**September
27-October 1, 2004**

Material
from Talks

**Martin
Z. Bazant**
(Department of Mathematics, Massachusetts Institute of Technology)
bazant@math.mit.edu
http://math.mit.edu/~bazant

**A
Theory of Cooperative Diffusion in Dense Granular Flows **(poster)

Co-authors:
Chris Rycroft, Jaehyuk
Choi, Ruben Rosales (Mathematics,
MIT), Arshad Kudrolli (Physics,
Clark University).

Many
attempts have been made to describe fast, dilute granular
flows starting from the kinetic theory of gases, but slow,
dense flows require a fundamentally different approach, due
to long-lasting, many-body contacts. In the case of slow drainage,
various continuum models have been proposed for the mean flow,
but no microscopic theory of fluctuations is available. Here,
a new model is proposed which postulates that particles undergo
cooperative random motion in response to diffusing "spots"
of free volume. The Spot Model may be used in discrete simulations
or analyzed in the continuum limit, where some new partial
differential equations arise. It predicts spatial velocity
correlations, slow cage breaking, and geometry-dominated diffusion
in good agreement with particle-tracking experiments in our
laboratory (http://math.mit.edu/~bazant/dryfluids).

**Yuxing
Ben**
(Department of Mathematics, Massachusetts Institute of Technology)
yben@mit.edu

**Nonlinear
Electrokinetics in Microfluidic Devices** (poster)

Co-Authors:
Martin Bazant [1,2], Jeremy
Levitan [1,3], Todd Thorsen
[1,3], H. C. Chang [4].

[1]
Institute for Soldier Nanotechnologies, MIT

[2] Applied Mathematics, MIT

[3] Mechanical Engineering, MIT

[4] Chemical Engineering, Notre Dame

We
study nonlinear electrokinetic mechanisms for transporting
fluid and particles in microfluidic devices with potential
applications to biomedical chips. Nonlinear electrokinetics
has many advantages, such as low voltage, low power, high
velocity, and no significant gas formation in the electrolyte.
It provides a challenge to theorists, however, because it
involves new and complex mechanisms of interfacial charging
and flow, which are not fully understood or explored.

Electrokinetics
is the motion of liquid or particle under an applied electric
field. In nonlinear electrokinetics, the flow has a nonlinear
dependence on the applied field, which is useful in microfluidics
because it allows steady fluid motion with AC forcing and
much larger flow speeds than linear electrokinetics at high
fields. We have been studied several such phenomena both theoretically
and numerically, which include the nonlinear electrokinetics
of an ion-exchange particle due to second-kind electrophoresis,
AC electro-osmosis around patterned-surface electrode arrays,
and induced-charge electro-osmosis around metallic or dielectric
structures, including colloidal particles as well as wires
and surface patterns in microfluidic devices. In all cases,
we are working with collaborators on experiments to test and
apply the theoretically predicted flows.

**Fulvio
Bisi** (Dipartimento di Matematica, Istituto
Nazionale di Fisica della Materia, Università di Pavia, via
Ferrata 1, 27100 Pavia, Italy) bisi@dimat.unipv.it

**Nanomechanics of Order Reconstruction in Nematic Liquid
Crystals** (poster)

Co-authors:
Epifanio G. Virga (Dipartimento
di Matematica, Istituto Nazionale di Fisica della Materia,
Università di Pavia, via Ferrata 1, 27100 Pavia, Italy) and
Georges E. Durand (Laboratoire
de Physique des Solides associ au CNRS (LA2), Universit Paris
Sud, F91405 Orsay Cedex, France)

The
occurrence of a classical bifurcation scenario in a nematic
twist cell with directors prescribed at right angles at the
cell's plates, as well as the unfolding of such bifurcation
upon perturbing the boundary conditions, has already been
shown (1). Within the Landau-de Gennes theory of liquid crystals,
we present a model to describe the order reconstruction in
a twist cell subject to uniaxial boundary conditions for the
order tensor. A variational approach allows us to compute
both the nanoforce and the nanotorque exerted on the plates
of the cell by the intervening nematic liquid crystal; these
mechanical quantities can in principle be measured (2). We
show how the torque can indeed be used as a bifurcation parameter,
giving a physically measurable quantity that could be used
to classify the type of pattern for the director field across
the cell. This means that the occurrence of the order reconstruction,
obtained upon reducing the distance between the plates, could
be revealed by an abrupt change in the torque measured. Furthermore,
we study the dependence of the force on the distance between
the plates for the different types of equilibrium solutions,
and the condition under which such a dependence lacks monotonicity
and unveils a hysteresis loop in a kind of molecular 'load
diagram.'

