相关论文: Isospectral flows for the inhomogeneous string den…

Hamilton flows on K\"ahler manifold for which all trajectories are $H$-planar curves (complex analog of geodesics) are considered. These flows are called $H$-planar. The equation which has to obey the Hamiltonian of $H$-planar Hamilton flow…

Over three decades ago the advection-diffusion equation for a steady fluid velocity field was homogenized, leading to a Stieltjes integral representation for the effective diffusivity, which is given in terms of a spectral measure of a…

We prove an integral formula for the spectral flow of differentiable loops of unitaries of the form ${\rm Id}+$Schatten. Our formula is in terms of a regularised winding number, expressed in terms of exact differential forms, and we show…

We derive an RG flow equation that is satisfied by the regularized partition function for noncritical strings in background fields. The flow refers to change in the position of a ``boundary'' in the liouville direction. The boundary is…

We present a fairly new and comprehensive approach to the study of stationary flows of the Korteweg-de Vries hierarchy. They are obtained by means of a double restriction process from a dynamical system in an infinite number of variables.…

We show a connection between the linear trace Li-Yau-Hamilton inequality for the Kaehler-Ricci flow and the monotonicity formula for the positive currents. As an application of the linear trace Li-Yau-Hamilton stated in this paper and the…

A free boundary problem for the dynamics of a glasslike binary fluid naturally leads to a singular perturbation problem for a strongly degenerate parabolic partial differential equation in 1D. We present a conjecture for an asymptotic…

A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the…

We review recent results relating linear stability to dynamical stability and the scalar curvature rigidity of Einstein manifolds. We discuss closed and open Einstein manifolds as well as complete noncompact Einstein manifolds which are…

The linear boundary value problem under consideration describes time-harmonic motion of water in a horizontal three-dimensional layer of constant depth in the presence of an obstacle adjacent to the upper side of the layer (floating body).…

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models…

We consider fixed boundary flow with canonical interpretability as principal components extended on non-linear Riemannian manifolds. We aim to find a flow with fixed starting and ending points for noisy multivariate data sets lying on an…

We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.

We study the long-time dynamics of two-dimensional linear Fokker-Planck equations driven by a drift that can be decomposed in the sum of a large shear component and the gradient of a regular potential depending on one spatial variable. The…

We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear structure of the anisotropic momentum equations. Unlike the isotropic flows, the…

Poincare's invariance principle for Hamiltonian flows implies Kelvin's principle for solution to Incompressible Euler Equation. Iyer-Constantin Circulation Theorem offers a stochastic analog of Kelvin's principle for Navier-Stokes Equation.…

The empirical measure flow of a McKean-Vlasov $n$-particle system with common noise is a measure-valued process whose law solves an associated martingale problem. We obtain a stability result for the sequence of martingale problems: all…

We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…

We prove that a class of superlinear indefinite problems with homogeneous Neumann boundary conditions admits an arbitrarily high number of positive solutions, provided that the parameters of the problem are adequately chosen. The…

A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is…