Related papers: Shock formation in an exclusion process with creat…
We study the fluctuations of the current J(t) of the totally asymmetric exclusion process with open boundaries. Using a density matrix renormalization group approach, we calculate the cumulant generating function of the current. This…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
In an exclusion process with avalanches, when a particle hops to a neighboring empty site which is adjacent to an island the particle on the other end of the island immediately hops and if it joins another island this triggers another hop.…
We develop a systematic analytic approach to the problem of branching and annihilating random walks, equivalent to the diffusion-limited reaction processes 2A->0 and A->(m+1)A, where m>=1. Starting from the master equation, a…
Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection $\alpha$ and death…
We prove a stable shock formation result for a large class of systems of quasilinear wave equations in two spatial dimensions. We give a precise description of the dynamics all the way up to the singularity. Our main theorem applies to…
We study the generic non-equilibrium steady states in asymmetric exclusion processes on a closed network with bottlenecks. To this end we proposes and study closed simple networks with multiply-connected non-identical junctions. Depending…
We investigate dynamic crack propagation and fragmentation with the phase-field fracture approach. The method was chosen for its ability to yield crack paths that are independent of the underlying mesh, thanks to the damage regularization…
We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a $2 \times L$ lattice. We propose a scenario which resolves a stark…
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…
We investigate the growth of the total number of particles in a symmetric exclusion process driven by a localized source. The average total number of particles entering an initially empty system grows with time as t^{1/2} in one dimension,…
Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. By analysing these equations in detail for the…
Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong…
We consider a system of $N$ Brownian particles, with or without inertia, interacting in the mean-field regime via a weak, smooth, long-range potential, and starting initially from an arbitrary exchangeable $N$-particle distribution. In this…
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously…
We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas. We prove that the well-known phenomenon of shock formation in simple…
We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…
We analyse the full shock formation process in electron-ion plasmas in theory and simulations. It is accepted that electromagnetic shocks in initially unmagnetised relativistic plasmas are triggered by the filamentation instability.…