(1)
F. Bisi, E. C. Gartland, R. Rosso and E.G. Virga, Phys. Rev.
E, 68, (2003)

(2)
R. G. Horn, J. N. Israelachvili, E. Perez, J. Physique 42,
39 (1981)

**Raphael
Blumenfeld** (Cavendish Laboratory) rbb11@phy.cam.ac.uk
http://www.poco.phy.cam.ac.uk/~rbb11

**Stress
Field Equations in Granular Solids - A Shift of Paradigm**

Slides:
pdf

A
key concept to the understanding of stress transmission in
granular materials is the Marginally Rigid State and an experiment
is described which establishes the relevance of this state.
The MRS can be regarded as a critical point wherein a particular
lengthscale diverges. Granular matter at the MRS is statically
determinate (isostatic), obviating elasticity theory. A new
"isostaticity theory" is formulated for stress transmission
at the MRS. It explains the force chains, frequently observed
in experiments, and makes it possible to predict their individual
trajectories.

The
insight from the static theory makes it possible to formulate
a theory for the yield and failuer of granular solids and
a new set of equations is presented for the flow of granular
matter in this regime.

**Zhenlu
Cui** (Department of Mathematics, Florida State
University) zcui@math.fsu.edu

**A
Second Order Tensor Theory for Flows of Cholesteric Liquid
Crystal Polymers** (poster)

Joint
work with Qi Wang.

We derive a second order tensor
based hydrodynamic theory for flows of cholesteric liquid
crystal polymers following the continuum mechanics formulation
of McMillan's second order tensor theory for liquid crystals.
We present some equilibrium solutions with various symmetries.
Then, we study the permeation modes in weak shear and Poiseuille
flows using a coarse-grained method. Our results extend those
obtained by LE theory.

**Antonio
DeSimone**
(International School of Advanced Studies (SISSA), Trieste,
Italy) desimone@sissa.it

**Soft
Elasticity of Nematic Elastomers and Wetting Properties of
Rough Surfaces**

Slides:
pdf

Bridging
across length scales is one of the fundamental challenges
in the modelling of soft material systems whose mechanical
response is driven by rough energy landscapes. We will illustrate
the use of relaxation and homogenization techniques through
two case studies.

**Brian
DiDonna**
(IMA Postdoc) didonna@ima.umn.edu

**Elasticity
of Random Spring Networks** (poster)

Some
microstructured materials, such as sparse crosslinked polymer
networks (e.g. actin networks in living cells) or open cell
metal foams, can be described mechanically as networks of
elastic rods with various bending potentials and force extension
relations.We study the fundamental problem of how a ball and
spring network with a known degree of randomness, either in
geometry or in spring constants, reacts to an externally applied
shear. Namely, how uniform is the local shear and displacement
field on different length scales, and how does relaxation
from an affine (stickly uniform) shear field soften the bulk
elastic constant. Scaling of spatial correlation functions
with distance, applied shear, and degree of randomness is
derived and demonstrated through numerical simulation.

**Masao
Doi **(Tokyo University) doi@ap.t.u-tokyo.ac.jp

**
Motion of Complex Shaped Particle in Newtonian Fluid**

Slides:
pdf

How
a small particle suspended in a Newtonian fluid moves under
an external force is a very classical problem of hydrodynamics,
but seems to be attracting a resurgent interest in some
recent technologies such as micro printing and micro electro
mechanical systems. Detailed studies have been done for
hydrodynamic problems such as how the mobility tensors depend
on particle shape, but not much studies have been done for
the statistical problems such as how the ensemble of complex
shaped particles move in flow field. We have constructed
a simulator which calculates the motion of rigid particles
of general shape under external fields (force, torque and
flow fields). Here we discuss two applications of the simulator,
the sedimentation and the migration of complex shaped particles.

