Related papers: Modelling one-dimensional driven diffusive systems…
Tensor networks are employed to characterize the current fluctuations in one-dimensional diffusion-reaction systems. The representative system under study is a semiconducting material where holes and electrons constitute two types of charge…
We consider a two-phase Darcy flow in a fractured and deformable porous medium for which the fractures are described as a network of planar surfaces leading to so-called hybrid-dimensional models. The fractures are assumed open and filled…
We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy…
We analyze the role of the interplay between on-site interaction and inhomogeneous diffusion on the phenomenon of condensation in the zero-range process. We predict a universal phase diagram in the plane of two exponents, respectively…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher…
In this article, we propose a novel scalar-transport model for the simulation of scalar quantities in two-phase flows with a phase-field method (diffuse-interface method). In a two-phase flow, the scalar quantities typically have disparate…
The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this…
We study a class of zero-range processes in which the real-space condensation phenomenon does not occur and is replaced by a saturated condensation: that is, an extensive number of finite-size "condensates" in the steady state. We determine…
Zero-range processes with decreasing jump rates are well known to exhibit a condensation transition under certain conditions on the jump rates, and the dynamics of this transition continues to be a subject of current research interest.…
We use fluctuating hydrodynamics to analyze the dynamical properties in the non-equilibrium steady state of a diffusive system coupled with reservoirs. We derive the two-time correlations of the density and of the current in the…
This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…
A procedure based on the recently developed ``adaptive'' time-dependent density-matrix-renormalization-group (DMRG) technique is presented to calculate the zero temperature conductance of nanostructures, such as a quantum dots (QD's) or…
We consider the asymmetric zero range process in dimensions $d \geq 2$. Assume the initial density profile is a perturbation of the constant density, which has order $N^{-\alpha}$, $\alpha \in (0,1)$, and is constant along the drift…
Single-file transport refers to the motion of particles in a narrow channel, such that they cannot bypass each other. This constraint leads to strong correlations between the particles, described by correlation profiles, which measure the…
The phase transitions of the recently introduced 2A -> 3A, 4A -> 0 reaction-diffusion model (G.Odor, PRE 69 036112 (2004)) are explored in two dimensions. This model exhibits site occupation restriction and explicit diffusion of isolated…
We present high-precision Monte Carlo data for the phase diagram of a two-species driven diffusive system, reminiscent of traffic across a narrow bridge. Earlier studies reported two phases with broken symmetry; the existence of one of…
A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some…