Related papers: Optimal dynamics of a spherical squirmer in Euleri…
Squirmers are models of a class of microswimmers, such as ciliated organisms and phoretic particles, that self-propel in fluids without significant deformation of their body shape. Available techniques for their simulation are based on the…
We consider arbitrary-shaped microswimmers of spherical topology and propose a framework for expressing their slip velocity in terms of tangential basis functions defined on the boundary of the swimmer using the Helmholtz decomposition.…
This paper discusses modelling, controllability and gait design for a spherical flexible swimmer. We first present a kinematic model of a low Reynolds number spherical flexible swimming mechanism with periodic surface deformations in the…
The swimming of a spheroid immersed in a viscous fluid and performing surface deformations periodically in time is studied on the basis of Stokes equations of low Reynolds number hydrodynamics. The average over a period of time of the…
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…
We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In particular we establish optimal order error bounds for a (fully…
A concentrated, vertical monolayer of identical spherical squirmers, which may be bottom-heavy, and which are subjected to a linear shear flow, is modelled computationally by two different methods: Stokesian dynamics, and a…
The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation…
We study, by means of an exact analytical solution, the motion of a spheroidal, axisymmetric squirmer in an unbounded fluid, as well as the low Reynolds number hydrodynamic flow associated to it. In contrast to the case of a spherical…
Microswimmers play an important role in shaping the world around us. The squirmer is a simple model for microswimmer whose cilia oscillations on its spherical surface induce an effective slip velocity to propel itself. The rapid development…
The rotational diffusive motion of a self-propelled, attractive spherical colloid immersed in a solution of self-avoiding polymers is studied by mesoscale hydrodynamic simulations. A drastic enhancement of the rotational diffusion by more…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…
The paper deals with three evolution problems arising in the physical modelling of acoustic phenomena of small amplitude in a fluid, bounded by a surface of extended reaction. The first one is the widely studied wave equation with acoustic…
In this paper we consider a layer of incompressible viscous fluid lying above a flat periodic surface in a uniform gravitational field. The upper boundary of the fluid is free and evolves in time. We assume that a mass of surfactants…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete…
The behaviour of microscopic swimmers has previously been explored near large scale confining geometries and in the presence of very small-scale surface roughness. Here we consider an intermediate case of how a simple microswimmer, the…
The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope…
We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…