(1)
Sedimentation: we discuss the sedimentation behavior of
particles of general shape under gravity. The set of particles
placed at the origin will disperse as they settle down.
We shall show that the dispersion behavior is strongly dependent
on the particle shape. We classify the types of the sedimentation
behavior and discuss how they are related to particle shape.

(2)
Separation: we discuss whether we can separate chiral particles
(i.e., the particle themirror image of which cannot be superimposed
on the original one by the operation of rotation) from its
racemic mixture by using the difference in the migration
velocity of the particle in a shear flow. Linear response
theory and symmetry consideration indicates, that such separation
is not possible. However, it can be shown that if strong
shear flow is used , one can separate the right handed particle
from the left handed particles.

**Masao
Doi **(Tokyo University) doi@ap.t.u-tokyo.ac.jp

**OCTA:
Open Computational Tool for Soft Matters** (poster)

OCTA
is an intergrated simulation programs for soft materials developed
by a joint project of industry and academia supported by Japanese
governemnt. It is a free software and can be downloaded at
[1]. OCTA consists of several simulators specialized to certain
phenomena of polymers (molecular dynamics, rheology, interfacial
phenomena, micro fluidics) and a simulation platform. The
role of the simulation platform is to facilitates the collaboration
of various simulation programs. The overview and the demonstrationo
of the OCTA system will be given [2].

[1]
OCTA - integrated simulation system for soft materials- ,
http://octa.jp.

[2]
M. Doi, J. Comp. App. Math. 149 13-25 (2002)

**James
J. Feng** (Department of Chemical & Biological
Engineering, University of British Columbia) jfeng@chml.ubc.ca
http://faculty.chml.ubc.ca/jfeng

**Simulating
Two-Phase Complex Fluids Using a Diffuse-Interface Model**
(poster)

In
two-phase complex fluids such as emulsions and polymer blends,
the components are often microstructured complex fluids themselves.
To model and simulate the fluid dynamics of such systems,
one has to deal with the dual complexity of non-Newtonian
rheology and evolving interfaces. Recently, we developed a
diffuse-interface formulation which incorporates complex rheology
and interfacial dynamics in a unified framework. This presentation
will describe recent results on drop deformation, coalescence
and self-assembly in a liquid crystalline matrix.

**Eliot
Fried** (Department of Mechanical Engineering,
Washington University in St. Louis) efried@me.wustl.edu
http://www.me.wustl.edu/ME/faculty/efried/

**Universal
States in Nematic Elastomers**

Slides:
pdf

For
a particular material model, a state that can be maintained
in equilibrium for by the action of surface tractions alone
is called controllable. If a state is controllable for all
material models in a particular class, that state is called
universal. Universal states are of central importance in the
design of experiments for the determination of constitutive
relations, as such experiments should not be based on specific
model expressions but, rather, should produce states sustainable
by the full range of material models belonging to a broadly
relevant class. Universal states have been used with benefit
for the study of elastomeric solids, viscoelastic fluids,
and uniaxial nematic liquid crystals. In addition to background
material, this talk will discuss recent results and open problems
related to universal states in nematic elastomers.

**Francois
Graner**
(Shannon Laboratory, Department of Physics, Université Joseph
Fourier) francois.graner@ujf-grenoble.fr
http://graner.net/francois/

**Models
for Elastic, Plastic, Fluid Materials**

Slides:
pdf

It
is difficult to predict the constitutive relations of foams,
emulsions, granular materials or gels from first principles.
Experimentally, the mechanical behaviors of such viscoplastic
materials do not appear to change discountinuously. However,
mathematical singularities appear as soon as a solid exhibits
plastic deformation, or a liquid a non-zero restoring force.
The continuum elasticity theory and the Navier-Stokes equations
break down.

Visco-elasto-plastic
theories require an interpolation between these apparently
orthogonal descriptions. We use physical quantities which
exist and are measurable in all regimes. We define generalized
stress and strain tensors as statistical averages over microscopical
details (avoiding the use of a microscopic reference state).
They recover each correct limiting behaviors when either classical
theory applies.

