Related papers: Control of harmonic map heat flow with an external…

The conformal heat flow of harmonic maps is a system of evolution equations combined with harmonic map flow with metric evolution in conformal direction. It is known that global weak solution of the flow exists and smooth except at mostly…

Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of…

In the present work the possibility of regulating local magnetic field in a quantum ring is investigated theoretically. The ring is coupled to a quantum wire and subjected to an in-plane electric field. Under a finite bias voltage across…

Using two different configurations of temperature and magnetic field gradients, we observed that, in a quasi one-dimensional magnetic fluid, magnetic force either reduces the temperature difference across the sample when the two gradients…

In this paper, we are concerned with the initial boundary values problem associated to the compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow, where the magnetic field is vertical. More precisely, by exploiting…

We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition on the data to be null controllable, i.e., can be driven to…

This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…

Unlike charge, heat flows are difficult to control. We show that, in mesoscopic conductors, electronic thermal currents can be manipulated with a magnetic field by using the Aharonov-Bohm effect: the magnetic control of the interference…

In this paper, we obtain the existence of Dirichlet problem for VT harmonic map from compact Riemannian manifold with or without boundary into compact manifold via the heat flow method. We also obtain the existence of V T geodesics uncer…

We deform a map into a Riemannian manifold that is horizontal with respect to a submersion onto a non-positively curved manifold and satisfies a Chow condition into a harmonic one through a horizontal homotopy.

In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework.…

In this paper we give a brief review of the relation between microscopic dynamical properties and the Fourier law of heat conduction as well as the connection between anomalous conduction and anomalous diffusion. We then discuss the…

Heat is detrimental for the operation of quantum systems, yet it fundamentally behaves according to quantum mechanics, being phase coherent and universally quantum-limited regardless of its carriers. Due to their robustness, superconducting…

In this paper we study the harmonic map heat flow problem for a radially symmetric case. The corresponding partial dfferential equation plays a key role in many analyses of harmonic map heat flow problems. We consider a basic discretization…

We discuss the problem of heat conduction in classical and quantum low dimensional systems from a microscopic point of view. At the classical level we provide convincing numerical evidence for the validity of Fourier law of heat conduction…

We consider a 1 1/2degrees of freedom Hamiltonian dynamical system, which models the chaotic dynamics of charged test-particles in a turbulent electric field, across the confining magnetic field in controlled thermonuclear fusion devices.…

Stabilizing plasma dynamics through externally applied electric and magnetic fields is a fundamental control problem. We study this question for a plasma evolving under a uniform external magnetic field. Although the governing dynamics are…

We consider a steady-state heat conduction problem in a multidimensional bounded domain Omega for the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion Gamma_1 of…

Let $B_1$ be the unit open disk in $\Real^2$ and $M$ be a closed Riemannian manifold. In this note, we first prove the uniqueness for weak solutions of the harmonic map heat flow in $H^1([0,T]\times B_1,M)$ whose energy is non-increasing in…

We show that the effective gauge field for photons provides a versatile platform for controlling the flow of light. As an example we consider a photonic resonator lattice where the coupling strength between nearest neighbor resonators are…