972 research outputs found
Differential growth of wrinkled biofilms
Biofilms are antibiotic-resistant bacterial aggregates that grow on moist
surfaces and can trigger hospital-acquired infections. They provide a classical
example in biology where the dynamics of cellular communities may be observed
and studied. Gene expression regulates cell division and differentiation, which
affect the biofilm architecture. Mechanical and chemical processes shape the
resulting structure. We gain insight into the interplay between cellular and
mechanical processes during biofilm development on air-agar interfaces by means
of a hybrid model. Cellular behavior is governed by stochastic rules informed
by a cascade of concentration fields for nutrients, waste and autoinducers.
Cellular differentiation and death alter the structure and the mechanical
properties of the biofilm, which is deformed according to Foppl-Von Karman
equations informed by cellular processes and the interaction with the
substratum. Stiffness gradients due to growth and swelling produce wrinkle
branching. We are able to reproduce wrinkled structures often formed by
biofilms on air-agar interfaces, as well as spatial distributions of
differentiated cells commonly observed with B. subtilis.Comment: 19 pages, 13 figure
Intrinsic viscosity of a suspension of weakly Brownian ellipsoids in shear
We analyze the angular dynamics of triaxial ellipsoids in a shear flow
subject to weak thermal noise. By numerically integrating an overdamped angular
Langevin equation, we find the steady angular probability distribution for a
range of triaxial particle shapes. From this distribution we compute the
intrinsic viscosity of a dilute suspension of triaxial particles. We determine
how the viscosity depends on particle shape in the limit of weak thermal noise.
While the deterministic angular dynamics depends very sensitively on particle
shape, we find that the shape dependence of the intrinsic viscosity is weaker,
in general, and that suspensions of rod-like particles are the most sensitive
to breaking of axisymmetry. The intrinsic viscosity of a dilute suspension of
triaxial particles is smaller than that of a suspension of axisymmetric
particles with the same volume, and the same ratio of major to minor axis
lengths.Comment: 14 pages, 6 figures, 1 table, revised versio
Effect of weak fluid inertia upon Jeffery orbits
We consider the rotation of small neutrally buoyant axisymmetric particles in
a viscous steady shear flow. When inertial effects are negligible the problem
exhibits infinitely many periodic solutions, the "Jeffery orbits". We compute
how inertial effects lift their degeneracy by perturbatively solving the
coupled particle-flow equations. We obtain an equation of motion valid at small
shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios.
We analyse how the linear stability of the \lq log-rolling\rq{} orbit depends
on particle shape and find it to be unstable for prolate spheroids. This
resolves a puzzle in the interpretation of direct numerical simulations of the
problem. In general both unsteady and non-linear terms in the Navier-Stokes
equations are important.Comment: 5 pages, 2 figure
Extensive chaos in Rayleigh-BĂ©nard convection
Using large-scale numerical calculations we explore spatiotemporal chaos in Rayleigh-BĂ©nard convection for experimentally relevant conditions. We calculate the spectrum of Lyapunov exponents and the Lyapunov dimension describing the chaotic dynamics of the convective fluid layer at constant thermal driving over a range of finite system sizes. Our results reveal that the dynamics of fluid convection is truly chaotic for experimental conditions as illustrated by a positive leading-order Lyapunov exponent. We also find the chaos to be extensive over the range of finite-sized systems investigated as indicated by a linear scaling between the Lyapunov dimension of the chaotic attractor and the system size
Rotation of a spheroid in a simple shear at small Reynolds number
We derive an effective equation of motion for the orientational dynamics of a
neutrally buoyant spheroid suspended in a simple shear flow, valid for
arbitrary particle aspect ratios and to linear order in the shear Reynolds
number. We show how inertial effects lift the degeneracy of the Jeffery orbits
and determine the stabilities of the log-rolling and tumbling orbits at
infinitesimal shear Reynolds numbers. For prolate spheroids we find stable
tumbling in the shear plane, log-rolling is unstable. For oblate particles, by
contrast, log-rolling is stable and tumbling is unstable provided that the
aspect ratio is larger than a critical value. When the aspect ratio is smaller
than this value tumbling turns stable, and an unstable limit cycle is born.Comment: 25 pages, 5 figure
Aperiodic tumbling of microrods advected in a microchannel flow
We report on an experimental investigation of the tumbling of microrods in
the shear flow of a microchannel (40 x 2.5 x 0.4 mm). The rods are 20 to 30
microns long and their diameters are of the order of 1 micron. Images of the
centre-of-mass motion and the orientational dynamics of the rods are recorded
using a microscope equipped with a CCD camera. A motorised microscope stage is
used to track individual rods as they move along the channel. Automated image
analysis determines the position and orientation of a tracked rods in each
video frame. We find different behaviours, depending on the particle shape, its
initial position, and orientation. First, we observe periodic as well as
aperiodic tumbling. Second, the data show that different tumbling trajectories
exhibit different sensitivities to external perturbations. These observations
can be explained by slight asymmetries of the rods. Third we observe that after
some time, initially periodic trajectories lose their phase. We attribute this
to drift of the centre of mass of the rod from one to another stream line of
the channel flow.Comment: 14 pages, 8 figures, as accepted for publicatio
Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method
We present a method for the direct calculation of the spin stiffness by means
of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on
the square, the triangular and the cubic lattices we calculate the stiffness in
high orders of approximation. For the square and the cubic lattices our results
are in very good agreement with the best results available in the literature.
For the triangular lattice our result is more precise than any other result
obtained so far by other approximate method.Comment: 5 pages, 2 figure
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