相关论文: On an evolution equation in sub-Finsler geometry

We study the transition to turbulence from the perspective of the velocity gradient tensor dynamics. Our work is motivated by the observation of nonlinear structures emerging during transition, as revealed by vortex identifiers such as the…

Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…

We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open…

Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to…

In these lecture notes, we provide an introduction to the theory of mixing for incompressible flows from a PDE perspective. We discuss both the Lagrangian (ODE) and Eulerian (PDE, continuity equation) viewpoints, and introduce suitable…

We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism involving the diffusion/Schrodinger…

We introduce the submersion between two spray structures and propose the submersion technique in spray geometry. Using this technique, as well as global invariant frames on a Lie group, we setup the general theoretical framework for…

The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are…

Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general…

A mathematical model to study the flow evolution in RB convection laden with finite-sized particles after a flow perturbation is developed with an Euler-Lagrange viewpoint. A linear analysis is conducted by combining the averaged flow-scale…

Mean curvature flow is the most natural evolution equation in extrinsic geometry, and shares many features with Hamilton's Ricci flow from intrinsic geometry. In this lecture series, I will provide an introduction to the mean curvature flow…

In this study, we introduce novel methodologies designed to adapt original data in response to the dynamics of persistence diagrams along Wasserstein gradient flows. Our research focuses on the development of algorithms that translate…

Hydrodynamics describes the evolution of macroscopic states in non--equilibrium thermodynamics. Following Onsager reciprocal relations, one can formulate a large class of hydrodynamic equations as gradient flows of free energies. In recent…

The spontaneous symmetry breaking taking place in the direction perpendicular to the energy flux in a dilute vibrofluidized granular system is investigated, using both a hydrodynamic description and simulation methods. The latter include…

The flow equation approach investigated by Wegner et al. is applied to an unbounded Hamiltonian system with a generalization. We show that a well-known quantized complex energy eigenvalues which is related to decay widths can be given with…

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slater type variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove that they are analytic homogeneous…

One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian…

The dynamics of gradient and Hamiltonian flows with particular application to flows on adjoint orbits of a Lie group and the extension of this setting to flows on a loop group are discussed. Different types of gradient flows that arise from…

We consider a pseudo-Riemannian metric that changes signature along a smooth curve on a surface, called the discriminant curve. The discriminant curve separates the surface locally into a Riemannian and a Lorentzian domain. We study the…

Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first…