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Nonlinear Collective Behaviour: Networks,
Swarming and Reaction Diffusion Dynamics

Continuum
models of largescale coherence in dense assemblies of selfpropelled particles Igor Aronson Dense
assemblies of active selfpropelled particles, such as vigorously shaken anisotropic
grains, microtubules interacting with molecular motor, and hydrodynamically
entrained swimming bacteria, often exhibit largescale patterns of collective
motion whose correlation length greatly exceeds the size of individual
particle. Despite
a vast difference in the physical mechanisms controlling onset of largescale
coherence, continuum description of such systems can be derived from an analogy
with a dilute gas of inelastically colliding granular
rods. Thus, starting from a generic stochastic microscopic model of inelastic
polar rodlike particles with an anisotropic interaction kernel, we derive set
of equations for the local rods concentration and orientation. Above certain
critical density of rods the model exhibits spontaneous orientation instability
and onset of largescale coherence. For
the system of microtubules interacting with molecular motors we demonstrate
that the orientation instability leads to the formation of vortices and asters
seen in recent experiments. Similar
approach is applied to colonies of swimming bacteria Bacillus subtilis confined in a thin fluid film. The model is
formulated in term of twodimensional equations for local density and
orientation of bacteria coupled to the low Reynolds number NavierStokes
equation for the fluid flow velocity. We
demonstrate that this system exhibits formation of dynamic largescale patterns
with the typical scale determined by the density of bacteria. ********************************** Modelling nonequilibrium clustering and active nematic
order in collective motion of selfpropelled rods Markus
Bär Motivated by observations regarding
collective motion of gliding bacteria on a substrate, we have derived two
models describing rodshaped selfpropelled particles. The first model takes into account explicitly the shape of the rods and
assumes interaction due to volume exclusion. Simulations with up to 200 rods
exhibit spontaneous formation of clusters indicated by a bimodal cluster size
distribution already at low densities. Clustering is shown to require both the
rodshape and the active motion of the particle and is hence a genuine nonequilibrium phenomenon. Equations for the cluster size
distribution are derived and reproduce the simulation findings well. Our second model describes selfpropelled particles with apolar liquidcrystal like interactions analogous to the Vicsek model for selfpropelled particles with polar
orientation. Such an interaction mimicks
the volume exclusion interaction of rods. Simulations carried out with
up to 16.384^{ }particles reveal different ordering scenarios upon
decrease of the noise. For high density, first nematic
order appears with homogeneous density and is connected with a phase transition
correctly described by a meanfield theory of the angular orientation of
particles. A second transition leading to clustering and inhomogeneous density
of particles is found in the ordered phase. At low transition, the homogeneous
state without orientational becomes directly unstable
to formation of clusters connected with orientational
order similar to the finding in the first model with hard rods. Again the
appearance of the ordered clustering phase is well described by a transition
from a unimodal to a bimodal cluster size
distribution. Joint work with Fernando Peruani and Andreas Deutsch ********************************** Spatial
Epidemics: Emergent Tradeoffs and Evolutionary Cycling Maarten Boerlijst* Spread
of diseases in human populations can exhibit large scale patterns. An often
observed pattern is a socalled "wave of epidemic spread". We
demonstrate that in a simple contact network model such epidemic waves can
emerge spontaneously. Spatial patterns can have profound effects on selection
of disease properties, such as infectiousness and duration of the infectious
period. We have recently shown [1] that in this system spatial pattern
formation and natural selection can generate an emergent tradeoff between
infectiousness and infection period, while the system is maximizing outbreak
frequency. However, for larger differences in outbreak frequency, the system
can display turbulent interface patterns, which can reverse the selection
pressure towards maximizing secondary infections. In this way the spatial
epidemic system can move into a socalled "evolutionary cycling"
regime, where the switch in direction of selection is caused by a phase
transition in the system's spatial pattern. *
Work in collaboration with Marijn van Ballegooijen [1]
van Ballegooijen W.M. & M.C. Boerlijst
(2004) "Emergent tradeoffs and selection for outbreak frequency in
spatial epidemics", Proc. Nat. Acad. Sci. 101:
1824618250. ********************************** Collective
dynamics of active particles Hugues Chaté I
will present an overview of recent results obtained about the collective motion
of active or selfpropelled particles, both polar and nematic.
