Related papers: Localization Study of a Non-Local Energetic Damage…
Local energy error estimates for the finite element method for elliptic problems were originally proved in 1974 by Nitsche and Schatz. These estimates show that the local energy error may be bounded by a local approximation term, plus a…
We study a nonlocal wave equation with logarithmic damping which is rather weak in the low frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in the whole space and we study…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based…
This paper is concerned with the energy decomposition of various nonlocal models, including elasticity, thin plates, and gradient elasticity, to arrive at bond-based nonlocal models in which the bond force depends only on the deformation of…
When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B.Sandstede and…
We investigate a state estimation problem for the dynamical system described by uncertain linear operator equation in Hilbert space. The uncertainty is supposed to admit a set-membership description. We present explicit expressions for…
Pairwise particle-exchange model on a linear lattice is solved exactly by a new rate-equation method. Lattice sites are occupied by particles A and B which can exchange irreversibly provided the local energy in reduced. Thus, the model…
We compute the distribution function of single-level curvatures, $P(k)$, for a tight binding model with site disorder, on a cubic lattice. In metals $P(k)$ is very close to the predictions of the random-matrix theory (RMT). In insulators…
We develop a novel analytical approach to the problem of single particle localization in infinite dimensional spaces such as Bethe lattice and random regular graphs. The key ingredient of the approach is the notion of the inverted order…
In the current work we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we study the…
ATMs enable the public to perform financial transactions. Banks try to strategically position their ATMs in order to maximize transactions and revenue. In this paper, we introduce a model which provides a score to an ATM location, which…
We study the three-dimensional cubic nonlinear wave equation (NLW) with random initial data below $L^2(\mathbb{T}^3)$. By considering the second order expansion in terms of the random linear solution, we prove almost sure local…
We study the Anderson model on the Bethe lattice by working directly with propagators at real energies $E$. We introduce a novel criterion for the localization-delocalization transition based on the stability of the population of the…
The aim of this study is to build a non-local homogenized model for three-dimensional composites with inclusions randomly embedded within a matrix according to a stochastic point process w in a bounded open set associated with a suitable…
We investigate many body localization in the presence of a single particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single particle mobility edge in…
This work proposes a data-driven approach for bifurcation analysis in nonlinear systems when the governing differential equations are not available. Specifically, regularized regression with barrier terms is used to learn a homeomorphism…
We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…
Modeling the interference effect is an important issue in the field of causal inference. Existing studies rely on explicit and often homogeneous assumptions regarding interference structures. In this paper, we introduce a low-rank and…
Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating…