相关论文: Flow of unitary matrices: Real-space winding numbe…

It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result,…

In a recent paper, Liu, Zhu and Wu (2015, {\it J. Fluid Mech.} {\bf 784}: 304) present a force theory for a body in a two-dimensional, viscous, compressible and steady flow. In this companion paper we do the same for three-dimensional flow.…

In this paper, we introduce a framework of $(\alpha,\beta)$-flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.

We propose a simple numerical method which computes an approximate value of the winding number of a mapping from 3D torus~$T^3$ to the unitary group~$U(N)$, when $T^3$ is approximated by discrete lattice points. Our method consists of a…

New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the…

In applied mathematics generally and fluid dynamics in particular, the role of complex variable methods is normally confined to two-dimensional motion and the association of points with complex numbers via the assignment w = x+i y. In this…

Generalizing a construction of A. Weil, we introduce a topological invariant for flows on compact, connected, finite dimensional, abelian, topological groups. We calculate this invariant for some examples and compare the invariant with…

Continuous normalizing flows are known to be highly expressive and flexible, which allows for easier incorporation of large symmetries and makes them a powerful computational tool for lattice field theories. Building on previous work, we…

The central result about fast rotating-flow structures is the Taylor-Proudman theorem (TPT) which connects various aspects of the dynamics. Taylor's geometrical proof of TPT is reproduced and extended substantially, with Lie's theory for…

The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform…

We study stability and input-state analysis of three dimensional (3D) incompressible, viscous flows with invariance in one direction. By taking advantage of this invariance property, we propose a class of Lyapunov and storage functionals.…

We present a general solution of relativistic (1+1)-dimensional hydrodynamics for a perfect fluid flowing along the longitudinal direction as a function of time, uniformly in transverse space. The Khalatnikov potential is expressed as a…

Framing triangulations of unit flow polytopes have received a great deal of recent study with rich connections to various generalizations of Catalan and Cambrian combinatorics as well as volume and h*-polynomial formulas. This story has…

Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow…

We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…

We introduce new families of combinatorial objects whose enumeration computes volumes of flow polytopes. These objects provide an interpretation, based on parking functions, of Baldoni and Vergne's generalization of a volume formula…

This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework of the flow in the manifold of unitarily equivalent matrices, as discovered in the mathematical literature before…

The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of…

A flow invariant in quantum field theory is a quantity that does not depend on the flow connecting the UV and IR conformal fixed points. We study the flow invariance of the most general sum rule with correlators of the trace Theta of the…

We prove an integral formula for the spectral flow of differentiable loops of unitaries of the form ${\rm Id}+$Schatten. Our formula is in terms of a regularised winding number, expressed in terms of exact differential forms, and we show…