Related papers: The bounded 19-vertex model
We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter…
Extensive optical measurements of canonical turbulent pipe flows have revealed the existence of structural boundary states (SBSs) -- near-wall low-speed streaks strongly correlated with pairs of counter-rotating quasi-streamwise vortices.…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
This treatise concerns shapes in the sense of constellations of points with various automorphisms quotiented out: continuous translations, rotations and dilations, and also discrete mirror image identification and labelling…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
We present a direct parametrization for continuous-time stochastic state-space models that ensures external stability via the stochastic bounded-real lemma. Our formulation facilitates the construction of probabilistic priors that enforce…
Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are…
This article is concerned with the kinetic modeling, by means of the Vlasov equation, of charged particles under the influence of a strong external electromagnetic field, i.e. when epsilon^2, the dimensionless cyclotron period, tends to…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
We study the classical statistical mechanics of a phase-space curve. This unveils a mechanism that, via the associated entropic force, provides us with a simple realization of effects such as confinement, hard core, and asymptotic freedom.…
In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $\Gamma$-limit of suitable scaled versions of the model…
The finite-size spectrum of the critical staggered six-vertex model with antidiagonal boundary conditions is studied. Similar to the case of periodic boundary conditions, we identify three different phases. In two of those, the underlying…
We construct a quantum system of spherical spins with a continuous local symmetry. The model is exactly soluble in the thermodynamic limit and exhibits a number of interesting properties. We show that the local symmetry is spontaneously…
This is an annotated bibliography on estimation and inference results for queues and related stochastic models. The purpose of this document is to collect and categorise works in the field, allowing for researchers and practitioners to…
Morphogenesis emerges from dynamic feedback among geometry, mechanics, and chemistry; however, disentangling these contributions in living systems remains challenging. Here, we focus on the interplay between geometry and mechanics by…
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and…
We address the co-existence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well known Bernevig-Hughes-Zhang model to introduce a smooth function…
Statistical mechanics of infinite avalanches is studied in the framework of nonequilibrium random-field Ising model. Critical behavior of the model on a random graph (dilute Bethe lattice) is analyzed in detail. We show that sites with a…