Related papers: Rank one and mixing differentiable flows
Compound flows consist of two or more parallel compressible streams in a duct and their theoretical treatment has gained attention for the analysis and modelling of ejectors. Recent works have shown that these flows can experience choking…
Understanding the mixing capability of mixing devices based on their geometric shape is an important issue both for predicting mixing processes and for designing new mixers. The flow patterns in mixers are directly connected with the modes…
We construct a ring of flows where we can decompose autonomous nonlinear dynamical systems into smaller parts, then solve each part and finally put everything together to obtain the exact solution of these systems.
Inserting a magnetic flux into a two-dimensional one-particle Hamiltonian leads to a spectral flow through a given gap which is equal to the Chern number of the associated Fermi projection. This paper establishes a generalization to higher…
We consider the enhanced mixing due to multiple cylinders organised in schools moving synchronously in a potential flow. Here simple interactions between cylinders are modelled by the method of image doublets. This is an extension to…
We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop…
Adapting Lindstr\"om's well-known construction, we consider a wide class of functions which are generated by flows in a planar acyclic directed graph whose vertices (or edges) take weights in an arbitrary commutative semiring. We give a…
We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is of Young class LU (i.e., it is the limit of an increasing…
Microscopic flows are almost universally linear, laminar and stationary because Reynolds number, $Re$, is usually very small. That impedes mixing in micro-fluidic devices, which sometimes limits their performance. Here we show that truly…
We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow-firing process, flow on the edges of a complex is…
On each compact, connected, orientable surface of genus greater than one we construct a class of flows without self-similarities.
We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any $f : \mathbb{N} \to \mathbb{N}$ with $f(n)/n$ increasing and…
Constructions of metrics with special holonomy by methods of exterior differential systems are reviewed and the interpretations of these construction as `flows' on hypersurface geometries are considered. It is shown that these hypersurface…
For a weakly mixing bounded rank-one construction the disjointness of its powers is proved. For non-rigid constructions we get minimal self-joinings. Examples of non-mixing rank one actions with explicit weak closure are proposed.
We construct a topological invariant for a Morse-Smale flow on a 3-manifold and prove that the flows are topologically equivalent iff their invariants are same.
We construct doubly periodic Stokes flows in two dimensions using elliptic functions. This method has advantages when the doubly periodic lattice of obstacles has less than maximal symmetry. We find the mean flow through an arbitrary…
We characterize Markov lattice semigroups induced by measurable semiflows on probability spaces by properties of their generators. In addition we construct topological models on compact spaces for such semigroups.
In this note we give simple examples of a one-dimensional mixing subshift with positive topological entropy which have two distinct measures of maximal entropy. We also give examples of subshifts which have two mutually singular equilibrium…
A mixing flow with homogeneous spectrum of multiplicity 2 is presented.
Accurate polyp segmentation remains challenging due to irregular lesion morphologies, ambiguous boundaries, and heterogeneous imaging conditions. While U-Net variants excel at local feature fusion, they often lack explicit mechanisms to…