相关论文: Integrability in the mesoscopic dynamics

Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures (plates or array of thin beams) with cross-sections of the order of microns and lengths of the order of tens or hundreds of microns. Electrostatic forces play…

We report on low temperature measurements performed on micro-electro-mechanical systems (MEMS) driven deeply into the non-linear regime. The materials are kept in their elastic domain, while the observed non-linearity is purely of…

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy…

The paper is devoted to the magnetic properties of isolated mesoscopic grains. We demonstrate that under very general conditions the electron - electron interactions in such grains can be taken into account by a simple interaction…

This study presents a generalized multiscale multimesh finite element method ($\text{M}^2$-FEM) that addresses several long-standing challenges in the numerical simulation of integral structural theories, often used to model multiscale and…

We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can…

Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…

In this paper, we study the Schr\"{o}dinger equation in the semiclassical regime and with multiscale potential function. We develop the so-called constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM), in…

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only,…

The standard physical model of contemporary mesoscopic noise and transport consists in a phenomenologically based approach, proposed originally by Landauer and since continued and amplified by Buettiker (and others). Throughout all the…

A self-consistent linear-response theory for a two-lead mesoscopic structure in Landauer's viewpoint for transport is developed. A density operator relevant in this viewpoint, in a uniform magnetic field is derived. It is shown that this…

In this paper, we introduce a new approach to solving the porous medium equation using a moving mesh finite element method that leverages the Onsager variational principle as an approximation tool. Both the continuous and discrete problems…

Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we…

We report electrical and magneto transport measurements in mesoscopic size, two-dimensional (2D) electron gas in a GaAs quantum well. Remarkably, we find that the probe configuration and sample geometry strongly affects the temperature…

The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics (EM) and magnetohydrodynamics (MHD) have benefited from a…

This thesis describes the merging of the two fields of Coulomb drag and mesoscopic physics. The thesis presents a theory for Coulomb drag between two mesoscopic systems based on linear-response theory. The formalism expresses the drag in…

We represent an algorithm reducing a big class of systems of ($M+1$)-dimensional nonlinear partial differential equations (PDEs) to the systems of $M$-dimensional first order PDEs. Thus, we integrate the original system with respect to only…

A global solution of the Schr\"odinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A: Math. Theor. 48, 225205 (2015)], is generalized to take into account the case of…

We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…

Magnetic gels with embedded micro/nano-sized magnetic particles in crosslinked polymer networks can be actuated by external magnetic fields, with changes in their internal microscopic structures and macroscopic mechanical properties. We…