Related papers: The autophoretic torus
We prove the existence of closed convex ancient solutions to curvature flows which become more and more oval for large negative times. The speed function is a general symmetric function of the principal curvatures, homogeneous of degree…
Cells swimming in viscous fluids create flow fields which influence the transport of relevant nutrients, and therefore their feeding rate. We propose a modeling approach to the problem of optimal feeding at zero Reynolds number. We consider…
The solution of the two-fluids plane or axisymetric Poiseuille flow is derived analytically. Then, the conditions for the maximum flow rate of the most viscous fluid are analyzed in terms of fluids volume fractions. The axisymmetric case is…
We study the microscale propulsion of a rotating helical filament confined by a cylindrical tube, using a boundary-element method for Stokes flow that accounts for helical symmetry. We determine the effect of confinement on swimming speed…
Two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube, and a concentric circular annulus. Here we study peristaltic flow in a…
Through billions of years of evolution, microorganisms mastered unique swimming behaviors to thrive in complex fluid environments. Limitations in nanofabrication have thus far hindered the ability to design and program synthetic swimmers…
The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus and high-multiplicity proton-proton collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed…
Selective heating of a microparticle surface had been observed to cause its autonomous movement in a fluid medium due to self-generated temperature gradients. In this work, we theoretically investigate the response of such an…
Both natural and artificial small-scale swimmers may often self-propel in environments subject to complex geometrical constraints. While most past theoretical work on low-Reynolds number locomotion addressed idealised geometrical…
We tackle the question of how anisotropy in flows subject to background rotation favours structures elongated along the rotation axis, especially in turbulent flows. A new, wave-free mechanism is identified that challenges the current…
This article concerns the description of the electron sea of an atomic ion with the Thomas-Fermi model. The normalized ion radius $X$, ionization potential $b$ and electronic binding energy $B$ of the Thomas-Fermi ion are functions of the…
This work studies Willmore flows of tori and their singularities via a dimension reduction approach. We introduce a Willmore flow that preserves the degenerate constraint of prescribed conformal class and, for rotationally symmetric initial…
The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold $M$ can give information about the stability of inviscid, incompressible fluid flows on $M$. We demonstrate that the submanifold of the…
Here we characterize the motility of athermal swimming droplets within the framework of active rotational diffusion. Just like active colloids, their trajectories can be modeled with a constant velocity $V$ and a slow angular diffusion, but…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
The connection between swimming and control theory is attracting increasing attention in the recent literature. Starting from an idea of Alberto Bressan [7] we study the system of a planar body whose position and shape are described by a…
This review treats asymmetric colloidal particles moving through their host fluid under the action of some form of propulsion. The propulsion can come from an external body force or from external shear flow. It may also come from…
We explicitly construct a pair of immersed tori in three dimensional Euclidean space that are related by a mean curvature preserving isometry. These Bonnet pair tori are the first examples of compact Bonnet pairs. This resolves a…
A small, bimetallic particle in a hydrogen peroxide solution can propel itself by means of an electrocatalytic reaction. The swimming is driven by a flux of ions around the particle. We model this process for the presence of a monovalent…
Many biological microswimmers locomote by periodically beating the densely-packed cilia on their cell surface in a wave-like fashion. While the swimming mechanisms of ciliated microswimmers have been extensively studied both from the…