相关论文: The gradient flow in a twisted box

In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular,…

The significance of small-scale forcing of particles on the carrier two-dimensional turbulent flow has been shown to influence the spectral scaling properties of the carrier fluid. We investigate possible consequences of such two-way…

This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…

We study a gradient flow on Sobolev diffeomorphisms for the problem of image registration. The energy functional quantifies the effect of transforming a template to a target, while also penalizing deformation of the metric tensor. The main…

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they…

We outline the steps in a derivation of the statement that the SU(2) gauge theory is in a confining phase for all values of the coupling, $0 < \beta <\infty$, defined at lattice spacing a. The approach employed is to obtain both upper and…

The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest…

This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…

A general, two-way coupled, point-particle formulation that accounts for the disturbance created by the dispersed particles in obtaining the undisturbed fluid flow field needed for accurate computation of the force closure models is…

In this paper we study the stable set of the gradient flow associated with a critical point of an analytic function. In particular we present simple topological conditions which imply that this set contains an infinite family of…

We examine a steepest energy descent flow with obstacle constraint in higher order energy frameworks where the maximum principle is not available. We construct the flow under general assumptions using De Giorgi's minimizing movement scheme.…

The critical behaviour of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described…

Trapping and manipulation of small particles underlies many scientific and technological applications. Recently, the precise manipulation of multiple small particles was demonstrated using a Stokes trap that relies only on fluid flow…

We show that the energy required by a turbulent flow to displace a given amount of fluid through a straight duct in a given time interval can be reduced by modulating in time the pumping power. The control strategy is hybrid: it is passive,…

We derive a system of coupled flow equations for the proper-vertices of the background effective average action and we give an explicit representation of these by means of diagrammatic and momentum space techniques. This explicit…

Passive scalars advected by a magnetically driven two-dimensional turbulent flow are analyzed using methods of statistical topography. The passive tracer concentration is interpreted as the height of a random surface and the scaling…

We use gradient flow to compute the static force based on a Wilson loop with a chromoelectric field insertion. The result can be compared on one hand to the static force from the numerical derivative of the lattice static energy, and on the…

Based on the gradient flow, we propose a new method to determine the bounce configuration for false vacuum decay. Our method is applicable to a large class of models with multiple fields. Since the bounce is a saddle point of an action, a…

We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is…

A multi-scale model for the evolution of the velocity gradient tensor in fully developed turbulence is proposed. The model is based on a coupling between a ``Restricted Euler'' dynamics [{\it P. Vieillefosse, Physica A, {\bf 14}, 150…