proposed as a mechanism of thermalization in isolated quantum systems. It has been suggested that an integrable system reaches a steady state described by a generalized Gibbs ensemble (GGE) instead of thermal equilibrium. We prove that a generalized version of the strong ETH holds for noninteracting integrable systems with translation invariance. Our generalized ETH states that any pair of energy eigenstates with similar values of local conserved quantities looks similar with respect to local observables, such as local correlations. This result tells us that an integrable system relaxes to a GGE for any initial state that has subextensive fluctuations of macroscopic local conserved quantities. Contrary to the previous derivations of the GGE, it is not necessary to assume the cluster decomposition property for an initial state.

We report the exact phase dynamics of Manakov bright and dark vector solitons in an inhomogeneous optical system by means of a variable coefficient coupled nonlinear Schrödinger equation. To investigate the phase dynamics, we have modified the Manakov system with a relation between two modes of propagation, that are obtained by the Hirota bilinear method. The importance of the phase study in soliton interaction is revealed by asymptotic analysis of two-soliton solutions. In contrast with the Manakov bright soliton, the time-dependent dark vector soliton exhibits a gradual phase shift due to the blackness factor. The various inhomogeneous effects on the soliton phase are investigated, with a particular emphasis on nonlinear tunneling. The intensity and corresponding phase of the tunneling soliton either forms a peak or valley and retains its shape after tunneling. Unlike the bright counterpart, the gain or loss term significantly affects the phase of the dark soliton. Apart from the study of soliton intensity, the phase profile of bright and dark vector solitons and its dynamical features are also explored. As the study is not limited to intensity description, the present study could serve as a reference for the future studies on multisolitons phase dynamics in photonics and related fields.

We investigate the simultaneous influence of spatially homogeneous multiplicative noise as well as of spatially $\delta$-correlated additive noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. Depending on the ratio between the strength of additive and multiplicative noise we find a number of distinctly different types of behavior including explosions, collapse, filling in, and spatio-temporal disorder as well as intermittent behavior of all types listed. Techniques used to analyze the results include snapshots, $x-t$ plots and plots of the spatially and temporally averaged amplitude as a function of the strength of multiplicative noise while keeping the strength of additive noise fixed. Typically 50 realizations are used for averaging to obtain the corresponding data points in these diagrams. For the widths of these distribution as a function of additive noise we obtain a linear decrease in the limit of fairly large, but fixed values of the multiplicative noise. To summarize our findings concisely we show three-dimensional plots of the mean pattern amplitude and the generalized susceptibility as a function of the strengths of additive and multiplicative noise. We critically compare the results of our investigations with those obtained in the two limiting cases of purely additive and of purely multiplicative noise.

Current studies have shown that there is a positive correlation between the network assortativity and robustness and that the assortativity also plays an important role in explosive synchronization. In this paper, taking the network robustness as a global property, we investigate its significance as well as the influence of its interaction with the assortativity on explosive synchronization. Our numerical results demonstrate that explosive synchronization is suppressed in extreme situations of both the robustness and assortativity. In addition, through appropriate adjustments of them, a maximum hysteresis area between the forward and backward transitions can be reached. Furthermore, our results might also provide reference for those who are interested in effects of network structure on synchronization, though this problem is still challenging as we show in the discussion.

Network robustness is a central point in network science, both from a theoretical and a practical point of view. In this paper, we show that layer degradation, understood as the continuous or discrete loss of links' weight, triggers a structural transition revealed by an abrupt change in the algebraic connectivity of the graph. Unlike traditional single layer networks, multiplex networks exist in two phases, one in which the system is protected from link failures in some of its layers and one in which all the system senses the failure happening in one single layer. We also give the exact critical value of the weight of the intralayer links at which the transition occurs for continuous layer degradation and its relation with the value of the coupling between layers. This relation allows us to reveal the connection between the transition observed under layer degradation and the one observed under the variation of the coupling between layers.

A simple model for estimating band edge wavelengths of selective reflection from cholesteric liquid crystals (CLCs) for oblique incidence is proposed. The proposed model and calculation method are based on a geometrical optics model and Bragg's law. Average refractive indices and Bragg angles in a CLC for the short- and long-wavelength edges of a reflection band are calculated using the model. The band edge wavelengths are determined by substituting the average refractive indices and Bragg angles into Bragg's law. The angular dependences of the band edge wavelengths show good agreement with those calculated by Berreman and Scheffer's [Phys. Rev. Lett. 25, 577 (1970)] $4\times 4$ matrix method. Although the derived equations are not exact solutions of Maxwell's equations, the proposed method can approximately predict the angular dependences of the center wavelength, bandwidth, and band edge wavelengths of the selective reflection in CLCs.

Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion-symmetric subspace. In particular, we find numerous isolated heteroclinic connections between different types of solutions—equilibria, periodic, and quasiperiodic orbits—as well as continua of connections forming higher-dimensional connecting manifolds. We also compute a homoclinic connection of a periodic orbit and provide strong evidence that the associated homoclinic tangle forms the chaotic repeller that underpins transient turbulence in the symmetric subspace.

The dynamics of an initial wave packet affected by random noise is considered in the framework of a comb model. The model is relevant to a diffusion problem in neurons where the transport of ions can be accelerated by an external random field due to synapse fluctuations. In the present specific case, it acts as boundary conditions, which lead to a reaction transport equation with multiplicative noise. The temporal behavior of the mean squared displacement is estimated analytically, and it is shown that the spreading of the initial wave packet corresponds to Richardson diffusion.

Maximum caliber (Max Cal) is purported to be a general variational principle for nonequilibrium statistical physics. But recently, Jack and Evans [J. Stat. Mech.: Theory Exp. (2016) 093305] and Maes [Non-Dissipative Effects in Nonequilibrium Systems (Springer, New York, 2018)] have raised concerns about how Max Cal handles dissipative processes. Here, we show that the problem does not lie in Max Cal; the problem is in the use of insufficient constraints. We also present an exactly solvable single-particle model of dissipation, valid far from equilibrium, and its solution by maximum caliber. The model illustrates how the influx and efflux of work and heat into a flowing system alters the distribution of trajectories. Maximum caliber is a viable principle for dissipative systems.

Subharmonic response is a well-known phenomenon in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics due to thermal fluctuations. In contrast to stochastic autonomous systems in a stationary state, for which the number of coherent oscillations is fundamentally bounded by the number of states in the underlying network, we demonstrate that in periodically driven systems, subharmonic oscillations can in principle remain coherent forever, even in networks with a small number of states. We also show that, inter alia, the thermodynamic cost rises only logarithmically with the number of coherent oscillations in a model calculation and that the possible periods of the persistent subharmonic response grow linearly with the number of states. We argue that our results can be relevant for biochemical oscillations and for stochastic models of time crystals.

By introducing a simple model based on two-dimensional cellular automata, we reveal the relationship between the routing strategies of individual vehicles and the global behavior of transportation networks. Specifically, we characterize the routing strategies by a single parameter called path-greediness, which corresponds to the tendency for individuals to travel via a shortest path to the destination. Remarkably, we found that the effective dimension of the system is reduced when the congested states emerge. We also found that a high individual tendency to travel via the shortest path does not necessarily shorten the average journey time, as the system may benefit from less greedy routing strategies in congested situations. Finally, we show that adaptive routing strategies outperform controlled strategies in the free-flow state but not in the congested state, implying that controlled strategies may increase coordination among vehicles and are beneficial for suppressing traffic congestion.