655 research outputs found
Microscale swimming: The molecular dynamics approach
The self-propelled motion of microscopic bodies immersed in a fluid medium is
studied using molecular dynamics simulation. The advantage of the atomistic
approach is that the detailed level of description allows complete freedom in
specifying the swimmer design and its coupling with the surrounding fluid. A
series of two-dimensional swimming bodies employing a variety of propulsion
mechanisms -- motivated by biological and microrobotic designs -- is
investigated, including the use of moving limbs, changing body shapes and fluid
jets. The swimming efficiency and the nature of the induced, time-dependent
flow fields are found to differ widely among body designs and propulsion
mechanisms.Comment: 5 pages, 3 figures (minor changes to text
Colloid-colloid and colloid-wall interactions in driven suspensions
We investigate the non-equilibrium fluid structure mediated forces between
two colloids driven through a suspension of mutually non-interacting Brownian
particles as well as between a colloid and a wall in stationary situations. We
solve the Smoluchowski equation in bispherical coordinates as well as with a
method of reflections, both in linear approximation for small velocities and
numerically for intermediate velocities, and we compare the results to a
superposition approximation considered previously. In particular we find an
enhancement of the friction (compared to the friction on an isolated particle)
for two colloids driven side by side as well as for a colloid traveling along a
wall. The friction on tailgating colloids is reduced. Colloids traveling side
by side experience a solute induced repulsion while tailgating colloids are
attracted to each other.Comment: 8 Pages, 8 figure
A Simplest Swimmer at Low Reynolds Number: Three Linked Spheres
We propose a very simple one-dimensional swimmer consisting of three spheres
that are linked by rigid rods whose lengths can change between two values. With
a periodic motion in a non-reciprocal fashion, which breaks the time-reversal
symmetry as well as the translational symmetry, we show that the model device
can swim at low Reynolds number. This model system could be used in
constructing molecular-size machines
Self-propelled micro-swimmers in a Brinkman fluid
We prove an existence, uniqueness, and regularity result for the motion of a self-propelled micro-swimmer in a particulate viscous medium, modelled as a Brinkman fluid. A suitable functional setting is introduced to solve the Brinkman system for the velocity field and the pressure of the fluid by variational techniques. The equations of motion are written by imposing a self-propulsion constraint, thus allowing the viscous forces and torques to be the only ones acting on the swimmer. From an infinite-dimensional control on the shape of the swimmer, a system of six ordinary differential equations for the spatial position and the orientation of the swimmer is obtained. This is dealt with standard techniques for ordinary differential equations, once the coefficients are proved to be measurable and bounded. The main result turns out to extend an analogous result previously obtained for the Stokes system
Effective surface shear viscosity of an incompressible particle-laden fluid interface
The presence of even a small amount of surfactant at the particle-laden fluid interface subjected to shear makes surface flow incompressible if the shear rate is small enough [T. M. Fischer et al., J. Fluid Mech. 558, 451 (2006)]. In the present paper the effective surface shear viscosity of a flat, low-concentration, particle-laden incompressible interface separating two immiscible fluids is calculated. The resulting value is found to be 7.6% larger than the value obtained without account for surface incompressibility
Rotational Diffusion in a Chain of Particles
We study the coupled rotational diffusion in a two-particle chain on the
basis of a Smoluchowski equation and calculate time-correlation functions that
are measurable in an experiment. This might be used to explore hydrodynamic
interactions in the limit where lubrication theory is valid.Comment: 7 pages, 2 figures, to be published in J. Phys.: Condens. Matte
Diffusion in pores and its dependence on boundary conditions
We study the influence of the boundary conditions at the solid liquid
interface on diffusion in a confined fluid. Using an hydrodynamic approach, we
compute numerical estimates for the diffusion of a particle confined between
two planes. Partial slip is shown to significantly influence the diffusion
coefficient near a wall. Analytical expressions are derived in the low and high
confinement limits, and are in good agreement with numerical results. These
calculations indicate that diffusion of tagged particles could be used as a
sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in
Liquids, Polymers, Biophysics and Chemical Dynamics
Categorification of skew-symmetrizable cluster algebras
We propose a new framework for categorifying skew-symmetrizable cluster
algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with
the action of a finite group G, we construct a G-equivariant mutation on the
set of maximal rigid G-invariant objects of C. Using an appropriate cluster
character, we can then attach to these data an explicit skew-symmetrizable
cluster algebra. As an application we prove the linear independence of the
cluster monomials in this setting. Finally, we illustrate our construction with
examples associated with partial flag varieties and unipotent subgroups of
Kac-Moody groups, generalizing to the non simply-laced case several results of
Gei\ss-Leclerc-Schr\"oer.Comment: 64 page
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