Related papers: On some integrable models in inhomogeneous space
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The…
We investigate topological phenomena in a spatially modulated Dirac-$\delta$ lattice, where the scattering potential varies periodically in space. Changing the potential modulation frequency leads to Hofstadter's butterfly-like energy…
Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group based moving…
We examine the behavior of a single impurity particle embedded within a Totally Asymmetric Simple Exclusion Process (TASEP). By analyzing the impurity's dynamics, characterized by two arbitrary hopping parameters $ \alpha $ and $\beta$, we…
We investigate the physics of quasicrystalline models in the presence of a uniform magnetic field, focusing on the presence and construction of topological states. This is done by using the Hofstadter model but with the sites and couplings…
We study the dynamics of spatially homogeneous Friedmann--Robertson--Walker universes filled with a massive scalar field in a neighbourhood of the massless transition $s=1$. At this point the Einstein--scalar system exhibits a…
This paper is concerned with the existence, shape and dynamical stability of infinite-energy equilibria for a general class of spatially homogeneous kinetic equations in space dimensions $d \geq 3$. Our results cover in particular…
We study a minimal lattice model which describes bidirectional transport of "particles" driven along a one dimensional track, as is observed in microtubule based, motor protein driven bidirectional transport of cargo vesicles, lipid bodies…
We revisit the defect-induced nonequilibrium phase transition from a largely homogeneous free-flow phase to a phase-separated congested phase in the sublattice totally asymmetric simple exclusion process (TASEP) with local deterministic…
We analyze a random lozenge tiling model of a large regular hexagon, whose underlying weight structure is periodic of period $2$ in both the horizontal and vertical directions. This is a determinantal point process whose correlation kernel…
The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for non-equilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments.…
We present in this paper a rigorous theoretical framework to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bESFEM and bFS-FEM) for nearly-incompressible elasticity problems.…
Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or…
We describe the translation invariant stationary states of the one dimensional discrete-time facilitated totally asymmetric simple exclusion process (F-TASEP). In this system a particle at site $j$ in $Z$ jumps, at integer times, to site…
We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP). Expectations of the duality functionals correspond…
We investigate the time-evolution of elastoplastic materials reinforced by randomly distributed long-range interactions. Starting from a rate-independent system on a discrete spring lattice that combines local linearized elasticity,…
Many integrable stochastic particle systems in one space dimension (such as TASEP - Totally Asymmetric Simple Exclusion Process - and its $q$-deformation, the $q$-TASEP) remain integrable if we equip each particle with its own speed…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli \rho measure as initial conditions, 0<\rho<1, is stationary in space and time. Let N_t(j) be the number of particles which have…
Let $Z$ be a Boolean model based on a stationary Poisson process $\eta$ of compact, convex particles in Euclidean space ${\mathbb{R}}^d$. Let $W$ denote a compact, convex observation window. For a large class of functionals $\psi$, formulas…