Related papers: Derivation and Equilibrium Analysis of a Regulariz…
We study effects of electron-electron interactions on the steady-state characteristics of a hexagonal molecular ring in a magnetic field, as a model for a benzene molecular junction. The system is driven out of equilibrium by applying a…
We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…
We derive a differential equation that is regular at the collision of two equal-mass bodies with attractive interaction in the relativistic action-at-a-distance electrodynamics. Our method uses the energy constant related to the…
We study the statics and dynamics of an elastic manifold in a disordered medium with quenched defects correlated as r^{-a} for large separation r. We derive the functional renormalization-group equations to one-loop order, which allow us to…
In this paper an experimental validation of numerical approaches aimed to predict the coupled behaviour of microbeams for out-of-plane bending tests is performed. This work completes a previous investigation concerning in plane microbeams…
Molecular Dynamics (MD) simulations of standard systems of interacting particles ("atoms") give excellent agreement with the equipartition theorem for the average energy, but we find that these simulations exhibit finite-size effects in the…
A brief derivation of a specific regularization for the magnetic gas dynamic system of equations is given in the case of general equations of gas state (in presence of a body force and a heat source). The entropy balance equation in two…
Within the framework of the Standard Model, the scale of electroweak symmetry breaking is unstable to radiative corrections. We discuss two broad classes of models of new physics (one with a strongly interacting and the other with a…
We study the three-dimensional Electron Magnetohydrodynamics (EMHD) equations without resistivity, a regime known to be ill-posed in Sobolev and Gevrey spaces due to the quasilinear nature of the system. Motivated by recent work on…
Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an…
As optical telecommunication networks become more complex, there is an emerging need for systems capable of very complex switching and manipulation of large numbers of optical signals. MEMS enable these systems by combining excellent…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
The mobility edges (MEs) in energy which separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the…
The evolution of physical systems are often modeled by simple Markovian processes. When settled into stationary states, the probability distributions of such systems are time independent, by definition. However, they do not necessarily fall…
In this paper we develop a metastability theory for a class of stochastic reaction-diffusion equations exposed to small multiplicative noise. We consider the case where the unperturbed reaction-diffusion equation features multiple…
Understanding how out-of-equilibrium states thermalize under quantum unitary dynamics is an important problem in many-body physics. In this work, we propose a statistical ansatz for the matrix elements of non-equilibrium initial states in…
This paper proposes a class of neural ordinary differential equations parametrized by provably input-to-state stable continuous-time recurrent neural networks. The model dynamics are defined by construction to be input-to-state stable (ISS)…
Strong coupling between electronic and mechanical degrees of freedom is a basic requirement for the operation of any nanoelectromechanical device. In this Review we consider such devices and in particular investigate the properties of small…
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…
Many of the large structures of the cell, such as the cytoskeleton, are assembled and maintained far from equilibrium. We study the stabilities of various structures for a simple model of such a far-from-equilibrium organized assembly in…