Related papers: Topology, Braids, and Mixing in Fluids
Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L.…
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…
The deep connections between braids and dynamics by way of the Nielsen-Thurston classification theorem have led to a wide range of practical applications. Braids have been used to detect coherent structures and mixing regions in oceanic…
There are many industrial situations where rods are used to stir a fluid, or where rods repeatedly stretch a material such as bread dough or taffy. The goal in these applications is to stretch either material lines (in a fluid) or the…
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,…
The growth rate of material interfaces is an important proxy for mixing and reaction rates in fluid dynamics, and can also be used to identify regions of coherence. Estimating such growth rates can be difficult, since they depend on…
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'…
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…
Even in simple geometries many complex fluids display non-trivial flow fields, with regions where shear is concentrated. The possibility for such shear banding has been known since several decades, but the recent years have seen an upsurge…
We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or…
In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure…
The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of…
Topological entropy is a common measure of the rate of mixing in a flow. It can be computed by partition methods, or by estimating the growth rate of material lines or other material elements. This requires detailed knowledge of the…
The detection of coherent structures is an important problem in fluid dynamics, particularly in geophysical applications. For instance, knowledge of how regions of fluid are isolated from each other allows prediction of the ultimate fate of…
Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae which coalesce due to molecular diffusion. Owing…
The mixing of binary fluids by stirrers is a commonplace procedure in many industrial and natural settings, and mixing efficiency directly translates into more homogeneous final products, more enriched compounds, and often substantial…
Fluidic devices are crucial components in many industrial applications involving fluid mechanics. Computational design of a high-performance fluidic system faces multifaceted challenges regarding its geometric representation and physical…
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…
Streamers are the first stage of sparks and lightning; they grow due to a strongly enhanced electric field at their tips; this field is created by a thin curved space charge layer. These multiple scales are already challenging when the…