Related papers: A calculus for flow categories
All phase transitions can be categorised into two different types: continuous and discontinuous phase transitions. Discontinuous phase transitions are normally accompanied with significant structural changes, and nearly all of them have the…
This expository note describes two convenient techniques in the context of homotopy type theory for proving and formalizing that a given map is an equivalence. The first technique decomposes the map as a series of basic equivalences, while…
Erratum, 11 July 2022: This is an updated version of the original paper in which the notion of reparametrization category was incorrectly axiomatized. Details on the changes to the original paper are provided in the Appendix. A…
The main aim of this paper is to describe the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In \cite{CGSW03}, the existence of a Hopf bifurcation in this model as…
Capillary driven flow is a famous problem in fluid dynamics which dates back to Leonardo da Vinci. In this paper, we apply an analytic approximation method for highly nonlinear problem, namely the homotopy analysis method (HAM), to a model…
We investigate the physical properties of steady flows in a holographic first-order phase transition model, extending from the thermodynamics at equilibrium to the real-time dynamics far from equilibrium. Through spinodal decomposition or…
In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of…
Let $\Phi$ be a flow on a smooth, compact, finite-dimensional manifold $M$. Consider the subsets $E(\Phi)$ and $D(\Phi)$ of $C^{\infty}(M,M)$ consisting of smoothh mappings and diffeomorphisms (respectively) of $M$ preserving the foliation…
Type systems hide data that is captured by function closures in function types. In most cases this is a beneficial design that favors simplicity and compositionality. However, some applications require explicit information about the data…
We consider arrow diagrams of links in $S^3$ and define $k$-moves on such diagrams, for any $k\in\mathbb N$. We study the equivalence classes of links in $S^3$ up to $k$-moves. For $k=2$, we show that any two knots are equivalent, whereas…
A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In…
In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solutions containing ten arbitrary parameter functions.
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
For flows the rank is an invariant by linear change of time. But what we can say about isomorphisms? It seems that in case of mixing flows this problem is the most difficult. However the known technique of joinings provides non-isomorphism…
We consider the problem of transporting \nota{one probability measure into another through} the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
This article deals with flow of plane curves driven by the curvature and external force. We make use of such a geometric flow for the purpose of image segmentation. A parametric model for evolving curves with uniform and curvature adjusted…
We establish a precise asymptotic formula for the number of homotopy classes of periodic orbits for the geodesic flow on rank one manifolds of nonpositive curvature. This extends a celebrated result of G. A. Margulis to the nonuniformly…
The paper establishes an equivalence between directed homotopy categories of (diagrams of) cubical sets and (diagrams of) directed topological spaces. This equivalence both lifts and extends an equivalence between classical homotopy…
We extend the concept of optical flow with spatiotemporal regularisation to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. The purpose of this paper is to introduce variational motion…