相关论文: A Zermelo navigation problem with a vortex singula…
This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…
Recent experiments on quantum turbulence in superfluid helium made use of small tracer particles to track the motion of quantized vortices, determine velocity statistics and visualize vortex reconnections. A problem with this visualization…
Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive…
Recent advances in cold-atom platforms have made real-time dynamics accessible, renewing interest in the motion of superfluid vortices in two-dimensional domains. Here we show that the energy and the trajectories of arbitrary vortex…
Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a novel approach using periodic orbit theory to analyze plasma turbulence, identifying fundamental structures…
This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with…
The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is…
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…
One of the fundamental problems in spacecraft trajectory design is finding the optimal transfer trajectory that minimizes the propellant consumption and transfer time simultaneously. We formulate this as a multi-objective optimal control…
We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected…
We consider, on a temporal star graph, the problem of optimal damping a control system is considered for a generalized pantograph equation, which is a neutral-type equation with a time-proportional delay. The delay in the system propagates…
We obtained new periodic solutions in the problems of three and four point vortices moving on a plane. In the case of three vortices, the system is reduced to a Hamiltonian system with one degree of freedom, and it is integrable. In the…
We study time-minimum optimal control for a class of quantum two-dimensional dissipative systems whose dynamics are governed by the Lindblad equation and where control inputs acts only in the Hamiltonian. The dynamics of the control system…
The theory of point vortex dynamics has existed since Kirchhoff's proposal in 1891 and is still under development with connections to many fields in mathematics. As a strong simplification of the concept of vorticity it excels in…
In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between…
The dynamics of gyrotropic vortex motion in a thin circular nanodisk of soft ferromagnetic material is considered. The demagnetization field is calculated using two-dimensional Green's functions for the thin film problem and fast Fourier…
Marine microorganisms must cope with complex flow patterns and even turbulence as they navigate the ocean. To survive they must avoid predation and find efficient energy sources. A major difficulty in analysing possible survival strategies…
We study dynamics of vortices in solutions of the Gross-Pitaevskii equation $i \partial_t u = \Delta u + \varepsilon^{-2} u (1 - |u|^2)$ on $\mathbb{R}^2$ with nonzero degree at infinity. We prove that vortices move according to the…
The initial value problem for the Ginzburg-Landau-Schr\"odinger equation is examined in the $\epsilon \rightarrow 0$ limit under two main assumptions on the initial data $\phi^\epsilon$. The first assumption is that $\phi^\epsilon$ exhibits…
This article is concerned with the study of existence and properties of stationary solutions for the dynamics of $N$ point vortices in an idealised fluid constrained to a bounded two--dimen\-sional domain $\Omega$, which is governed by a…