Related papers: The Euler-Poincare theory of Metamorphosis
The matching conditions at the interface between two non-mixed fluids at rest are obtained directly using the equation of movement of the whole media. This is a non-usual point of view in hydrodynamics courses and our aim is to fix ideas…
Mathematical morphology contributes many profitable tools to image processing area. Some of these methods considered to be basic but the most important fundamental of data processing in many various applications. In this paper, we modify…
The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete. The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field. The…
In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic…
Metasurfaces in metal/insulator/metal configuration have recently been widely used in photonics research, with applications ranging from perfect absorption to phase modulation, but why and when such structures can realize what kind of…
The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…
The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…
In this paper, we consider the flow of an incompressible fluid in a deformable porous solid. We present a mathematical model using the framework offered by the theory of interacting continua. In its most general form, this framework…
We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through…
Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…
For many of the physical phenomena around us, we have developed sophisticated models explaining their behavior. Nevertheless, inferring specifics from visual observations is challenging due to the high number of causally underlying physical…
The generally adopted approach in theory of relativistic strings and membranes, is similar to use of Lagrange coordinates in continious media mechanics. One can use an alternative approach, which is similar to use of Euler coordinates.…
We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems…
Phase transitions are in the focus of the modeling of multiphase flows. A large number of models is available to describe such processes. We consider several different two phase models that are based on the Euler equations of compressible…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second order geometry and Ito integration on manifolds, allows us to give a natural and effective…
This study aims to exploit the analogy of vortex dynamics in a 2D ideal fluid and 2D non-neutral plasma. Numerical simulations using contour dynamics with adaptive refinement are conducted to study the dynamics of one or more vortices…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…