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We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary conditions: free on both axes, periodic on…
Sticky diffusion processes on bounded domains spend finite time (and finite mean time) on the lower-dimensional space given by the boundary. Once the process hits the boundary, then it starts again after a random amount of time. While on…
We analytically and numerically study the effect of finite spatial boundaries on the Takayasu model of diffusing and aggregating particles with steady monomer input in one dimension. Exact expressions are derived for the steady-state…
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity of the solution, which introduces a nonlocal coupling…
We analyze the behavior of the eigenvalues of the following non local mixed problem $\left\{ \begin{array}{rcll} (-\Delta)^{s} u &=& \lambda_1(D) \ u &\inn\Omega,\\ u&=&0&\inn D,\\ \mathcal{N}_{s}u&=&0&\inn N. \end{array}\right $ Our goal…
Contrary to field theoretical calculations in the thermodynamic limit where the volume is assumed to be infinitely large, the heavy-ion collisions always carry the effects of finite size. A sufficiently small system size is expected to…
The Chern-Simons Ginzburg-Landau theory for the fractional Quantum Hall effect is studied in the presence of a confining potential. We review the bulk properties of the model and discuss how the plateau formation emerges without any…
The influence of short-range interactions between a multi-phase, multi-component mixture and a solid wall in confined geometries is crucial in life sciences and engineering. In this work, we extend the Cahn-Hilliard model with dynamic…
Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality…
In the paper, assuming that the motion of rarefied gases in a bounded domain is governed by the angular cutoff Boltzmann equation with diffuse reflection boundary, we study the effects of both soft intermolecular interaction and…
Nonstationary and nonequilibrium processes are considered on the basis of an Enskog-Landau kinetic equation using a boundary conditions method. A nonstationary solution of this equation is found in the pair collision approximation. This…
In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…
Mixed boundary conditions are introduced to finite element exterior calculus. We construct smoothed projections from Sobolev de Rham complexes onto finite element de Rham complexes which commute with the exterior derivative, preserve…
Many elliptic boundary value problems exhibit an interior regularity property, which can be exploited to construct local approximation spaces that converge exponentially within function spaces satisfying this property. These spaces can be…
The imposition of inhomogeneous Dirichlet (essential) boundary conditions is a fundamental challenge in the application of Galerkin-type methods based on non-interpolatory functions, i.e., functions which do not possess the Kronecker delta…
We consider the quantisation of linearised fluctuations of the metric and matter fields about a Lifshitz background, exploring the possibility of alternative boundary conditions, allowing the slow fall-off modes to fluctuate. We find that…
We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a…
This paper presents a theoretical study on the influence of a discrete element in the nonlinear dynamics of a continuous mechanical system subject to randomness in the model parameters. This system is composed by an elastic bar, attached to…