相关论文: Long time behaviour of generalised gradient flows …
The paper is devoted to the isotropic realizability of a regular gradient field u or a more general vector field b, namely the existence of a continuous positive function $\sigma$ such that $\sigma$b is divergence free in R d or in an open…
This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical…
We develop a general mathematical framework to analyze scaling regimes and derive explicit analytic solutions for gradient flow (GF) in large learning problems. Our key innovation is a formal power series expansion of the loss evolution,…
How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest, and has stimulated a lot of activities in dynamical and stochastic systems…
In this paper, we use a generic and general variational method to obtain solutions to the flow of generalized Newtonian fluids through circular pipes and plane slits. The new method is not based on the use of the Euler-Lagrange variational…
The effects of global flow rotation and curvature on the subcritical transition to turbulence in shear flows are examined. The relevant time-scales of the problem are identified by a decomposition of the flow into a laminar and a deviation…
In this paper, we study gradient-based classical extremum seeking (ES) for uncertain n-dimensional (nD) static quadratic maps in the presence of known large constant distinct input delays and large output constant delay with a small…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
This report is actually the in-class project of MATH489 FA2022, Dynamics and Differential Equations in University of Illinois Urbana-Champaign. The report is mainly about gradient flow of a Morse-type functions (Morse functions, Morse--Bott…
The volatile transition from quiescent laminar to strongly fluctuating turbulent dynamics in shear flows remains only poorly understood despite its practical importance and more than a century of intense research. The theoretical…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e. the…
We study the distribution of work induced by the two-point measurement protocol for a driven open quantum system. We first derive a general form for the generating function of work for the total system, bearing in mind that the Hamiltonian…
To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is…
Third-order approximate solutions for surface gravity waves in the finite water depth are studied in the context of potential flow theory. This solution provides explicit expressions for the surface elevation, free-surface velocity…
We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities or criticalities, where the roof function defining the…
An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate…
The gradient expansion is the fundamental organising principle underlying relativistic hydrodynamics, yet understanding its convergence properties for general nonlinear flows has posed a major challenge. We introduce a simple method to…