Related papers: Finite time singularity in a MEMS model revisited
We introduce non-Hermitian plasmonic waveguide-cavity systems with topological edge states (TESs) at singular points. The compound unit cells of the structures consist of metal-dielectric-metal (MDM) stub resonators side-coupled to an MDM…
This thesis studies three kinds of mesoscopic systems and how one of their collective degrees of freedom is affected by a dissipative environment: a)Nanoelectromechanical systems based on semiconductor materials, and how surface friction…
The modeling of finite-extent semiconductor nanostructures that are embedded in a host material requires the numerical treatment of the boundary in a finite simulation domain. For the study of a self-assembled InAs dot embedded in GaAs,…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
The stability theory for hyperbolic initial boundary value problems relies most of the time on the Laplace transform with respect to the time variable. For technical reasons, this usually restricts the validity of stability estimates to the…
A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
In this review we define and discuss metastates, mathematical tools with general applicability to thermodynamic systems which are particularly useful when working with disordered or inhomogeneous short-range systems. In an infinite such…
We consider the class of dual-unitary quantum circuits in $1+1$ dimensions and introduce a notion of ``solvable'' matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We…
Abstract: Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here a formal interpretation will be discussed of the widespread idea…
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 consider a nonlocal parabolic model for a micro-electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a…
Numerical simulations and experiments on nanostructures out of equilibrium usually exhibit strong finite size and finite measuring time $t_m$ effects. We discuss how these affect the determination of the full counting statistics for a…
Metasurfaces, the two-dimensional counterpart of metamaterials, have caught great attention thanks to their powerful control over electromagnetic waves. Recent times have seen the emergence of a variety of metasurfaces exhibiting not only…
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can…
We study the quenching behavior for a semilinear heat equation arising in models of micro-electro mechanical systems (MEMS). The problem involves a source term with a spatially dependent potential, given by the dielectric permittivity…
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the interface breaks down…
It is known that a large neutrino number, of the order of a few percent of the entropy of the universe, leads to symmetry breaking at high temperature. We show here that in the minimal supersymmetric standard model (MSSM) this implies the…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…