The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.

We study a seven-state Potts glass model in three dimensions with first-, second-, and third-nearest-neighbor interactions with a bimodal distribution of couplings by Monte Carlo simulations. Our results show the existence of a spin-glass transition at a finite temperature $T_c$, a discontinuous jump of an order parameter at $T_c$ without latent heat, and a nontrivial structure in the order parameter distribution below $T_c$. They are compatible with one-step replica symmetry breaking.

We investigate the influence of large noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. The interaction of localization and noise can lead to filling in or noisy localized structures for fixed noise strength. To focus on the interaction between noise and localization we cover a region in parameter space, in particular, subcriticality, for which stationary stable deterministic pulses do not exist. Possible experimental tests of the work presented for autocatalytic chemical reactions and bioinspired systems are outlined.

We endow a system of interacting particles with two distinct, local, Markovian, and reversible microscopic dynamics that both converge to the Boltzmann-Gibbs equilibrium of standard liquids. While the first, standard, one leads to glassy dynamics, we use field-theoretical techniques to show that the latter displays no sign of glassiness. The approximations we use, akin to the mode-coupling approximation, are famous for magnifying glassy aspects of the dynamics, supposedly through the neglect of activated events. Despite this, the modified dynamics seem to stick to standard liquid relaxation. This finding singles out as applying to a realistic system of interacting particles in low dimensions and questions the role of the dynamical rules used to explore a given static free-energy landscape. Moreover, our peculiar choice of dynamical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.

We propose an analytical method to determine the shape of density profiles in the asymptotic long-time limit for a broad class of coupled continuous-time random walks which operate in the ballistic regime. In particular, we show that different scenarios of performing a random-walk step, via making an instantaneous jump penalized by a proper waiting time or via moving with a constant speed, dramatically effect the corresponding propagators, despite the fact that the end points of the steps are identical. Furthermore, if the speed during each step of the random walk is itself a random variable, its distribution gets clearly reflected in the asymptotic density of random walkers. These features are in contrast with more standard nonballistic random walks.

Soliton transport in tubelike networks is studied by solving the nonlinear Schrödinger equation (NLSE) on finite thickness (“fat”) graphs. The dependence of the solution and of the reflection at vertices on the graph thickness and on the angle between its bonds is studied and related to a special case considered in our previous work, in the limit when the thickness of the graph goes to zero. It is found that both the wave function and reflection coefficient reproduce the regime of reflectionless vertex transmission studied in our previous work.

We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the corresponding trajectory-dependent work performed on the system and derive the integral fluctuation theorem and the Jarzynski equality for nearly adiabatic driving. We show that such identities hold as long as the stochastic dynamics and work variable are consistently defined. We numerically study the emerging work statistics for a two-level quantum system and find that the conventional diabatic approximation is unable to capture some prominent features arising from driving, such as the continuity of the probability density of work. Our results reveal the necessity of using accurate expressions for the drive-dressed heat exchange in future experiments probing jump time distributions.

In this paper various eccentric hole dynamics are presented in defect turbulence of the one-dimensional complex Ginzburg-Landau equation. Each hole shows coherent particlelike motion with nonconstant velocity. On the other hand, successive hole velocities without discriminating each hole exhibit anomalous intermittent motions being subject to multi-time-scale non-Gaussian statistics. An alternate non-Markov stochastic differential equation is proposed, by which all these observed statistical properties can be described successfully.

We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modeled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation-dissipation relation between friction and noise for probe motion in a nonequilibrium fluid.

We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.

Passive particles exhibit unique properties when immersed in an active bath of self-propelling entities. In particular, an effective attraction can appear between particles that repel each other when in a passive solution. Here we numerically study the effect of hydrodynamics on an active-passive hybrid system, where we observe qualitative differences as compared to simulations with excluded volume effects alone. The results shed light on an existing discrepancy in pair lifetimes between simulation and experiment, due to the hydrodynamically enhanced stability of coupled passive particles.

Self-assembly of polypeptides into fibrillar structures can be initiated by planar surfaces that interact favorably with certain residues. Using a coarse-grained model, we systematically studied the folding and adsorption behavior of a $\beta$-roll forming polypeptide. We find that there are two different folding pathways depending on the temperature: (i) at low temperature, the polypeptide folds in solution into a $\beta$-roll before adsorbing onto the attractive surface; (ii) at higher temperature, the polypeptide first adsorbs in a disordered state and folds while on the surface. The folding temperature increases with increasing attraction as the folded $\beta$-roll is stabilized by the surface. Surprisingly, further increasing the attraction lowers the folding temperature again, as strong attraction also stabilizes the adsorbed disordered state, which competes with folding of the polypeptide. Our results suggest that to enhance the folding, one should use a weakly attractive surface. They also explain the recent experimental observation of the nonmonotonic effect of charge on the fibril formation on an oppositely charged surface [C. Charbonneau et al., ACS Nano 8, 2328 (2014)].

In this paper we investigate the influence of the plasma properties on the charge state distribution of a swift heavy ion beam interacting with a plasma. The main finding is that the charge state in plasma can be lower than in cold matter. The charge state distribution is determined by the ionization and recombination rates which are balancing each other out. Both, ionization and recombination rates, as well as atomic excitation and decay rates, depend on the plasma parameters in different ways. These effects have been theoretically studied by Monte Carlo simulations on the example of an argon ion beam at an energy of $4\mathrm{MeV}/\mathrm{u}$ in a carbon plasma. This study covers a plasma parameter space ranging from ion densities from ${10}^{18}$ to ${10}^{23}$ ${\mathrm{cm}}^{-3}$ and electron temperatures from 10 to 200 eV.

In the present work we test experimentally and compute numerically the stability and dynamics of harmonically driven monoatomic granular chains composed of an increasing number of particles $N(N=1–50)$. In particular, we investigate the inherent effects of dissipation and finite size on the evolution of bifurcation instabilities in the statically compressed case. The findings of the study suggest that the nonlinear bifurcation phenomena, which arise due to finite size, can be useful for efficient energy transfer away from the drive frequency in transmitted waves.

A bulk metallic glass forming alloy is subjected to shear flow in its supercooled state by compression of a short rod to produce a flat disk. The resulting material exhibits enhanced crystallization kinetics during isothermal annealing as reflected in the decrease of the crystallization time relative to the nondeformed case. The transition from quiescent to shear-accelerated crystallization is linked to strain accumulated during shear flow above a critical shear rate ${\dot{\gamma }}_c\approx 0.3$ ${\mathrm{s}}^{-1}$ which corresponds to Péclet number, $\text{Pe}\sim O\left(1\right)$. The observation of shear-accelerated crystallization in an atomic system at modest shear rates is uncommon. It is made possible here by the substantial viscosity of the supercooled liquid which increases strongly with temperature in the approach to the glass transition. We may therefore anticipate the encounter of nontrivial shear-related effects during thermoplastic deformation of similar systems.

The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. (2012) P05014] is an integrable generalization of the TASEP equipped with an interaction, which enhances the clustering of particles. The process interpolates between two extremal cases: the TASEP with parallel update and the process with all particles irreversibly merging into a single cluster moving as an isolated particle. We are interested in the large time behavior of this process on a ring in the whole range of the parameter $\lambda$ controlling the interaction. We study the stationary state correlations, the cluster size distribution, and the large-time fluctuations of integrated particle current. When $\lambda$ is finite, we find the usual TASEP-like behavior: The correlation length is finite; there are only clusters of finite size in the stationary state and current fluctuations belong to the Kardar-Parisi-Zhang universality class. When $\lambda$ grows with the system size, so does the correlation length. We find a nontrivial transition regime with clusters of all sizes on the lattice. We identify a crossover parameter and derive the large deviation function for particle current, which interpolates between the case considered by Derrida-Lebowitz and a single-particle diffusion.

Merging of granular flows is ubiquitous in industrial, mining, and geological processes. However, its behavior remains poorly understood. This paper studies the phase transition and flow-rate behavior of two granular flows merging into one channel. When the main channel is wider than the side channel, the system shows a remarkable two-sudden-drops phenomenon in the outflow rate when gradually increasing the main inflow. When gradually decreasing the main inflow, the system shows obvious hysteresis phenomenon. We study the flow-rate-drop phenomenon by measuring the area fraction and the mean velocity at the merging point. The phase diagram of the system is also presented to understand the occurrence of the phenomenon. We find that the dilute-to-dense transition occurs when the area fraction of particles at the joint point exceeds a critical value ${\varphi }_c=0.65\pm 0.03$.

A novel approach is presented for analyzing the double-layer interaction force between charged particles in electrolyte solution, in the limit where the Debye length is small compared with both interparticle separation and particle size. The method, developed here for two planar convex particles of otherwise arbitrary geometry, yields a simple asymptotic approximation limited to neither small zeta potentials nor the “close-proximity” assumption underlying Derjaguin's approximation. Starting from the nonlinear Poisson-Boltzmann formulation, boundary-layer solutions describing the thin diffuse-charge layers are asymptotically matched to a WKBJ expansion valid in the bulk, where the potential is exponentially small. The latter expansion describes the bulk potential as superposed contributions conveyed by “rays” emanating normally from the boundary layers. On a special curve generated by the centers of all circles maximally inscribed between the two particles, the bulk stress—associated with the ray contributions interacting nonlinearly—decays exponentially with distance from the center of the smallest of these circles. The force is then obtained by integrating the traction along this curve using Laplace's method. We illustrate the usefulness of our theory by comparing it, alongside Derjaguin's approximation, with numerical simulations in the case of two parallel cylinders at low potentials. By combining our result and Derjaguin's approximation, the interaction force is provided at arbitrary interparticle separations. Our theory can be generalized to arbitrary three-dimensional geometries, nonideal electrolyte models, and other physical scenarios where exponentially decaying fields give rise to forces.