Related papers: Topology, Braids, and Mixing in Fluids
Let $T=(T_t^f)_{t\in \mathbb{R}}$ be a special flow built over an IET $T : T \to T$ of bounded type, under a roof function f with symmetric logarithmic singularities at a subset of discontinuities of T. We show that $T$ satisfies so-called…
Effective mixing of fluids at the microfluidic scale is important for future applications in biology, medicine, and chemistry. A promising type of micromixers are magnetic filaments, which can be activated by an external magnetic field.…
The interplay of twist and strain in bilayer graphene enables the formation of moir\'e patterns and narrow bands that host correlated and topological phases. While magic-angle twisted bilayer graphene has been widely studied, strain…
When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological…
The design of strategies to generate efficient mixing is crucial for a variety of applications, particularly digital microfluidic devices that use small "discrete" fluid volumes (droplets) as fluid carriers and microreactors. In recent…
Twisted and rope-like assemblies of filamentous molecules are common and vital structural elements in cells and tissue of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
There are several physical situations in which the `tangling' of a loop is relevant: the game of cat's cradle is a simple example, but a more important application involves the stirring of a fluid by rods. Here we discuss how elementary…
We explore the mechanisms and regimes of mixing in yield-stress fluids by simulating the stirring of an infinite, two-dimensional domain filled with a Bingham fluid. A cylindrical stirrer moves along a circular path at constant speed to…
Path planning for multiple tethered robots is a challenging problem due to the complex interactions among the cables and the possibility of severe entanglements. Previous works on this problem either consider idealistic cable models or…
The elastic coupling between plastic events is generally invoked to interpret plastic properties and failure of amorphous soft glassy materials. We report an experiment where the emergence of a self-organized plastic flow is observed well…
We develop a formalism that describes the bending and twisting of axoneme-like filament bundles. We obtain general formulas to determine the relative sliding between any arbitrary filaments in a bundle subjected to unconstrained…
Topological entanglements are abundant, and often detrimental, in polymeric systems in biology and materials science. Here we theoretically investigate the topological simplification of knots by diffusing slip-links (SLs), which may…
We present a new algorithm for the design of the connection region between different lattice materials. We solve a Stokes-type topology optimization problem on a narrow morphing region to smoothly connect two different unit cells. The…
Complex fluids exhibit a variety of exotic flow behaviours under high stresses, such as shear thickening and shear jamming. Rheology is a powerful tool to characterise these flow behaviours over the bulk of the fluid. However, this…
Combing hair involves brushing away the topological tangles in a collective curl. Using a combination of experiment and computation, we study this problem that naturally links topology, geometry and mechanics. Observations show that the…
Shear banding is a material instability in large strain plastic deformation of solids, where otherwise homogeneous flow becomes localized in narrow micrometer-scale bands. Shear bands have broad implications for materials processing and…
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…
We point out an interesting connection between fluid dynamics and minimal surface theory: When gluing helicoids into a minimal surface, the limit positions of the helicoids correspond to a "vortex crystal", an equilibrium of point vortices…
Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…