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We introduce and study a class of particle hopping models consisting of a single box coupled to a pair of reservoirs. Despite being zero-dimensional, in the limit of large particle number and long observation time, the current and activity…
The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional…
Semi-infinite $d$-dimensional systems with an $m$-axial bulk Lifshitz point are considered whose ($d-1$)-dimensional surface hyper-plane is oriented perpendicular to one of the $m$ modulation axes. An $n$-component $\phi^4$ field theory…
Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the driving force and that slip along at least one of the directions…
We introduce a deterministic self-organized critical system that is one dimensional and bulk driven. We find that there is no universality class associated with the system. That is, the critical exponents change as the parameters of the…
A set of classical solutions of a singular type is found in a 5D SUSY bulk-boundary system. The "parallel" configuration, where the whole components of fields or branes are parallel in the iso-space, naturally appears. It has three {\it…
Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The…
We analyze systems where an effective large-N expansion arises naturally in gauge theories without a large number of colors: a sufficiently large charge density alone can produce a perturbative string ('tHooft) expansion. One example is…
We consider quadrangulations with a boundary and derive explicit expressions for the generating functions of these maps with either a marked vertex at a prescribed distance from the boundary, or two boundary vertices at a prescribed mutual…
We study dynamic networks under an undirected consensus communication protocol and with one state-dependent weighted edge. We assume that the aforementioned dynamic edge can take values over the whole real numbers, and that its behaviour…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling…
We study the analytic structure of loop Witten diagrams in Euclidean AdS represented by their conformal partial wave expansions. We show that, as in flat space, amplitude's singularities are associated with non-trivial cuts of the diagram…
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite…
We give a characterisation of the singular points of the free boundary $\partial \{u>0\}$ for viscosity solutions of the nonlinear equation \begin{equation}F(D^2 u)=-\chi_{\{u>0\}},\tag{0.1} \end{equation} where $F$ is a fully nonlinear…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…
Finite-size effects in systems with diverging characteristic lengthscale have been addressed via state-of-the-art Monte Carlo and molecular dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid…
We perform large-scale simulations of directed sandpile models with both deterministic and stochastic toppling rules. Our results show the existence of two distinct universality classes. We also provide numerical simulations of directed…
We introduce a new model to study the oscillations of opposite flows sharing a common bottleneck and moving on two Totally Asymmetric Simple Exclusion Process (TASEP) lanes. We provide a theoretical analysis of the phase diagram, valid when…
We provide a characterisation of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to…