We
perform local and averaged measurements on foam flowing past
an obstacle or through a constriction, or under Couette shear.
Applications include discrete mechanics, where the sample
size (upper cut-off) is not significantly larger than the
individual size (lower cut-off): granular materials, nano-fluidics.

**Alexander
Grosberg** (Department of Physics and Astronomy,
University of Minnesota) grosberg@physics.umn.edu

**Knots
in Polymer Physics**

We
report a series of computer simulations and related analytical
studies of the role of topological constraints in the equilibroium
properties of polymeric loops. We show that no-knots loops
exhibit swelling similar to that of self-avoiding chains even
when polymer has negligible excluded volume. We further show
that global topology of the loop has a profound effect on
the local fractal geometry of the polymer. For compact polymers,
this leads to locally shrunken conformations. We discuss implications
of these findings for a number of polymer systems.

**Andrei
A. Gusev** (Institute of Polymers, Department
of Materials, ETH Hoenggerberg, HCI H527, CH-8093 Zurich,
Switzerland) gusev@mat.ethz.ch

**Finite
Element Mapping for Spring Network Representations of the
Mechanics of Solids**

Slides:
pdf

We
present a general finite element mapping procedure for defining
spring network representations of solid mechanics. The procedure
is rigorous and equally suitable for setting regular and unstructured
spring network models of generally anisotropic solids. We
use the procedure to define close-packed triangular and simple
cubic lattice spring models of isotropic 2D and 3D elastic
media, respectively. We extend the study to heterogeneous
solids and show that the mapped spring network approach constitutes
an appealing route for incorporating subelement level constitutive
equations.

**Cheng-Cher
Huang** (School of Physics and Astronomy, University
of Minnesota) huang001@umn.edu

**Experimental
and Theoretical Studies of Liquid crystal SmC* Variant Phases**

Slides: pdf

In
1989, the discovery of antiferroelectric response in a liquid
crystal mesophase (SmCA*) is an important landmark in soft
condensed matter physics. Soon after, at least, three new
mesophases (i.e. SmC.*, SmCFI2*, and SmCFI1*) were identified.
Collectively, all these four new mesophases and SmC* are called
SmC* variant phases. Since then, enormous experimental and
theoretical effort has been aimed at addressing the following
two important questions. Experimentally, our research group
has accomplished remarkable tasks to identify the molecular
arrangements in the SmC* variant phases [1]. Theoretically,
one would like to figure out the origin or mechanism of such
a rich phase sequence within a temperature window less than
50K. As a starting point, a phenomenological model based on
mean-filed approaches will be presented [2].

1.
A. Cady, et al., Phys. Rev. E 64, 050702 (2001) and Ref found
therein.

2.
D. A. Olson, et al., Phys. Rev. E 66, 021702 (2002).

**Cheng-Cher
Huang** (School of Physics and Astronomy, University
of Minnesota) huang001@umn.edu

**Optical
Investigations on the Biaxial Smectic A Phase of a Bent-Core
Compound** (poster)

We
report an antiferroelectric biaxial Smectic A liquid crystal
phase from one bent-core molecule 1g14. We also extracted
the critical exponent associated with the biaxiality, which
is different from the one that is associated with the uniaxial
- antiferroelectric biaxial SmA phase transition.

**Antal
Jákli** (Liquid Crystal Institute, Kent State
University) jakli@lci.kent.edu
http://www.lci.kent.edu/jakli.html

**Electric Field-Induced Motion of Solid Particles in
Smectic Liquid Crystals **(poster)

Joint
work with G. Liao, J.
R. Kelly, O.D. Lavrentovich
(Liquid
Crystal Institute, Kent State University, Kent, OH 44242,
USA).

Accurate
characterization of rheological properties of smectic liquid
crystals is a very difficult task due to the formation of
defects during flow processes. The study of motion of colloid
particles in smectic liquid crystals is important not only
from the standpoint of the rheology of smectics, but is also
of biological relevance, as similar phenomena might be expected
for proteins in cell membranes. We studied electric field-induced
rotational and translational motion of spherical and cylindrical
glass particles embedded in the SmA slab of octyl cyanobiphenyl
(8CB) and in SmA* and SmC* slab of ferroelectric liquid crystal
CS2003 (from Chisso Co.). Above a threshold electric field
the particles rotate about their symmetry axes analogous to
the Quincke observed in isotropic fluids.[LINK][i] At higher
fields some of them also begin to move along the smectic layers
perpendicular to the electric field. Studying the movement
of the particles allows us to study the flow behavior of the
smectic A and smectic C liquid crystals around the spheres.
We find that the flow is purely viscous and does not involve
any permeation at sufficiently large speeds in accordance
with the theory of de Gennes.[LINK][ii] We also observed a
very interesting new phenomenon: when the sample contains
air bubbles, the moving spheres stick to the bubbles and rotate
collectively with a field- dependent (linear) speed that is
independent of the radius of the bubbles. At higher fields
even the bubbles can move and tend to stick together. The
details of the motion and the underlying physical mechanism
will be discussed.

[LINK] [i] T.B. Jones, "Electromechanics of Particles", Cambridge
Univ. Press., New York, (1995)

[LINK] [ii] P.G. de Gennes, Phys. Fluids, 17, 1645 (1974)

**Sookyung
Joo** (IMA Postdoc) sjoo@ima.umn.edu

**The
Phase Transition Between Chiral Nematic and Smectic Liquid
Crystals** (poster)

We
study the Chen-Lubensky model to investigate the phase transition
between chiral nematic and smectic liquid crystals. First,
we prove the existence of the minimizers in an admissible
set where the order parameter vanishes on the boundary. The
splay, twist, and bend Frank constants are considered to diverge
near N* -- C* phase transition based on physical observation,
while only twist and bend constants can be assumed to diverge
near N* -- A* transition. Then we describe the transition
temperatures for both smectic A side and smectic C side when
a domain is a considerably large liquid crystal region confined
in two plates.

**Randall
D. Kamien** (Department of Physics & Astronomy,
University of Pennsylvania ) kamien@physics.upenn.edu
http://www.physics.upenn.edu/~kamien/

**Bending
The Rules**

Slides:
pdf

We
discuss the ordering of liquid crystalline phases which possess
both cubic symmetry and smectic-like, lamellar ordering. We
will show that there is a fundamental frustration in this
system. We propose an ansatz based on triply-periodic minimal
surfaces. We discuss more general constructions based on topological
field configurations and tesselation of the hyperbolic plane.

**David
Kinderlehrer **(Department of Mathematical Sciences,
Carnegie Mellon University) davidk@andrew.cmu.edu
http://www.math.cmu.edu/people/fac/kinderlehrer.html

**Cooperative
Effects in a Dye/Liquid Crystal System**

We
discuss the dichroic dye/liquid crystal interaction known
as the Janossy effect and studied by Palffy-Muhoray, Kosa
and E. A consistent variational principle is offered that
takes advantage of Monge-Kantorovich mass transport ideas
and some consequences, like whether or not such a formulation
can actually predict the observed Janossy effect, are discussed.
As time permits, we shall discuss the general issue of diffusion
mediated transport, the interaction of transport mechanisms
and diffusion at extremely small scale with hints to other
systems. This is joint work with Stuart
Hastings and Michael Kowalczyk.

**Issac
Klapper** (Department of Mathematical Sciences,
Montana State University) klapper@math.montana.edu

**Biofilms
As Soft Materials **(poster)

Biofilms
are complex polymeric materials consisting of microorganisms
protected within a self-secreted extracellular polymeric matrix.
They are ubiquitous - for example, it has been estimated that
approximately %75 of bacteria are found in the biofilm phenotype.
Material properties of biofilms play an important role in
their extraordinary resistance to mechanical and chemical
stresses. This poster is intended as a brief introduction
to biofilms including some discussion of their rheological
properties and attempts to model them as continuum materials.

**Frédéric
Legoll **(IMA Postdoc)

**High-Order Averaging Schemes for Molecular Dynamics
Simulations** (poster)

Many
thermodynamical properties of chemical systems are defined
as averages of observables over the phase space of the underlying
microscopic system. A way to compute these ensemble averages
is to use Molecular Dynamics and to compute time averages
on long trajectories. In this work, we propose high-order
averaging formulae to compute time averages. In some cases,
these formulae significantly improve the convergence rate
with respect to the simulation time. Many numerical examples
will be provided, as well as error bounds.

This
is joint work with Eric Cancès,
Claude Le Bris and Gabriel
Turinici (CERMICS ENPC and INRIA Rocquencourt, France),
and with François Castella, Philippe
Chartier and Erwan Faou
(INRIA Rennes, France).

**Didier
Long** (Laboratoire de Physique des Solides,
Université Paris-Sud, Bat. 510) long@lps.u-psud.fr
legoll@ima.umn.edu

**Non-Linear
Behavior of Filled Elastomers by Molecular Dissipative Dynamics**

Slides:
pdf

Whereas
non-reinforced rubbers have a low resistance to tear and wear,
reinforced elastomers can be used under very demanding conditions.
The corresponding effects are very important since the energy
of tearing can be hundred of times larger than that for the
non-reinforced material. Recent progress regarding the glass
transition mechanisms in the vicinity of interfaces have allowed
for understanding some aspects of the reinforcement, such
as the high shear modulus and some dissipative properties.
By implementing this picture in dissipative molecular dynamics
simulations, we show here how one can account for some of
the striking non-linear properties of these systems, such
as the Payne effect (strong drop of the shear modulus at a
few percents deformation) and the Mullins effect (hysteresis
of mechanical properties, partially recoverable after waiting
or thermal treatment of the system). We show also that the
associated mechanisms lead to some specific plastic properties.

**Robert
B. Meyer**
(Martin Fisher School of Physics, Brandeis University) meyer@brandeis.edu

**Electrically
and Mechanically Driven Instabilities in Thin Layers of Nematic
Liquid Crystal Gel**

Slides:
pdf

A
layer of nematic liquid crystal is aligned as a single crystal
between rigid plates, and gelled into a soft solid by formation
of a crosslinked polymer network within the nematic phase.
Changing the temperature produces changes in the nematic order
parameter, resulting in stresses in the gel, due to its confinement.
Likewise, an applied electric field produces a torque on the
nematic director, either stabilizing or destabilising its
initial orientation. The combination of elastic and electric
stresses leads to buckling instabiltites in the sample, which
are observed by polarized light microscopy. Experimental results
and theoretical analysis will be presented.

**Robert
Pelcovits**
(Department of Physics, Brown University) pelcovits@physics.brown.edu

**Visualization
of Topological Defects in Liquid Crystals**

Slides:
pdf

I
will discuss our ongoing work on the visualization of topological
defects in numerical simulations of liquid crystals. We are
collaborating with a computer scientist who has developed
techniques which allow easy visualization of the features
of tensor fields, originally in the context of MRI scans of
the brain. In our case we wish to visualize the nematic order
parameter tensor in order to locate and characterize defects
in our data set. Our data set is produced by quenching a Gay-Berne
nematic fluid of 65K particles. I will discuss the challenges
faced in the study of defects in fluid (as opposed to lattice)
models of liquid crystals and the significant progress we
have made to date.

**Harald
Pleiner **(Max Planck Institute for Polymer
Research, D 55021 Mainz, Germany) pleiner@mpip-mainz.mpg.de
http://www.mpip-mainz.mpg.de/~pleiner

**A
Physicists' View on Constitutive Equations**

Joint
work with M. Liu (Inst. f. Theoret.
Physik, Universitaet Tuebingen, D 72076 Tuebingen, Germany),
and Helmut R. Brand (Theoret.
Physik III, Universitaet Bayreuth, D 95440 Bayreuth, Germany)

Hydrodynamic
equations for various kinds of complex fluids (simple liquids,
binary mixtures, liquid crystals, superfluids, crystals, etc.)
can be derived rigorously using general physical laws and
principles. This hydrodynamic method is generalized to include
slowly relaxing quantities, in particular those describing
viscoelasticity. By this procedure it is guaranteed that the
resulting equations are in agreement with basic physical laws
and requirements.

We
start with the nonlinear hydrodynamic equations for elastic
media derived from basic physical principles. For the Eulerian
strain tensor the lower convected time derivative is obtained,
unambiguously [1-3]. Adding a relaxation term the permanent
elasticity is transformed into viscoelasticity [1,2], where
both, the short time and the long time limit, are given correctly.
The dynamic equation for the strain tensor obtained that way
still shows the lower convected derivative universally. It
covers the usual non-Newtonian effects, like shear thinning,
strain hardening, stress overshoot, normal stress differences
and Weissenberg effect, non exponential stress relaxation,
etc. [4]. When brought into the more familiar form of a dynamic
equation for the stress tensor ("constitutive equation"),
it comprises most of the well-known ad-hoc models (Maxwell,
Oldroyd, Giesekus), and is more general in structure than
those, but is in disagreement with some of them (Johnson-Segalman,
Jeffries) [5]. It imposes some restrictions on, and reveals
some interdependencies of, the various non-Newtonian contributions
that are otherwise introduced heuristically. It is shown how
these contributions originate from (nonlinear) elasticity,
viscosity, strain relaxation and convection. The time derivative
for the stress tensor is no longer of the lower convected
type, but is material dependent. We also discuss the connection
to those descriptions of viscoelasticity that utilize an orientational
(or configurational) order parameter [6].

[1]
H. Temmen, H. Pleiner, M. Liu, and H.R. Brand, Phys. Rev.
Lett. 84 (2000) 3228; 86 (2001) 745.

[2]
H. Pleiner, M. Liu, and H.R. Brand, Rheol. Acta 39 (2000)
560.

[3]
M. Grmela, Phys. Lett. A, 296 (2002) 97.

[4]
O. Mueller, M. Liu, H. Pleiner, and H.R. Brand, to be published.

[5]
H. Pleiner, M. Liu, and H.R. Brand, Rheol. Acta, DOI: 10.1007/s00397-004-0365-8
(2004).

[6]
H. Pleiner, M. Liu, and H.R. Brand, Rheol. Acta 41 (2002)
375.

**Riccardo
Rosso** (Dipartimento di Matematica, Università
di Pavia) rosso@dimat.unipv.it

**Periodic
Saddle-Splay Freedericksz Transition in a Nematic Cell**
(poster)

By
use of a local stability analysis, we predict the existence
of a Periodic Saddle-Splay Freedericksz (PSSF) transition,
supplementing the existing set of external-field-driven Freedericksz
transitions in a nematic cell. The onset of the PSSF transition
requires a weaker field than the classical, aperiodic, splay
Freedericksz transition, provided that the saddle-splay elastic
constant is large enough, and the anchoring strengths at the
plates of the cell differ from one another. We determine the
threshold condition for the PSSF transition and the structure
of the associated unstable mode.

**André
M. Sonnet**
(Department of Mathematics, University of Strathclyde) ams@maths.strath.ac.uk
http://www.maths.strath.ac.uk/~aas02102

**Defect
Dynamics in Liquid Crystals** (poster)

The
dynamics of topological defects is of interest in many different
branches of physics. Liquid crystals are of particular importance
because they allow to conduct easily accessible experiments
for many effects. One example that has recently attracted
a lot of attention is the annihilation of defect pairs in
nematic and smectic liquid crystals. Somewhat surprisingly,
it was found that the speed with which a defect moves depends
strongly on its topological charge. Numerical explorations
for nematic disclination lines and defects in smectic films
have established that material flow plays a major role in
the pair annihilation process. We present an analytical argument
to show that the origin of the asymmetry can be retraced to
the opposite parity of elastic and viscous forces under topological
charge change.

**Eugene
M. Terentjev** (Cavendish Laboratory, University
of Cambridge) emt1000@cam.ac.uk
http://www.poco.phy.cam.ac.uk/~emt1000

**Kinetic
Theory of Rotational Diffusion and Anisotropic Viscosity of
Liquid Crystals**

Slides:
pdf

We
shall discuss the molecular-statistical approach to describing
the rotational diffusion of anisotropic molecules (rods or
disks) in a mean field of liquid crystalline order (nematic
or smectic-C). The issues of microscopic stress tensor and
its averaging, of the spectrum of relaxation times, of the
role of more delicate ordering (e.g. smectic layering or biaxiality),
and of the route to the full pair-correlation theory will
be considered.