Related papers: Iterative Schemes for Bump Solutions in a Neural F…
In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called…
This article continues the research initiated in [17]. We derive explicit formulae for the leading order profiles of eleven types of stationary solutions to a one-dimensional two-layer thin-film liquid model considered with an…
This work proposes a fast iterative method for local steric Poisson--Boltzmann (PB) theories, in which the electrostatic potential is governed by the Poisson's equation and ionic concentrations satisfy equilibrium conditions. To present the…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
In this paper, we consider a non-local (in time) two-phase flow model. The non-locality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed-point iterative linearization…
This paper investigates the conditions for the formation of local bumps in the activity of binary attractor neural networks with spatially dependent connectivity. We show that these formations are observed when asymmetry between the…
We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using…
We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is prescribed. We apply sharp interface methods to develop an…
We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the…
We generalize the Lee-Suzuki iteration method for summing the folded diagram series to the case where the unperturbed model-space energies are non-degenerate. A condition is derived for the convergence of the iteration scheme and this…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0,T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
Callaway's dual relaxation times model, which takes into account the normal and resistive scatterings of phonon, is used to describe the heat conduction in materials like graphene. For steady-state problems, the Callaway model is usually…
Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit…
Mesoscopic numerical simulation has become an important tool in thermal management and energy harvesting at the micro/nano scale, where the Fourier's law failed. However, it is not easy to efficiently solve the phonon Boltzmann transport…
We consider localised bulging/necking in an inflated hyperelastic membrane tube with closed ends. We first show that the initiation pressure for the onset of localised bulging is simply the limiting pressure in uniform inflation when the…
We propose a method to obtain iterative schemes guarantee unique solutions for systems of partial differential equations that are not symmetric with respect to the time by generalizing He variational iteration method and using Banach fixed…
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…
We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…