相关论文: Zero-Preserving Iso-spectral Flows Based on Parall…

Subdivision surfaces are considered as an extension of splines to accommodate models with complex topologies, making them useful for addressing PDEs on models with complex topologies in isogeometric analysis. This has generated a lot of…

We investigate the geometry of a family of equations in two dimensions which interpolate between the Euler equations of ideal hydrodynamics and the inviscid surface quasi-geostrophic equation. This family can be realised as geodesic…

Isospectral flows are abundant in mathematical physics; the rigid body, the the Toda lattice, the Brockett flow, the Heisenberg spin chain, and point vortex dynamics, to mention but a few. Their connection on the one hand with integrable…

We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to temporal scalings and Galilean transformations, we define a…

We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target supported on finitely many points. This semi-discrete regime is the theoretical setting behind the use of Flow Matching for…

In 2007, Chow and Glickenstein considered a linear semi-discrete analogue of the second-order curve shortening flow for smooth closed curves. In this article, we consider linear semi-discrete analogues of the polyharmonic curve diffusion…

In this work, we consider a Shallow-Water Quasi Geostrophic equation on the sphere, as a model for global large-scale atmospheric dynamics. This equation, previously studied by Verkley (2009) and Schubert et al. (2009), possesses a rich…

The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…

A consistent kinetic modeling and discretization strategy for compressible flows across all Prandtl numbers and specific heat ratios is developed using the quasi-equilibrium approach within two of the most widely used double-distribution…

Dense flow visualization is a popular visualization paradigm. Traditionally, the various models and methods in this area use a continuous formulation, resting upon the solid foundation of functional analysis. In this work, we examine a…

We study mean curvature flows in a warped product manifold defined by a closed Riemannian manifold and $\mathbb{R}$. In such a warped product manifold, we can define the notion of a graph, called a geodesic graph. We prove that the curve…

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…

We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that…

In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…

We introduce two notions for flows on quasi-diagonal C*-algebras, quasi-diagonal and pseudo-diagonal flows; the former being apparently stronger than the latter. We derive basic facts about these flows and give various examples. In addition…

A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of velocity field on three coordinate planes is proposed. It is argued that such divergence-free projections satisfying all the…

We provide an alternative construction of the quasi-Fuchsian flows introduced by Ghys in \cite{Ghys-92}. Our approach is based on the coupled vortex equations that allows to see these flows as thermostats on the unit tangent bundle of the…

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…

This expository paper presents the current knowledge of particular fully nonlinear curvature flows with local forcing term, so-called locally constrained curvature flows. We focus on the spherical ambient space. The flows are designed to…

We give a new application of the theory of holomorphic motions to the study the distortion of level lines of harmonic functions and stream lines of ideal planar fluid flow. In various settings, we show they are in fact quasilines - the…