Related papers: On the Voltage-Conductance kinetic equation
We prove a stability result in the hybrid inverse problem of recovering the electrical conductivity from partial knowledge of one current density field generated inside a body by an imposed boundary voltage. The region where interior data…
A vortex-induced transverse voltage in a superconducting film, previously predicted theoretically, has been seen experimentally for the first time. The magnitude of this voltage and its nonmonotonic current dependence are explained on the…
A system of phase-field equations with strong-coupling through state and gradient dependent non-diagonal mobility matrices is studied. Existence of weak solutions is established by the Galerkin approximation and a-priori estimates in strong…
We consider closed planar curves with fixed length and arbitrary winding number whose elastic energy depends on an additional density variable and a spontaneous curvature. Working with the inclination angle, the associated $L^2$-gradient…
We review all the calculations necessary for the construction of a Lyapunov like functional for nonlinear stability analysis of steady states in thermodynamically isolated/open systems composed of compressible heat conducting fluids.
Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are $q$-exponentials of an appropriate potential function, are…
We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
We study the asymptotic behavior of the forced linear Euler and nonlinear Navier-Stokes equations close to Couette flow in a periodic channel. As our main result we show that for smooth time-periodic forcing linear inviscid damping…
We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory,…
We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…
Based on the numerical solution non-stationary Ginzburg-Landau equations, we investigated the evolution of the order parameter of superconducting channels with different lengths under applied voltage (so-called voltage-driven regime). We…
We develop a kinetic-theory framework to investigate the steady rheology of a dilute gas interacting via a repulsive potential under uniform shear flow. Starting from the Boltzmann equation with a restitution coefficient that depends on the…
We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy…
Superconducting systems may display different types of nonequilibrium states depending on the specific constraints imposed for measurement. We probe current-voltage relations of three-dimensional superconducting films by allowing finite…
Nonlinear non-stationary equation describing evolution of weakly curved premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus instability, is derived. The new equation respects all the conservation laws to be…
Recent work has revealed a general procedure for incorporating disorder into the semiclassical model of carrier transport, whereby the predictions of quantum linear response theory can be recovered within a quantum kinetic approach based on…
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando--Trebeschi (2008) [20]. The…
We consider the steady state non-equilibrium physics of the multichannel interacting resonant level model in the weak coupling regime. By using the scattering state method we show in agreement with the rate equations that the negative…
We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations…