Related papers: Front progression for the East model
We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution…
In the EPR experiment, each measurement addresses the question "What spin value has this particle along this orientation?" The outcome then proves that the spin value has been affected by the distant experimenter's choice of spin…
The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions,…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable…
The cutoff phenomenon describes a sharp transition in the convergence of a Markov chain to equilibrium. In recent work, the authors established cutoff and its location for the stochastic Ising model on the $d$-dimensional torus $(Z/nZ)^d$…
We rigorously analyze the low temperature non-equilibrium dynamics of the East model, a special example of a one dimensional oriented kinetically constrained particle model, when the initial distribution is different from the reversible one…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
A dynamical version of the Widom-Rowlinsom model in the continuum is considered. The dynamics is modelled by a spatial two-component birth-and-death Glauber process where particles, in addition, are allowed to change their type with density…
We establish selection of critical pulled fronts in invasion processes. Our result shows convergence to a pulled front with a logarithmic shift for open sets of steep initial data, including one-sided compactly supported initial conditions.…
Confinement describes the phenomenon when the attraction between two particles grows with their distance, most prominently found in quantum chromodynamics (QCD) between quarks. In condensed matter physics, confinement can appear in quantum…
This article addresses the issue of global convergence towards pushed travelling fronts for solutions of parabolic systems of the form \[ u_t = - \nabla V(u) + u_{xx} \,, \] where the potential $V$ is coercive at infinity. It is proved…
The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique…
In this paper we study the oriented swap process on the positive integers and its asymptotic properties. Our results extend a theorem by Angel, Holroyd, and Romik regarding the trajectories of particles in the finite oriented swap process.…
The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently…
We study a chaotic particle-conserving kinetically constrained model, with a single parameter which allows us to break reflection symmetry. Through extensive numerical simulations we find that the domain wall state shows a variety of…
We investigate the dynamical fixed points of the zero temperature Glauber dynamics in Ising-like models. The stability analysis of the fixed points in the mean field calculation shows the existence of an exponent that depends on the…
This thesis consists of two parts, connected by one central theme: the dynamics of the "shape of space". The first part of the thesis concerns the construction of a theory of gravity dynamically equivalent to general relativity (GR) in 3+1…
Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic…