
Abstract:
The dynamics and
deformations of immersed
flexible fibers are at the
heart of important
industrial and biological
processes, induce peculiar
mechanical and
transport properties in
the fluids that contain
them, and are the basis
for novel methods
of flow control. Here we
focus on the low–Reynolds
number regime where
advances in studying these
fiber–fluid systems have
been especially rapid. On
the experimental side,
this is due to new methods
of fiber synthesis,
microfluidic flow control,
and microscopebased
tracking measurement
techniques. Likewise,
there have been continuous
improvements in
the specialized
mathematical modeling and
numerical methods needed
to capture the
interactions of slender
flexible fibers with
flows, boundaries, and
each other. 

Abstract:
In this work we
provide a solution to
the problem of
computing collision
stress in
particletracking
simulations. First,
a formulation for the
collision stress
between particles is
derived as an
extension of the
virial stress formula
to generalshaped
particles with uniform
or nonuniform
density. Second, we
describe a
collisionresolution
algorithm based on
geometric constraint
minimization which
eliminates the stiff
pairwise potentials in
traditional methods.
The method is
validated with a
comparison to the
equation of state of
Brownian spherocylinders.
Then we demonstrate
the application of
this method in several
emerging problems of
soft active
matter. 

Abstract:
We investigate the dynamics of a
dilute suspension of hydrodynamically
interacting motile or immotile
stressgenerating swimmers or
particles as they invade a surrounding
viscous fluid. Colonies of aligned
pusher particles are shown to elongate
in the direction of particle
orientation and undergo a cascade of
transverse concentration
instabilities, governed at small times
by an equation which also describes
the SaffmanTaylor instability in a
HeleShaw cell, or RayleighTaylor
instability in twodimensional flow
through a porous medium. Thin sheets
of aligned pusher particles are
always unstable, while sheets of
aligned puller particles can either be
stable (immotile particles),
or unstable (motile particles) with a
growth rate which is nonmonotonic in
the force dipole strength. We also prove a surprising “noflow theorem”: a distribution initially isotropic in orientation loses isotropy immediately but in such a way that results in no fluid flow everywhere and for all time. 

Abstract: Many
subcellular structures
contain large numbers of
cytoskeletal filaments.
Such assemblies underlie
much of cell division,
motility, signaling,
metabolism, and growth.
Thus, understanding
cell biology requires
understanding the properties
of networks of cytoskeletal
filaments. While there are
well established
disciplines in biology
dedicated to studying isolated
proteins — their structure
(Structural Biology) and
behaviors (Biochemistry)
— it is much less clear how
to investigate, or
even just describe, the
structure and behaviors of
collections of cytoskeletal
filaments. One approach is
to use methodologies
from Mechanics and Soft
Condensed Matter Physics,
which have been phenomenally
successful in the domains
where they have been
traditionally applied. From
this perspective,
collections of cytoskeletal
filaments are viewed as materials,
albeit very complex,
‘active’ materials, composed
of molecules which
use chemical energy to
perform mechanical work.


Abstract:
The 3D spatiotemporal organization of
the human genome inside the
cell nucleus remains a major open
question in cellular biology. In the
time between two cell divisions,
chromatin—the functional form
of DNA in cells—fills the nucleus in
its uncondensed polymeric form. Recent
in vivo imaging experiments reveal
that the chromatin moves coherently,
having displacements with longranged
correlations on the scale of
micrometers and lasting for
seconds. To elucidate the mechanism(s)
behind these motions, we
develop a coarsegrained active
polymer model where chromatin
is represented as a confined flexible
chain acted upon by molecular
motors that drive fluid flows by
exerting dipolar forces on the system.
Numerical simulations of this model
account for steric and hydrodynamic
interactions as well as internal chain
mechanics. These demonstrate that
coherent motions emerge in
systems involving extensile dipoles
and are accompanied by
largescale chain reconfigurations and
nematic ordering. Comparisons
with experiments show good qualitative
agreement and support the
hypothesis that selforganizing
longranged hydrodynamic couplings
between chromatinassociated active
motor proteins are responsible for the
observed coherent dynamics.

Abstract:
It is wellknown that by placing
judiciously chosen image point
forces and doublets to the Stokeslet
above a flat wall, the noslip
boundary condition can be
conveniently imposed on
the wall Blake (1971) [8].
However, to further impose
periodic boundary conditions on
directions parallel to the wall
usually involves tedious
derivations because single or double
periodicity in Stokes flow may
require the periodic unit to have
no net force, which is not
satisfied by the wellknown image
system. In this work we present a
forceneutral image system. This
neutrality allows us to represent
the Stokes image system in a
universal formulation for
nonperiodic, singly periodic and
doubly periodic geometries. This
formulation enables the blackbox
style usage of fast kernel
summation methods. We
demonstrate the efficiency and
accuracy of this new image method
with the periodic kernel
independent fast multipole method
in both nonperiodic and periodic
geometries. We then extend
this new image system to other
widely used Stokes fundamental
solutions, including the
Laplacian of the Stokeslet and the
Rotne–Prager–Yamakawa
tensor. 

Abstract:
In suspensions of microorganisms,
pattern formation can arise from
the interplay of chemotaxis and
the fluid flows
collectively generated by the
organisms themselves. Here we
investigate the resulting pattern
formation in square and
elongated domains in the context
of two distinct models of
locomotion in which the
chemoattractant dynamics
is fully coupled to the fluid
flows and swimmer motion. Analyses
for both models reveal an
aggregative instability
due to chemotaxis, independent of
swimmer shape and type, and a
hydrodynamic instability for “pusher”
swimmers. We discuss the
similarities and differences
between the models. Simulations
reveal a critical length
scale of the swimmer aggregates
and this feature can be utilized
to stabilize swimmer concentration
patterns into
quasionedimensional bands by
varying the domain size. These
concentration bands transition
to traveling pulses under an
external chemoattractant gradient,
as observed in experiments with
chemotactic bacteria.


Abstract:We
study how a suspended liquid film is
deformed by an external flow en route
to forming a bubble through
experiments and a model. We identify a
family of nonminimal but stable
equilibrium shapes for flow
speeds up to a critical value beyond
which the film inflates unstably, and
the model accounts for the observed
nonlinear deformations and forces. A
saddlenode or fold bifurcation in the
solution diagram suggests that
bubble formation at high speeds
results from the loss of equilibrium
and at low speeds from the
loss of stability for overly inflated
shapes. 
Abstract:
An important but missing component in
the application of the kernel
independent fast multipole
method (KIFMM) is the capability for
flexibly and efficiently imposing singly,
doubly, and triply periodic boundary
conditions. In most popular packages
such periodicities are imposed
with the hierarchical repetition of
periodic boxes, which may give
an incorrect answer due to the
conditional convergence of some kernel
sums. Here we present an
efficient method to properly impose
periodic boundary conditions using
a nearfar splitting scheme. The
nearfield contribution is directly
calculated with the KIFMM
method, while the farfield
contribution is calculated with a
multipoletolocal (M2L)
operator which is independent of the
source and target point distribution.
The M2L operator is
constructed with the farfield portion
of the kernel function to generate the
farfield contribution with the
downward equivalent source points in
KIFMM. This method guarantees
the sum of the nearfield &
farfield converge pointwise to
results satisfying periodicity
and compatibility conditions. The
computational cost of the farfield
calculation observes the same
O ( N ) complexity as FMM and is
designed to be small by reusing the
data computed by KIFMM for the
nearfield. The farfield calculations
require no additional control
parameters, and observes the same
theoretical error bound as KIFMM. We
present accuracy and timing
test results for the Laplace kernel in
singly periodic domains and the Stokes
velocity kernel in doubly and triply
periodic domains. 

Abstract:The cellular cytoskeleton is an active material, driven out of equilibrium by molecular motor proteins. It is not understood how the collective behaviors of cytoskeletal networks emerge from the properties of the network’s constituent motor proteins and filaments. Here we present experimental results on networks of stabilized microtubules in Xenopus oocyte extracts, which undergo spontaneous bulk contraction driven by the motor protein dynein, and investigate the effects of varying the initial microtubule density and length distribution. We find that networks contract to a similar final density, irrespective of the length of microtubules or their initial density, but that the contraction timescale varies with the average microtubule length. To gain insight into why this microscopic property influences the macroscopic network contraction time, we developed simulations where microtubules and motors are explicitly represented. The simulations qualitatively recapitulate the variation of contraction timescale with microtubule length, and allowed stress contributions from different sources to be estimated and decoupled. 

Abstract:
Onedimensional
crystals of
passivelydriven
particles in
microfluidic
channels
exhibit
collective
vibrational
modes
reminiscent of
acoustic
‘phonons’.
These phonons
are induced by
the longrange
hydrodynamic
interactions
among the
particles and
are neutrally
stable at the
linear level.
Here, we
analyze the
effect of particle
activity –
selfpropulsion
– on the
emergence and
stability of
these phonons.
We show that
the direction
of wave
propagation in
active
crystals is
sensitive to
the intensity
of the
background
flow. We also
show that
activity
couples, at
the linear
level,
transverse
waves to the
particles’
rotational
motion,
inducing a
new mode of
instability
that persists
in the limit
of large
background
flow, or,
equivalently,
vanishingly 

Abstract:Spindles
are selforganized microtubulebased
structures that segregate chromosomes
during cell division. The mass
of the spindle is controlled by the
balance between microtubule turnover
and nucleation. The mechanisms
that control the spatial regulation of
microtubule nucleation remain poorly
understood. While previous work found
that microtubule nucleators bind to
preexisting microtubules in
the spindle, it is still unclear
whether this binding regulates the
activity of those nucleators.
Here we use a combination of
experiments and mathematical modeling
to investigate this issue. We
measured the concentration of
microtubules and soluble tubulin in
and around the spindle. We
found a very sharp decay in the
concentration of microtubules at the
spindle interface. This is inconsistent
with a model in which the activity of
nucleators is independent of their
association with microtubules
but consistent with a model in which
microtubule nucleators are only active
when bound to preexisting
microtubules. This argues that the
activity of microtubule nucleators is
greatly enhanced when bound to
preexisting microtubules. Thus,
microtubule nucleators are both
localized and activated by the
microtubules they
generate. 

Abstract:
Achieving macroscopic
directed migration of
microscale swimmers in
a fluid is an important
step towards utilizing
their autonomous
motion. It has been
experimentally shown
that directed
motion can be induced,
without any external
fields, by certain
geometrically
asymmetric obstacles
due to interaction
between their
boundaries and the
swimmers. In this
paper, we propose a
kinetictype model to
study swimming and
directional migration
of microscale
bimetallic rods in
a periodic array
of posts with
noncircular
crosssections. Both
rod position and
orientation are taken
into account; rod
trapping and release
on the post boundaries
are modeled by
empirically characterizing
curvature and
orientational
dependence of the
boundary absorption
and desorption. Intensity
of the directed rod
migration, which we
call the normalized
net flux, is then
defined and computed
given the geometry of
the post array. We
numerically study the
effect of post
spacings on the
flux; we also apply
shape optimization to
find better post
shapes that can induce
stronger flux. Inspired
by preliminary
numerical results on
two candidate posts,
we perform an
approximate analysis
on a simplified
model to show the key
geometric features
that a good post
should have. Based on
this, three new
candidate shapes are
proposed which give
rise to large fluxes.
This approach provides
an effective tool
and guidance for
experimentally
designing new devices
that induce strong
directed migration
of microscale
swimmers. 

Abstract:The cellular cytoskeleton is an active material, driven out of equilibrium by molecular motor proteins. It is not understood how the collective behaviors of cytoskeletal networks emerge from the properties of the network’s constituent motor proteins and filaments. Here we present experimental results on networks of stabilized microtubules in Xenopus oocyte extracts, which undergo spontaneous bulk contraction driven by the motor protein dynein, and investigate the effects of varying the initial microtubule density and length distribution. We find that networks contract to a similar final density, irrespective of the length of microtubules or their initial density, but that the contraction timescale varies with the average microtubule length. To gain insight into why this microscopic property influences the macroscopic network contraction time, we developed simulations where microtubules and motors are explicitly represented. The simulations qualitatively recapitulate the variation of contraction timescale with microtubule length, and allowed stress contributions from different sources to be estimated and decoupled. 

Abstract: The swimming direction of biological or artificial microscale swimmers tends to be randomised over long timescales by thermal fluctuations. Bacteria use various strategies to bias swimming behaviour and achieve directed motion against a flow, maintain alignment with gravity or travel up a chemical gradient. Herein, we explore a purely geometric means of biasing the motion of artificial nanorod swimmers. These artificial swimmers are bimetallic rods, powered by a chemical fuel, which swim on a substrate printed with teardropshaped posts. The artificial swimmers are hydrodynamically attracted to the posts, swimming alongside the post perimeter for long times before leaving. The rods experience a higher rate of departure from the higher curvature end of the teardrop shape, thereby introducing a bias into their motion. This bias increases with swimming speed and can be translated into a macroscopic directional motion over long times by using arrays of teardropshaped posts aligned along a single direction. This method provides a protocol for concentrating swimmers, sorting swimmers according to different speeds, and could enable artificial swimmers to transport cargo to desired locations. 

Abstract:We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile “extensor” particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a DoiOnsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rodlike particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau–deGennes Qtensor theories for active nematic fluids, as well as by more complex DoiOnsager theories for polar microtubule–motorprotein systems. We apply the quasiequilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a nonstandard Qtensor theory. We demonstrate through simulation that this BQtensor theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the BQtensor model to study the dynamics of extensor suspensions in circular and biconcave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment we find unusual dynamics with activitycontrolled defect production and absorption at the boundaries of the domain. In biconcave domains, a Frederickslike transition occurs as the width of the neck connecting the two disks is varied. 

Abstract:
We explore theoretically the
aerodynamics of a recently fabricated
jellyfishlike flying machine (Ristroph &
Childress, J. R. Soc. Interface , vol. 11 (92),
2014, 20130992). This experimental device achieves
flight and hovering by opening and closing
opposing sets of wings. It displays orientational
or postural flight stability without additional
control surfaces or feedback control. Our model
‘machine’ consists of two mirrorsymmetric
massless flapping wings connected to a volumeless
body with mass and moment of inertia. A vortex
sheet shedding and wake model is used for the flow
simulation. Use of the fast multipole method
allows us to simulate for long times and resolve
complex wakes. We use our model to explore the
design parameters that maintain body hovering and
ascent, and investigate the performance of steady
ascent states. We find that ascent speed and
efficiency increase as the wings are brought
closer, due to a mirrorimage ‘groundeffect’
between the wings. Steady ascent is approached
exponentially in time, which suggests a linear
relationship between the aerodynamic force and
ascent speed. We investigate the orientational
stability of hovering and ascent states by
examining the flyer’s free response to
perturbation from a transitory external torque.
Our results show that bottomheavy flyers (centre
of mass below the geometric centre) are capable of
recovering from large tilts, whereas the
orientation of the topheavy flyers diverges.
These results are consistent with the experimental
observations in Ristroph & Childress ( J. R.
Soc. Interface , vol. 11 (92), 2014, 20130992),
and shed light upon future designs of
flappingwing micro aerial vehicles that use
jetbased mechanisms. 

Abstract: We present a novel platform for the largescale simulation of threedimensional fibrous structures immersed in a Stokesian fluid and evolving under confinement or in freespace in three dimensions. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling. This work, to our knowledge, is the first technique to include manybody hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular assemblies of flexible fibers.... 

Abstract: The proper positioning of the mitotic spindle is crucial for asymmetric cell division and generating cell diversity during development. Proper position in the singlecell embryo of Caenorhabditis elegans is achieved initially by the migration and rotation of the pronuclear complex (PNC) and its two associated centrosomal arrays of microtubules (MTs). We present here the first systematic theoretical study of how these O(1000) centrosomal microtubules (MTs) interact through the immersing cytoplasm, the cell periphery and PNC, and with each other, to achieve proper position. This study is made possible through our development of a highly efficient and parallelized computational framework that accounts explicitly for longranged hydrodynamic interactions (HIs) between the MTs, while also capturing their flexibility, dynamic instability, and interactions with molecular motors and boundaries. First, we show through direct simulation that previous estimates of the PNC drag coefficient, based on either ignoring or partially including HIs, lead to misprediction of the active forces and timescales of migration. We then directly study the dynamics of PNC migration under various forcetransduction models, including the pushing or pulling of MTs at the cortex, and the pulling of MTs by cytoplasmicallybound force generators. While achieving proper position and orientation on physiologically reasonable timescales does not uniquely choose a model, we find that each model produces a different signature in its induced cytoplasmic flow and MT conformations. We suggest then that cytoplasmic flows and MT conformations can be used to differentiate between mechanisms and to determine their contribution to the migration process. 

Abstract: The mitotic spindle ensures the faithful segregation of chromosomes. To discover the nature of the crucial centrosometochromosome connection during mitosis, we combined the first largescale serial electron tomography of whole mitotic spindles in early C. elegans embryos with livecell imaging. Using tomography, we reconstructed the positions of all microtubules in 3D, and identified their plus and minusends. We classified them as kinetochore (KMTs), spindle (SMTs), or astral microtubules (AMTs) according to their positions, and quantified distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs are directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minusends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient. 

Abstract:
The position of the
spindle determines the position of the
cleavage plane, and is thus crucial for cell
division. Although spindle positioning has
been extensively studied, the underlying
forces ultimately responsible for moving the
spindle remain poorly understood. A recent
pioneering study by GarzonCoral et al. uses
magnetic tweezers to perform the first direct
measurements of the forces involved in
positioning the mitotic spindle. Combining
this with molecular perturbations and
geometrical effects, they use their data to
argue that the forces that keep the spindle in
its proper position for cell division arise
from astral microtubules growing and pushing
against the cell's cortex. Here, we review
these groundbreaking experiments, the various
biomechanical models for spindle positioning
that they seek to differentiate, and discuss
new questions raised by these measurements. 

Abstract: Biological systems often involve the selfassembly of basic components into complex and functioning structures. Artificial systems that mimic such processes can provide a wellcontrolled setting to explore the principles involved and also synthesize useful micromachines. Our experiments show that immotile, but active, components selfassemble into two types of structure that exhibit the fundamental forms of motility: translation and rotation. Specifically, micronscale metallic rods are designed to induce extensile surface flows in the presence of a chemical fuel; these rods interact with each other and pair up to form either a swimmer or a rotor. Such pairs can transition reversibly between these two configurations, leading to kinetics reminiscent of bacterial runandtumble motion. 

Introduction: A very common
class of fluidstructure interaction problems
involves the dynamics of flexible fibers
immersed in a Stokesian fluid. In biology this
arises in modeling the flagellae or cilia
involved in microorganismal locomotion and
mucal transport, in determining the shape of
biofilm streamers, and in understanding how
biopolymers such as microtubules respond to
the active coupling afforded by motor
proteins. In engineering it arises in the
paper processing industry, where wood pulp
suspensions can show the abrupt appearance of
normal stress differences, and in
microfluidic engineering where flow control
using flexible particles has lately been
explored. Flow induced buckling of fibers is
an important determinant on fiber transport in
those flows, as well as for the fluid
mechanical stresses that develop... 

Abstract:
Many important processes in the cell are
mediated by stiff microtubule polymers and
the active motor proteins moving upon them.
This includes the transport of subcellular
structures (nuclei, chromosomes,
organelles), and the selfassembly and
positioning of the mitotic spindle. Very
little is yet understood of these processes
but they all present fascinating problems in
fluid/structure interactions. Microtubules and
motor proteins are also the building blocks of
new "biosynthetic" active suspensions driven
by motorprotein activity. These reduced
systems can probed, and modeled, more easily
than the fully biological ones and show their
own aspects of selfassembly and complex
dynamics. I will review recent work modeling
such systems as uid/structure
interaction problems, and as multiscale
complex fluids. 

Abstract: Many cellular processes are driven
by cytoskeletal assemblies. It remains unclear
how cytoskeletal filaments and motor proteins
organize into cellular scale structures and
how molecular properties of cytoskeletal
components affect the large scale behaviors of
these systems. Here we investigate the
selforganization of stabilized microtubules
in Xenopus oocyte extracts and find that they
can form macroscopic networks that
spontaneously contract. We propose that these
contractions are driven by the clustering of
microtubule minus ends by dynein. Based on
this idea, we construct an active fluid theory
of network contractions which predicts a
dependence of the timescale of contraction on
initial network geometry, a development of
density inhomogeneities during contraction, a
constant final network density, and a strong
influence of dynein inhibition on the rate of
contraction, all in quantitative agreement
with experiments. These results demonstrate
that the motordriven clustering of filament
ends is a generic mechanism leading to
contraction 

Abstract: Microtubules and motor proteins selforganize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubulemotor mixtures can form novel active liquidcrystalline materials driven out of equilibrium by adenosine triphosphate�consuming motor proteins. Microscopic motor activity causes polaritydependent interactions between motor proteins and microtubules, but how these interactions yield such largerscale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubulemotor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motormediated microtubule interactions. We identify polaritysorting and crosslink tether relaxation as two polarspecific sources of active destabilizing stress. We then develop a continuum DoiOnsager model that captures polarity sorting and the hydrodynamic flows generated by these polarspecific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the DoiOnsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation. 

Abstract: Fish schools and bird flocks are fascinating examples of collective behaviours in which many individuals generate and interact with complex flows. Motivated by animal groups on the move, here we explore how the locomotion of many bodies emerges from their flowmediated interactions. Through experiments and simulations of arrays of flapping wings that propel within a collective wake, we discover distinct modes characterized by the group swimming speed and the spatial phase shift between trajectories of neighbouring wings. For identical flapping motions, slow and fast modes coexist and correspond to constructive and destructive wing�wake interactions. Simulations show that swimming in a group can enhance speed and save power, and we capture the key phenomena in a mathematical model based on memory or the storage and recollection of information in the flow field. These results also show that fluid dynamic interactions alone are sufficient to generate coherent collective locomotion, and thus might suggest new ways to characterize the role of flows in animal groups. 

Abstract:
Microtubules and motor proteins are building
blocks of selforganized subcellular
biological structures such as the mitotic
spindle and the centrosomal microtubule array.
These same ingredients can form new
�bioactive� liquidcrystalline fluids that are
intrinsically out of equilibrium and which
display complex flows and defect dynamics. It
is not yet well understood how microscopic
activity, which involves polarity dependent
interactions between motor proteins and
microtubules, yields such largerscale
dynamical structures. In our multiscale
theory, Brownian dynamics simulations of polar
microtubule ensembles driven by crosslinking
motors allow us to study microscopic
organization and stresses. Polarity sorting
and crosslink relaxation emerge as two
polarspecific sources of active destabilizing
stress. On larger length scales, our continuum
DoiOnsager theory captures the hydrodynamic
flows generated by polaritydependent active
stresses. The results connect local polar
structure to flow structures and defect
dynamics. 

Abstract:
We
study, using both experiment and
theory, the coupling of transport
and shape dynamics for
elastomeric fibres moving through
an inhomogeneous flow. The
cellular flow, created
electromagnetically in our
experiment, comprises many
identical cells of
counterrotating vortices, with a
global flow geometry characterized
by a backbone of stable
and unstable manifolds connecting
hyperbolic stagnation points. Our
mathematical model is based
upon slenderbody theory for the
Stokes equations, with the
fibres modelled as inextensible
elastica. Above a certain
threshold of the control
parameter, the elastoviscous
number, transport of fibres is
mediated by their episodic
buckling by compressive stagnation
point flows, lending an
effectively chaotic
component to their dynamics. We
use simulations of the model to
construct phase diagrams
of the fibre state (buckled or
not) near stagnation points in
terms of two variables
that arise in characterizing the
transport dynamics. We show that
this reduced statistical
description quantitatively
captures our experimental
observations. By carefully
reproducing the experimental
protocols and time scales of
observation within our
numerical simulations, we also
quantitatively explain features of
the measured buckling
probability curve as a function of
the effective flow forcing. Finally,
we show within both experiment and
simulation the existence of short
and long time scales in
the evolution of fibre
conformation. 

Abstract: Active suspensions, of which a bath of swimming microorganisms is a paradigmatic example, denote large collections of individual particles or macromolecules capable of converting fuel into mechanical work and microstructural stresses. Such systems, which have excited much research in the last decade, exhibit complex dynamical behaviors such as largescale correlated motions and pattern formation due to hydrodynamic interactions. In this chapter, we summarize efforts to model these systems using particle simulations and continuum kinetic theories. After reviewing results from experiments and simulations, we present a general kinetic model for a suspension of selfpropelled rodlike particles and discuss its stability and nonlinear dynamics. We then address extensions of this model that capture the effect of steric interactions in concentrated systems, the impact of confinement and interactions with boundaries, and the effect of the suspending medium rheology. Finally, we discuss new active systems such as those that involve the interactions of biopolymers with immersed motor proteins, and surfacebound suspensions of chemicallypowered particles. 