相关论文: Topological Mixing with Ghost Rods

Topologically chaotic fluid advection is examined in two-dimensional flows with either or both directions spatially periodic. Topological chaos is created by driving flow with moving stirrers whose trajectories are chosen to form various…

A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at…

Stirring of fluid with moving rods is necessary in many practical applications to achieve homogeneity. These rods are topological obstacles that force stretching of fluid elements. The resulting stretching and folding is commonly observed…

The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a…

Stirring a two-dimensional viscous fluid with rods is often an effective way to mix. The topological features of periodic rod motions give a lower bound on the topological entropy of the induced flow map, since material lines must `catch'…

'Ghost Rods' are periodic structures in a two-dimensional flow that have an effect on material lines that is similar to real stirring rods. An example is a periodic island: material lines exterior to it must wrap around such an island,…

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that…

It is shown that the addition of small amounts of microscopic rods in a viscous fluid at low Reynolds number causes a significant increase of the flow resistance. Numerical simulations of the dynamics of the solution reveal that this…

In this work we study chaotic mixing induced by point micro-rotors in a bounded two dimensional Stokes flow. The dynamics of the pair of rotors, modeled as rotlets, are non Hamiltonian in the bounded domain and produce chaotic advection of…

In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…

The flow of Newtonian fluid at low Reynolds number is, in general, regular and time-reversible due to absence of nonlinear effects. For example, if the fluid is sheared by its boundary motion that is subsequently reversed, then all the…

We investigate the enhancement of both mixing and heat transfer in a two-rod mixer for highly-viscous non-Newtonian fluids. The mixer is composed of two vertical, circular rods in a cylindrical tank. Chaotic flows are obtained by imposing…

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually…

In this article, we present experimental results of chaotic mixing of Newtonian uids and yield stress fluids using rod-stirring protocol with rotating vessel. We show how the mixing of yield stress fluids by chaotic advection is reduced…

Efficient mixing of fluids is essential in many practical applications to achieve homogeneity. For microscopic systems, however, both diffusion and turbulence are ineffective methods to achieve chaotic mixing due to the low Reynolds number,…

We study phase-separating fluid mixtures as they demix in the presence of chemical reactions that maintain them away from thermodynamic equilibrium. We show that in such chemically active emulsions the interplay of chemical reactions, phase…

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rod-like components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in…

By a classical result of Kathleen Alligood and James Yorke we know that as we isotopically deform a map $f:ABCD\to\mathbb{R}^2$ to a Smale horseshoe map we should often expect the dynamical complexity to increase via a period--doubling…

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…