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A case study in bifurcation and stability analysis is presented, in which reduced dynamical system modelling yields substantial new global and predictive information about the behaviour of a complex system. The first smooth pathway, free of…
We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a…
The encapsulation of active particles, such as bacteria or active colloids, inside a droplet gives rise to nontrivial shape dynamics and droplet motility. To understand this behavior, we derive an asymptotic solution for the fluid flow…
In fluid dynamics experiments, flake-based flow visualization is a common technique to capture flow structures through the rays reflected from flat tracers suspended in the fluid. However, the correspondence between light intensity patterns…
Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point…
Molecular dynamics simulations of a glass-forming model system are performed under application of a microrheological perturbation on a tagged particle. The trajectory of that particle is studied in its underlying potential energy landscape.…
In this paper, we present a new self-supervised scene flow estimation approach for a pair of consecutive point clouds. The key idea of our approach is to represent discrete point clouds as continuous probability density functions using…
Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature, typically a solid body or a bubble. The ability of such features to locally concentrate stresses produces strong…
We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for…
We consider stagnation point flow away from a wall for creeping flow of dilute polymer solutions. For a simplified flow geometry, we explicitly show that a narrow region of strong polymer extension (a birefringent strand) forms downstream…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
We describe all possible topological structures of Morse flows and typical gradient saddle-nod bifurcation of flows on the 2-dimensional torus with a hole in the case that the number of singular point of flows is at most six. To describe…
Granular particles vibrated in a fluid have been found to exhibit self-organization with attractive and repulsive interactions between the particles. These interactions have been attributed to the steady streaming flow around oscillating…
The acoustofluidic method holds great promise for manipulating microorganisms. When exposed to the steady vortex structures of acoustic streaming flow, these microorganisms exhibit intriguing dynamic behaviors, such as hydrodynamic trapping…
Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation…
Vorticity describes the spinning motion of a fluid, i.e., the tendency to rotate, at every point in a flow. The interest in performing accurate and localized measurements of vorticity reflects the fact that many of the quantities that…
Fluid flow through intricate confining geometries often exhibits complex behaviors, certainly in porous materials, e.g. in groundwater flows or the operation of filtration devices and porous catalysts. However, it has remained extremely…
We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise,…
Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class. Simply put, different objects move…
Single-molecule pulling techniques have emerged as versatile tools for probing the noncovalent forces holding together the secondary and tertiary structure of macromolecules. They also constitute a way to study at the single-molecule level…