Related papers: Stokes' Theorem for Smooth Singular Cubes in Lean …

Peskin's Immersed Boundary (IB) model and method are among one of the most important modeling tools and numerical methods. The IB method has been known to be first order accurate in the velocity. However, almost no rigorous theoretical…

We present a modification of the Crouzeix-Raviart discretization of the Stokes equations in arbitrary dimension which is quasi-optimal, in the sense that the error of the discrete velocity field in a broken $H^1$-norm is proportional to the…

This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for…

In the present paper, by approximating the derivatives in the Kou et al. \cite{Kou} fourth-order method by central difference quotient, we obtain new modification of this method free from derivatives. We prove the important fact that the…

In this paper we introduce and study the theories of pseudo links and singular links in the Solid Torus, ST. Pseudo links are links with some missing crossing information that naturally generalize the notion of knot diagrams, and that have…

One of the most fascinating and technically demanding parts of the theory of two-dimensional integrable systems constitute the models with the spectral parameter on an elliptic curve, including Landau-Lifshitz and Krichever-Novikov…

A fully discrete Lagrangian scheme for numerical solution of the nonlinear fourth order DLSS equation in one space dimension is analyzed. The discretization is based on the equation's gradient flow structure in the $L^2$-Wasserstein metric.…

Generalizing work of Smith and Hara, we give a new characterization of log-terminal singularities for finitely generated algebras over $\mathbb C$, in terms of purity properties of ultraproducts of characteristic $p$ Frobenii. The first…

We propose a novel construction of the Floquet 3D toric code and Floquet $X$-cube code through the coupling of spin chains. This approach not only recovers the coupling layer construction on foliated lattices in three dimensions but also…

We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the circle. Our choice of discretization is motivated by a novel gradient flow formulation with respect to a metric that generalizes martingale transport.…

We present type $\theta$ Stokes' theorem for type $\theta$ $k$-chains which extends the fundamental theorem of calculus in higher dimensions.

We present a formalism to derive the stochastic differential equations (SDEs) for several solid-on-solid growth models. Our formalism begins with a mapping of the microscopic dynamics of growth models onto the particle systems with…

A 2018 paper by A. Levine and T. Lidman outlines a proof of the following interesting result in topology of manifolds: there is a compact smooth 4-manifold $W$ with boundary such that $W$ is homotopy equivalent to $S^2$ but there does not…

We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic p (as defined by Abramovich, Olsson, and Vistoli) which lift mod p^2 degenerates. We push the result to the coarse spaces of such…

We study divisors on moduli spaces of cubic fourfolds with simple singularities and of quasi-polarized K3 surfaces of degree $2d$. For the moduli space of cubic fourfolds, we introduce a slope quantity to characterize the effective cone and…

We apply the method of [arXiv:1705.07610] to compute the Stokes matrices of non-resonant confluent hypergeometric differential equations. We discuss the ambiguity of the presentation of the Stokes matrices regarding different choices. The…

Using an obstruction based on Donaldson's theorem, we derive strong restrictions on when a Seifert fibered space $Y = F(e; \frac{p_1}{q_1}, \ldots, \frac{p_k}{q_k})$ over an orientable base surface $F$ can smoothly embed in $S^4$. This…

Let V be a compact real analytic surface with isolated singularities embedded in $R^N$, and assume its smooth part is equipped with a Riemannian metric that is induced from some analytic Riemannian metric on $R^N$. We prove: 1. Each point…

In this article, we introduce fundamental notions and results about pullback formalisms, building on work of Drew-Gallauer. Our main application is producing a pullback formalism $\mathbf{SH}^{\mathrm{hol}}$ that encodes a version of…

Consider an It\^{o} process $X$ satisfying the stochastic differential equation $dX=a(X)\,dt+b(X)\,dW$ where $a,b$ are smooth and $W$ is a multidimensional Brownian motion. Suppose that $W_n$ has smooth sample paths and that $W_n$ converges…