Related papers: Approximate calculation of multidimensional first …
We study the limiting behavior of the solutions of Euler equations of one-dimensional compressible fluid flow as the pressure like term vanishes. This system can be thought of as an approximation for the one dimensional model for large…
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…
In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between…
Given a one-dimensional stochastic differential equation, one can associate to this equation a stochastic flow on $[0,+\infty )$, which has an absorbing barrier at zero. Then one can define its dual stochastic flow. In \cite{AW}, Akahori…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…
In this paper we investigate the porous medium equation with a fractional temporal derivative. We justify that the resulting equation emerges when we consider the waiting-time (or trapping) phenomenon that can happen in the medium. Our…
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed…
The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two-…
We investigate the short-time dynamics of a delta-function potential barrier on an initially confined wave-packet. There are mainly two conclusions: A) At short times the probability density of the first particles that passed through the…
We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
We study the three-dimensional compressible Navier-Stokes equations coupled with the $Q$-tensor equation perturbed by a multiplicative stochastic force, which describes the motion of nematic liquid crystal flows. The local existence and…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
A method for approximate solution of initial value and spectral problems for one dimensional Dirac equation based on an analytic approximation of the transmutation operator is presented. In fact the problem of numerical approximation of…
This paper analyzes a method to approximate the first passage time probability density function which turns to be particularly useful if only sample data are available. The method relies on a Laguerre-Gamma polynomial approximation and…
Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation…