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Wedge-shaped geometries in low-Reynolds-number flows are of increasing importance, for instance, in the design of microfluidic devices. The corresponding Green's functions describing the induced flow in response to a locally applied force…

A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal…

Despite their advantages, normalizing flows generally suffer from several shortcomings including their tendency to generate unrealistic data (e.g., images) and their failing to detect out-of-distribution data. One reason for these…

We perform the homogenization process avoiding the necessity of testing the weak formulation of the initial and homogenized systems by corresponding weak solutions. We show that the stress tensor for homogenized problem depends on the…

A complete analysis is presented for the far-field creeping flow produced by a multipolar force distribution in a fluid confined between two parallel planar walls. We show that at distances larger than several wall separations the flow…

Consider the resolvent problem associated with the linearized viscous flow around a rotating body. Within a setting of classical Sobolev spaces, this problem is not well posed on the whole imaginary axis. Therefore, a framework of…

We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…

To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered…

This work deals with the obtaining of solutions of first and second order Stieltjes differential equations. We define the notions of Stieltjes derivative on the whole domain of the functions involved, provide a notion of n-times…

In this paper, we use regularized theta liftings to construct weak Maass forms weight 1/2 as lifts of weak Maass forms of weight 0. As a special case we give a new proof of some of recent results of Duke, Toth and Imamoglu on cycle…

We study reductions of the Hamiltonian flows restricted to their invariant submanifolds. As examples, we consider partial Lagrange-Routh reductions of the natural mechanical systems such as geodesic flows on compact Lie groups and…

In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…

The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…

Recently, meshless methods have become popular in numerically solving partial differential equations and have been employed to solve equations governing fluid flows, heat transfer, and species transport. In the present study, a numerical…

This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this…

A simple analytical solution is obtained for the MHD stokeslet in a homogeneous magnetic field. This solution represents the flow past a small particle and can also be interpreted as the flow sufficiently far away from a body of finite…

A convenient approach to derive simple expressions for properties of Stokes flows with low levels of slip is presented. The method is based on a series expansion of a Stokes-flow solution (one satisfying a Navier slip boundary condition)…

This article proposes modifications to standard low order finite element approximations of the Stokes system with the goal of improving both the approximation quality and the parallel algebraic solution process. Different from standard…

We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field, valid on balls of radius $R$, are…

Manipulation of small-scale particles across streamlines is the elementary task of microfluidic devices. Many such devices operate at very low Reynolds numbers and deflect particles using arrays of obstacles, but a systematic quantification…