Related papers: Finding Transition Pathways on Manifolds
We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for…
The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…
Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…
We study the spectrum of phase transitions with prescribed mean curvature in Riemannian manifolds. These phase transitions are solutions to an inhomogeneous semilinear elliptic PDE that give rise to diffuse objects (varifolds) that limit to…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
The quantitative study of traffic dynamics is crucial to ensure the efficiency of urban transportation networks. The current work investigates the spatial properties of congestion, that is, we aim to characterize the city areas where…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
We perform molecular dynamics simulation of a small number of particles in a box with periodic boundary conditions from a view point of chaotic dynamical systems. There is a transition at a critical energy E_c that each particle is confined…
We propose a comprehensive dynamical model for cooperative motion of self-propelled particles, e.g., flocking, by combining well-known elements such as velocity-alignment interactions, spatial interactions, and angular noise into a unified…
In this article, we present an analysis of the effects of singular perturbations on the sliding motion in Filippov systems. We show that singular perturbations may lead to qualitatively distinct topologies of phase space on the switching…
We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…
For controller design for systems on manifolds embedded in Euclidean space, it is convenient to utilize a theory that requires a single global coordinate system on the ambient Euclidean space rather than multiple local charts on the…
Structural and static properties of a classical two-dimensional (2D) system consisting of a finite number of charged particles which are laterally confined by a parabolic potential are investigated by Monte Carlo (MC) simulations and the…
We study small white noise perturbations of planar dynamical systems with heteroclinic networks in the limit of vanishing noise. We show that the probabilities of transitions between various cells that the network tessellates the plane into…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
We present an explicit construction of the Freidlin-Wentzell quasipotential of a stochastic system with two degrees of freedom and nonreciprocal interactions. This model undergoes noise-induced transitions between four metastable…
A new type of noised-induced phase transitions that should occur in systems of elements with motivated behavior is considered. By way of an example, a simple oscillatory system {x,v} with additive white noise is analyzed numerically. A…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large.…