相关论文: A Zermelo navigation problem with a vortex singula…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
The magnetic field $h_z$ of a moving Pearl vortex in a superconducting thin-film in $(x,y)$ plane is studied with the help of time-dependent London equation. It is found that for a vortex at the origin moving in $+x$ direction, $h_z(x,y)$…
We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…
The dynamical formulation of optimal transport, also known as Benamou-Brenier formulation or Computational Fluid Dynamics formulation, amounts to write the optimal transport problem as the optimization of a convex functional under a PDE…
This is the final version of a Thesis presented to the PostGrad Program in Physics of the Physics Institute of the Federal University of Rio de Janeiro (UFRJ), as a necessary requirement for the title of Ph.D. in Science (Physics). The…
We derive the exact equation of motion for a vortex in two- and three- dimensional non-relativistic systems governed by the Ginzburg-Landau equation with complex coefficients. The velocity is given in terms of local gradients of the…
The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite…
In this work we are interested in extreme vortex states leading to the maximum possible growth of palinstrophy in 2D viscous incompressible flows on periodic domains. This study is a part of a broader research effort motivated by the…
The motion of three interacting point vortices in the plane can be thought of as the motion of three geometrical points endowed with a dynamics. This motion can therefore be re-formulated in terms of dynamically evolving geometric…
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…
This paper deals with the one perturbed vortex dynamics problem which describes the system of two point vortices in a Bose-Einstein condensate enclosed in a cylindrical trap. This system is a completely integrable Hamiltonian system with…
We investigate the relation between energy minimizing maps valued into spheres having topological singularities at given points and optimal networks connecting them (e.g. Steiner trees, Gilbert-Steiner irrigation networks). We show the…
This work is concerned with the necessary conditions of optimality for a minimal time control problem $(P)$ for the linearized Navier-Stokes periodic flow in a 2D-channel, subject to a boundary input which acts on the transversal component…
As a model for vortex-wall interactions, we consider the two-dimensional incompressible Navier--Stokes equations in the half-plane $R^2_+$ with no-slip boundary condition and point vortices as initial data. We focus on the paradigmatic…
The quest for the optimal navigation strategy in a complex environment is at the heart of microswimmer applications like cargo carriage or drug targeting to cancer cells. Here, we formulate a variational Fermat's principle for microswimmers…
The vortex velocity probability distribution for two distinct vortices is determined for the case of phase-ordering kinetics in systems with point defects. The n-vector model driven by time-dependent Ginzburg-Landau dynamics for a…
In this work, we study the transport of vorticity on curved dynamical two-dimensional magnetic membranes. We find that topological transport can be controlled by geometrically reducing symmetries, enabling processes absent from flat…
Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a non-existence theorem for relative equilibria is proved, equilibria are classified when all vorticities have the same sign,…
We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et…
A general exact weak solution to the nonlinear equation of the conservation of the absolute vorticity in a thin layer of an incompressible medium on a rotating sphere is proposed. It takes into account the helicity of the point vortices and…