Related papers: A simple and more general approach to Stokes' theo…
The aim of Part II is to explore the technique of invariance of tautological equations in the realm of Gromov--Witten theory. The main result is a proof of Invariance Theorem (Invariance Conjecture~1 in [14]), via the techniques from…
In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by utilizing the perturbation method originally proposed for pure waves that was recently published. The present…
In this paper we prove that the quantum Stokes matrices of the quantum differential equation at a second order pole give rise to representations of the quantum group $U_q(\frak{gl}_n)$. We explain our results from the viewpoint of…
This paper explores the relationship between closed curves on surfaces and their intersections. Like Dehn-Thurston coordinates for simple curves, we explore how to determine closed curves using the number of times they intersect other…
Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…
Lubrication theory makes use of the assumptions of a long and thin fluid domain and a small scaled Reynolds number to formulate a linearized approximation to the Navier-Stokes equations. Extended lubrication theory aims to improve the model…
The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds number problems analytically and computationally. Alternatively, one can solve…
There are numerous ways to control objects in the Stokes regime, with microscale examples ranging from the use of optical tweezers to the application of external magnetic fields. In contrast, there are relatively few explorations of…
We prove a variational principle for stochastic Lagrangian Navier-Stokes trajectories on manifolds. We study the behaviour of such trajectories concerning stability as well as rotation between particles; the two-dimensional torus case is…
We generalise Livens theorem, showing that Hamiltonian equation on the vector bundle $E^\ast\rightarrow M$, dual to a general algebroid $E\rightarrow M$, can be derived by means of a variational principle. The framework can be used to…
The Poincar\'e-Hopf Theorem is a conservation law for real-analytic vector fields, which are tangential to a closed surface (such as a torus or a sphere). The theorem also governs real-analytic vector fields, which are tangential to…
We give a geometric approach to proving know regularity and existence theorems for the 2D Navier-Stokes Equations. We feel this point of view is instructive in better understanding the dynamics. The technique is inspired by constructions in…
Within the framework of general relativity, in some cases at least, it is a delicate and interesting question just what it means to say that an extended body is or is not "rotating". It is so for two reasons. First, one can easily think of…
Statistical learning theory is often associated with the principle of Occam's razor, which recommends a simplicity preference in inductive inference. This paper distills the core argument for simplicity obtainable from statistical learning…
A linear defect, viz. an elastic string, diffusing on a planar substrate traversed by a travelling wave experiences a drag known as Stokes' drift. In the limit of an infinitely long string, such a mechanism is shown to be characterized by a…
We revisit Ahlfors theory of covering surfaces thanks to Stokes theorem.
This is a series of lecture notes, with embedded problems, aimed at students studying differential topology. Many revered texts, such as Spivak's "Calculus on Manifolds" and Guillemin and Pollack's "Differential Topology" introduce forms by…
Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order…
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…
In this article, we study the behavior of the stability of pullback of a vector bundle under a finite morphism from a (not necessarily smooth) stacky curve to an orbifold curve. We establish a categorical equivalence between proper formal…