Related papers: Intersection Numbers from Higher-order Partial Dif…

We study Stokes phenomena of the k \times k isomonodromy systems with an arbitrary Poincar\'e index r, especially which correspond to the fractional-superstring (or parafermionic-string) multi-critical points (\hat p,\hat q)=(1,r-1) in the…

In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…

A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…

This paper is devoted to the well-posedness analysis of a nonstationary Stokes hemivariational inequality for an incompressible fluid flow described by the Stokes equations subject to a nonsmooth boundary condition of friction type…

Logarithmic differential forms and logarithmic vector fields associated to a hypersurface with an isolated singularity are considered in the context of computational complex analysis. As applications, based on the concept of torsion…

In this paper we prove a residue formula for intersection pairings of reduced spaces of certain quasi-Hamiltonian G-spaces, by constructing the corresponding Hamiltonian G-space. Our argument closely follows the methods of a 1998 paper of…

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…

We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle…

This paper attacks the following problem. We are given a large number $N$ of rectangles in the plane, each with horizontal and vertical sides, and also a number $r<N$. The given list of $N$ rectangles may contain duplicates. The problem is…

We apply methods of derived and non-commutative algebraic geometry to understand intersection theoretic phenomena on arithmetic schemes. Specifically, we categorify Bloch's intersection number (in the formulation provided by Kato--Saito).…

Present article deals with trajectorial intersections in linear fractional systems ('systems'). We propose a classification of intersections of trajectories in three classes viz. trajectories intersecting at same time(EIST), trajectories…

There are few approaches to the solution of a system of nonlinear differential equations in partial derivatives, for example $\cite{NK87} - \cite{EK98}$. In our paper we propose an approach that was used to solve the Navier-Stokes equations…

Using a quadratic version of the Bott residue theorem, we give a quadratic refinement of the count of twisted cubic curves on hypersurfaces and complete intersections in a projective space.

Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…

Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…

In this paper, we study the performance of the non-conforming least-squares spectral element method for Stokes problem. Generalized Stokes problem has been considered and the method is shown to be exponential accurate. The numerical method…

We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid and serve as a model problem in the dynamics of material…

This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…

This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…

We obtain bounds on the number of maximal torsion cosets for algebraic subvarieties of n-tori, defined over the rationals, using model theoretic methods.