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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 investigate a class of Mean Field Games (MFGs) in which the state dynamics are governed by multidimensional reflected stochastic differential equations (SDEs). We establish the existence of an equilibrium and show that it…
In the past fifteen years mathematical models for microelectromechanical systems (MEMS) have been the subject of several studies, in particular due to the interesting qualitative properties they feature. Still most research is devoted to an…
This work presents the mathematical modeling and numerical investigation of a thermo-controlled Micro-Electro-Mechanical System (MEMS) obtained by coupling an HP memristor with mechanical and electrical resonators. Using the linear drift HP…
The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems (MEMS)…
Local well-posedness for a nonlinear parabolic-hyperbolic coupled system modelling Micro-Electro-Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has…
We study periodic solutions of a one-degree of freedom micro-electro-mechanical system (MEMS) with a parallel-plate capacitor under $T$--periodic electrostatic forcing. We obtain analytical results concerning the existence of $T-$ periodic…
Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically…
This thesis is devoted to the study of dynamical properties of diluted models. These are mean field statistical mechanics systems, but with finite local connectivity. Among other reasons, the interest for these models arises from their deep…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
In this perspective article, we discuss the scenario of dynamically emergent correlation (DEC) arising in classical and quantum noninteracting systems when they are subjected to a common fluctuating stochastic environment. The key property…
Touchdown is shown to be the only possible finite time singularity that may take place in a free boundary problem modeling a three-dimensional microelectromechanical system. The proof relies on the energy structure of the problem and uses…
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…
How stochastic, microscopic events generate deterministic, macroscopic properties is a fundamental question in physics. We address this question by developing a quantum master equation model for concentrated radical solutions, where random…
In the magnetic Eden model (MEM), particles have a spin and grow in contact with a thermal bath. Although Ising-like interactions affect the growth dynamics, deposited spins are frozen and not allowed to flip. This review article focuses on…
The electronic structure of heavy elements, when described in a space-time which the metric is affected by the electromagnetic interaction, presents instabilities. These instabilities increase with the atomic number, and above a critical…
Accompanied by the development of microfabrication techniques, such as MEMS and micro-TAS, there has been increasing interests on the methodology to generate a desired motion on a micro object in a solution environment. It is well know that…
The precise characterization of dynamics in open quantum systems often presents significant challenges, leading to the introduction of various approximations to simplify a model. One commonly used strategy involves Markovian approximations,…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
Emergent behavior is a key feature defining a system under study as a complex system. Simulation has been recognized as the only way to deal with the study of the emergency of properties (at a macroscopic level) among groups of system…