Related papers: Singular perturbation analysis of a regularized ME…
This paper investigates the dynamic stability of an electromagnetically suspended vehicle, encountered in Hyperloop and Maglev systems, subject to periodic excitations caused by surface irregularities or vibration of the support induced by…
In this paper, we provide a geometric analysis of a new hysteresis model that is based upon singular perturbations. Here hysteresis refers to a type of regularization of piecewise smooth differential equations where the past of a…
A free boundary problem describing small deformations in a membrane based model of electrostatically actuated MEMS is investigated. The existence of stationary solutions is established for small voltage values. A justification of the widely…
Spontaneous symmetry breaking (SSB) and exceptional points (EPs) are often assumed to be inherently linked. Here we investigate the intricate relationship between SSB and specific classes of EPs across three distinct, real-world scenarios…
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…
In this work, singularly perturbed energies arising from discrete $J_1$-$J_3$-models are studied. The energies under consideration consist of a non-convex bulk term and a higher-order regularizing term and are subject to incompatible…
In simulations, particles are traditionally treated as rigid platforms with variable sizes, shapes and interaction parameters. While this representation is applicable for rigid core platforms, particles consisting of soft platforms (e.g.…
In this work we study the mass-spring system \begin{equation} \ddot x + \alpha \dot x + x = - \frac{\lambda} {(1+x)^{2}}, \label{e:inertia} \end{equation} which is a simplified model for an electrostatically actuated MEMS device. The static…
The Maximum Eccentricity Method (MEM) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions. The present paper…
The mobility edge (ME) is a crucial concept in understanding localization physics, marking the critical transition between extended and localized states in the energy spectrum. Anderson localization scaling theory predicts the absence of ME…
The moir\'e superlattice system provides an excellent platform for exploring various novel quantum phenomena. To theoretically tackle the diverse correlated and topological states emerging from moir\'e superlattices, one usually adopts an…
The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…
In the region between close-to-touching hard inclusions, the stress may be arbitrarily large as the inclusions get closer. The stress is represented by the gradient of a solution to the Lam\'e system of linear elasticity. We consider the…
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…
The objective of this thesis is to advance the understanding of complex physical phenomena through the lens of statistical physics. Specifically, it addresses two fundamental questions: What types of interactions can induce buckling of…
Edge localised modes (ELMs) allow maintaining sufficient purity of tokamak H-mode plasmas and thus enable stationary H-mode. On the other hand in a future device ELMs may cause divertor power flux densities far in excess of tolerable…
A library of C functions yielding exact solutions of potential and flux influences due to uniform surface distribution of singularities on flat triangular and rectangular elements has been developed. This library, ISLES, has been used to…
Understanding the yielding of glass-forming systems upon shearing is notoriously difficult since it is a strong non-equilibrium effect. Here we show that the concept of the potential energy landscape (PEL), developed for the quiescent…
Recently, in Applied Mathematics and Computation 474 (2024) 128688, a Levenberg-Marquardt method (LMM) with Singular Scaling was analyzed and successfully applied in parameter estimation problems in heat conduction where the use of a…
Theoretical studies of nearly spherical vesicles and microemulsion droplets, that present typical examples for thermally-excited systems that are subject to constraints, are reviewed. We consider the shape fluctuations of such systems…