Related papers: Kinetically constrained models
The goal of this paper is to review the advances that were made during the last few decades in the study of the entropy, and in particular the entropy method, for Kac's many particle system.
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. So far kinetic constraints have been introduced in idealised models aiming to capture…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
Kinetically constrained models (KCMs) are models of glass formers based on the concept of dynamic facilitation. This concept accounts for many of the characteristics of the glass transition. KCMs usually display a combination of simple…
Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The…
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special…
This is a continuation of the previous work (Takata & Noguchi, J. Stat. Phys., 2018) that introduces the presumably simplest model of kinetic theory for phase transition. Here, main concern is to clarify the stability of uniform equilibrium…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…
The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important…
Soft robotic manipulators provide numerous advantages over conventional rigid manipulators in fragile environments such as the marine environment. However, developing analytic inverse models necessary for shape, motion, and force control of…
A brief survey of the author and collaborators' work in compressive sensing applications to continuous imaging models.
The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…