Related papers: The Euler-Poincare theory of Metamorphosis

A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…

The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincar\`e maps in geometric models of well-known Lorenz attractor. Using both analytical and symbolic approaches, we study connections between…

We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of new generalized Eulerian configuration coordinates. After the separation of the relativistic center of mass from the relative variables on…

A general relativistic version of the Euler equation for perfect fluid hydrodynamics is applied to a system of two neutron stars orbiting each other. In the quasi-equilibrium phase of the evolution of this system, a first integral of motion…

We find the Euler-Lagrangian equation by maximising the total entropy. Hence we obtain an expression for mass of the spherically symmetric system by solving the Euler-Lagrangian equation where the Homotopy Perturbation Method has been…

We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…

Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

We critically compare thermodynamic and kinetic approaches, that have been recently used to study relations between the spin polarization and fluid vorticity in systems consisting of spin-one-half particles. The thermodynamic approach…

The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…

In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…

The formation of dynamical patterns is one of the most striking features of nonequilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as nonreciprocal…

Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: Subgrid processes that the model cannot resolve, and diabatic sources in the equations, due to radiation for example.…

Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in…

Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…

We study Tao's finitary viewpoint of convergence in metric spaces, as captured by the notion of metastability. We adopt the perspective of continuous model theory. We show that, in essence, metastable convergence with a given rate is the…

Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…

Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…

In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…

We tackle the problem of modeling sequential visual phenomena. Given examples of a phenomena that can be divided into discrete time steps, we aim to take an input from any such time and realize this input at all other time steps in the…