Related papers: Singular perturbation analysis of a regularized ME…
We consider a parabolic problem with Robin boundary condition which arises when the edge of a micro-electro-mechanical-system (MEMS) device is connected with a flexible nonideal support. Then via a rigorous analysis we investigate the…
Singular exponential nonlinearities of the form $e^{h(x)\epsilon^{-1}}$ with $\epsilon>0$ small occur in many different applications. These terms have essential singularities for $\epsilon=0$ leading to very different behaviour depending on…
The relativistic membrane equation can be rewritten as a first order hyperbolic system. Making use of the characteristic decomposition method, a new blow-up theorem is established. As an application, it demonstrates the formation of…
Many new possibilities to observe and use novel physical effects are discovered at so called exceptional points (EPs). This is done by using parity-time (PT) -symmetric non-Hermitian systems and balancing gains and losses. When combined…
Emergent phenomena share the fascinating property of not being obvious consequences of the design of the system in which they appear. This characteristic is no less relevant when attempting to simulate such phenomena, given that the outcome…
Nonlocal MEMS equations exhibit finite-time quenching, or touchdown, which is difficult to capture numerically. We study a stagewise rescaling algorithm for a two-dimensional nonlocal MEMS equation in an asymptotically constant-feedback…
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…
This paper investigates the stability and stabilization of semilinear single-track vehicle models with distributed tire friction dynamics, modeled as interconnections of ordinary differential equations (ODEs) and hyperbolic partial…
The origin of disentanglement for two specific sub-classes of $X$-states namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed states (MEMSs) is investigated analytically for a physical system consisting of two…
Mobility edge (ME) has played an essential role in disordered models. However, while this concept has been well established in disordered single-particle models, its existence in disordered many-body models is still under controversy. Here,…
The singular parabolic problem $u_t-\triangle u=\lambda{\frac{1+\delta|\nabla u|^2}{(1-u)^2}}$ on a bounded domain $\Omega$ of $\mathbb{R}^n$ with Dirichlet boundary condition, models the Microelectromechanical systems (MEMS) device with…
The current state of the art for analytical and computational modelling of deformation in nonlinear electroelastic and magnetoelastic membranes is reviewed. A general framework and a list of methods to model large deformation and associated…
The simultaneous estimation of multiple unknown parameters is the most general scenario in quantum sensing. Quantum multi-parameter estimation theory provides fundamental bounds on the achievable precision of simultaneous estimation.…
The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow…
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for three classes of periodically forced equations with singularities, including the equations…
The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size…
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has…
This dissertation presents a new coupled electro-mechanical model that is an improvement on the classical parallel-plate approximation. The model employs a hyperbolic function to account for the beam deformed shape and electrostatic field.…
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…
To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an $\ns$-species hard core lattice gas. On introducing $\ns$ spherical constraints, the free energy may be expressed…