Related papers: Resurgent Stokes Data for Painleve Equations and T…
In this paper we study the Gauss and Kummer hypergeometric equations in depth. In particular, we focus on the confluence of two regular singularities of the Gauss hypergeometric equation to produce the Kummer hypergeometric equation with an…
The asymptotic expansion of quantum knot invariants in complex Chern-Simons theory gives rise to factorially divergent formal power series. We conjecture that these series are resurgent functions whose Stokes automorphism is given by a pair…
In this paper we study analytic (linear or) nonlinear systems of ordinary differential equations, at an irregular singularity of rank one, under nonresonance conditions. It is shown that the formal asymptotic exponential series solutions…
We study coupled motion of a 1-D closed elastic string immersed in a 2-D Stokes flow, known as the Stokes immersed boundary problem in two dimensions. Using the fundamental solution of the Stokes equation and the Lagrangian coordinate of…
Unstable separatrix solutions for the first and second Painlev\'e transcendents are studied both numerically and analytically. For a fixed initial condition, say $y(0)=0$, there is a discrete set of initial slopes $y'(0)=b_n$ that give rise…
Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudo-differential equation, involving a periodic…
Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…
This is an introductory level review of recent applications of resurgent trans-series and Picard-Lefschetz theory to quantum mechanics and quantum field theory. Resurgence connects local perturbative data with global topological structure.…
We study polynomials that are orthogonal with respect to a varying quartic weight \exp(-N(x^2/2+tx^4/4)) for t<0, where the orthogonality takes place on certain contours in the complex plane. Inspired by developments in 2D quantum gravity,…
We consider several examples of nonautonomous systems of difference equations coming from semi-classical orthogonal polynomials via recurrence coefficients and ladder operators, with respect to various generalisations of Laguerre and…
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…
Magnetic reconnection is an important driving mechanism of many chromospheric phenomena, e.g., UV bursts and chromospheric jets. Information about magnetic field is indispensable for analyzing chromospheric magnetic reconnection, which is…
Intersection numbers of Stokes polytopes living in complex projective space are computed using the techniques employed to find the inverse string KLT matrix elements in terms of intersection numbers of associahedra. To do this requires an…
We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an…
We consider meromorphic transforms given by meromorphic kernels and study their asymptotic expansions under a certain rescaling. Under decay assumptions we establish the full asymptotic expansion in the rescaling parameter of these…
Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…
Bender-Canfield showed that a plethora of graph counting problems in oriented/unoriented surfaces involve two constants $t_g$ and $p_g$ for the oriented and the unoriented case respectively. T.T.Q. Le and the authors recently discovered a…
Strong Disorder Renormalization for the Random Transverse Field Ising model leads to a complicated topology of surviving clusters as soon as $d>1$. Even if one starts from a Cayley tree, the network of surviving renormalized clusters will…
New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from…