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We study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and any diffusion matrix…

We demonstrate that the functorial properties of the symplectic field theory under strong cobordisms and surgery cobordisms can produce finite algebraic (planar) torsions from simple examples, which gives a unified treatment of most of the…

We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A…

We develop a general formalism to describe the interactions between a discrete set of plasmonic resonators mediated by the electromagnetic field. The resulting system of equations for closely-spaced meta-atoms represents a cooperative…

We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle…

The band structures describing non-interacting particles in one-dimensional superlattices of arbitrary periodicity are obtained by an analytical diagonalization of the Hamiltonian without adopting the popular tight-binding approximation.…

This review work addresses the recent advances in solving more comprehensive Hamiltonians. The generalized tight-binding model is developed to investigate the feature-rich quantization phenomena in emergent 2D materials. The mutli-orbital…

In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…

Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…

By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic…

We study dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional (2D) polygons. These systems are described by a nematic order parameter and a spontaneous magnetization, in the absence of any external fields. We…

We consider substitution tilings and Delone sets without the assumption of finite local complexity (FLC). We first give a sufficient condition for tiling dynamical systems to be uniquely ergodic and a formula for the measure of cylinder…

We study the entropy of a set of identical hard objects, of general shape, with each object pivoted on the vertices of a d-dimensional regular lattice of lattice spacing a, but can have arbitrary orientations. When the pivoting point is…

Nanolayered lamellae are common structures in nanoscience and nanotechnology, but most are nearly symmetric in layer thickness. Here, we report on the structure and mechanics of highly asymmetric and thermodynamically stable soft--hard…

Recent experiments and simulations have demonstrated that particle-covered interfaces can exist in stable non-spherical shapes as a result of the steric jamming of the interfacially trapped particles, which confers the interface with…

Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur…

The experimental observations of many interaction-driven electronic phases in moir\'e superlattices have stimulated intense theoretical and experimental efforts to understand and engineer these correlated physics. Strain is a powerful tool…

Realistic applications in metal detection involve multiple inhomogeneous conducting permeable objects and the aim of this paper is to characterise such objects by polarizability tensors. We show that, for the eddy current model, the leading…

This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…

Transition metal dichalcogenides (TMDs) are regarded as a possible materials platform for quantum information science and related device applications. In TMD monolayers, the dephasing time and inhomogeneity are crucial parameters for any…