1,354,420 research outputs found
On the rate of convergence of solutions in domain with periodic multilevel oscillating boundary
No full textIn this paper we deal with the homogenization problem for the Poisson equation in a singularly perturbed domain
with multilevel periodically oscillating boundary. This domain consists of the body, a large number of thin cylinders
joining to the body through the thin transmission zone with rapidly oscillating boundary. Inhomogeneous Fourier
boundary conditions with perturbed coefficients are set on the boundaries of the thin cylinders and on the boundary
of the transmission zone. We prove the homogenization theorems and derive the estimates for the convergence of the
solutions
Asymptotic Analysis of a Boundary Value Problem in a Cascade Thick Junction with a Random Transmission Zone
No full textIn the article we deal with the homogenization of a boundary-value problem
for the Poisson equation in a singularly perturbed two-dimensional junction
of a new type. This junction consists of a body and a large number of thin
rods, which join the body through the random transmission zone with
rapidly oscillating boundary. Inhomogeneous Fourier boundary conditions
with perturbed coefficients are set on the boundaries of the thin rods and
with random perturbed coefficients on the boundary of the transmission
zone. We prove the homogenization theorems and the convergence of the
energy integrals. It is shown that there are three qualitatively different cases
in the asymptotic behaviour of the solutions
Homogenization of 3D Thick Cascade Junction with a Random Transmission Zone Periodic in One direction
No full textIn the paper, we deal with the homogenization problem for the Poisson equation in a singularly perturbed three-dimensional junction of a new type. This junction consists of a body and a large number of thin curvilinear cylinders, joining to body through a random transmission zone with rapidly oscillating boundary, periodic in one direction. Inhomogeneous Fourier boundary conditions with perturbed coefficients are set on the boundaries of the thin cylinders and with random perturbed coefficients on the boundary of the transmission zone. We prove the homogenization theorems and the convergence of the energy integrals
On a singularly perturbed Steklov problem in a domain perforated along the boundary
No full textWe study the asymptotic behavior of solutions and eigenelements to a boundary value problem for the Laplace equation in a domain perforated along part of the boundary. On the boundary of holes, we set the homogeneous Dirichlet boundary condition and the Steklov spectral condition on the mentioned part of the outer boundary of the domain. Assuming that the boundary microstructure is periodic, we construct the limit problem and prove the homogenization theorem
Detecting temporal correlations in hopping dynamics in Lennard-Jones liquids
No full textLennard-Jones mixtures represent one of the popular systems for the study of glass-forming liquids. Spatio/temporal heterogeneity and rare (activated) events are at the heart of the slow dynamics typical of these systems. Such slow dynamics is characterised by the development of a plateau in the mean-squared displacement (MSD) at intermediate times, accompanied by a non-Gaussianity in the displacement distribution identified by exponential tails. As pointed out by some recent works, the non-Gaussianity persists at times beyond the MSD plateau, leading to a Brownian yet non-Gaussian regime and thus highlighting once again the relevance of rare events in such systems. Single-particle motion of glass-forming liquids is usually interpreted as an alternation of rattling within the local cage and cage-escape motion and therefore can be described as a sequence of waiting times and jumps. In this work, by using a simple yet robust algorithm, we extract jumps and waiting times from single-particle trajectories obtained via molecular dynamics simulations. We investigate the presence of correlations between waiting times and find negative correlations, which becomes more and more pronounced when lowering the temperature
Constructing a Stochastic Model of Bumblebee Flights from Experimental Data
No full textPMCID: PMC3592844This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
On the Steklov problem in a domain perforated along a part of the boundary
No full textWe study the asymptotic behavior of solutions and eigenelements to a 2-dimensional and
3-dimensional boundary value problem for the Laplace equation in a domain perforated along part of the boundary. On the boundary of holes we set the homogeneous Dirichlet boundary condition and the Steklov spectral condition on the mentioned part of the outer boundary of the domain. Assuming that the boundary microstructure is periodic, we construct the limit problem and prove the homogenization theorem
On the Steklov problem in a domain perforated along a part of the boundary
No full textWe study the asymptotic behavior of solutions and eigenelements to a 2-dimensional and 3-dimensional boundary value problem for the Laplace equation in a domain perforated along part of the boundary. On the boundary of holes we set the homogeneous Dirichlet boundary condition and the Steklov spectral condition on the mentioned part of the outer boundary of the domain. Assuming that the boundary microstructure is periodic, we construct the limit problem and prove the homogenization theorem
Homogenization in Domains Randomly Perforated Along the Boundary
No full textWe study the asymptotic behavior of the solution of the Laplace equation in a domain perforated along the boundary. Assuming that the boundary microstructure is random, we construct the limit problem and prove the homogenization theorem. Moreover we apply those results to some spectral
problems
On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary
No full textWe consider a boundary value problem for a homogeneous elliptic equation with an inhomogeneous Steklov boundary condition. The problem involves a singular perturbation, which is the Dirichlet condition imposed on a small piece of the boundary. We rewrite such problem to a resolvent equation for a self-adjoint operator in a fractional Sobolev space on the boundary of the domain. We prove the norm convergence of this operator to a limiting one associated with an unperturbed problem involving no Dirichlet condition. We also establish an order sharp estimate for the convergence rate. The established convergence implies the convergence of the spectra and spectral projectors. In the second part of the work we study perturbed eigenvalues converging to limiting simple discrete ones. We construct two-terms asymptotic expansions for such eigenvalues and for the associated eigenfunctions
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