I will in particular discuss the nature of the transition to orientational order in such systems, the properties of the
ordered phase specific to the nonequilibrium nature of the problem, and
candidates for continuous mesoscopic descriptions. ********************************** Collective
motion and decisionmaking in animal groups Iain Couzin Collective
organization is everywhere, both around us and within us. Our brains are
composed of billions of interconnected cells communicating with chemical and
electrical signals. Our bodies are formed from clustering, communicating cells,
and we ourselves are integrated in our own collective human society. Elsewhere
in the natural world hundreds of thousands of blind army ants coordinate a
massive raid across the rainforest floor, a flock of birds arcs and ripples
while descending to roost and a fish school convulses, as if one entity, when
attacked by a predator. How can animal groups move in unison? How does
individual behaviour produce group dynamics? How do
animal societies make informed unanimous decisions? From ant swarms to flocking
birds, from consensus decisionmaking in fish schools to that among humans, I
will discuss how, and why, coordinated collective patterns are generated in
biological systems. ********************************** Epidemics
on networks Odo Diekman From
the point of view of an infective agent, contacts between two already infected
hosts are wasted. And if the host population is structured as a network,
repeated contacts between the same individuals are bound to occur. Accordingly
the structure can have a large impact on the spread of the infective agent and
one would like to determine this impact more precisely by way of an analysis of
models. So far this is largely wishful thinking! In the lecture I'll review
some known results and then try to formulate open questions. ********************************** Differential
and Mutual (Cross)Diffusion Effects on Pattern
Formation in ReactionDiffusion Systems Irving Epstein Turing was among the first to point out that
substantial differences in diffusion rates between reactive species can lead to
new types of pattern formation. Recent
experimental work on chemically reactive microemulsions
has revealed a variety of novel patterns, which can be simulated if one
incorporates the differences in diffusion rates between aqueous and nonaqueous species.
Models in which the diffusion of one species depends upon the spatial
distribution of another (mutual or crossdiffusion) give rise to a similarly
rich variety of patterns, even with equal diagonal diffusion coefficients, and
we have obtained experimental evidence that crossdiffusion occurs in BZAOT microemulsions. Both
mechanisms may be relevant to the nonlinear collective behavior of biological
and social systems. ********************************** Spatiotemporal Patterns of Infectious Diseases  New
Approaches to the Forecast of Epidemics T. Geisel* Many infectious diseases are transmitted
from person to person and human travel is responsible for their geographical
spread. In order to model, forecast, and control the spread of epidemics, one needs to know the statistical mechanics of human travel. How
can we obtain reliable information on travelling statistics, if people can
travel using very different means of transportation from bikes to planes? We
have studied this problem empirically and theoretically using the dispersal of
dollar bills as a proxy. The time dependent probability density obtained in
this way exhibits pronounced spatiotemporal scaling and anomalous diffusion,
which mathematically can be described very accurately in terms of a bifractional diffusion equation with few parameters. *work in collaboration with D. Brockmann and L. Hufnagel References: [1] D. Brockmann,
L. Hufnagel, and T. Geisel, "The scaling laws of
human travel", Nature 439, 462
(2006). [2] L. Hufnagel, D. Brockmann, and T.
Geisel, "Forecast and control of epidemics in a globalized
world", PNAS, 101, 15124 (2004). ********************************** Physical
Aspects of Evolutionary Transitions to Multicellularity Raymond E. Goldstein An
important issue in evolutionary biology is the emergence of multicellular
organisms from unicellular individuals. The accompanying differentiation from
motile totipotent unicellular organisms to multicellular ones having cells specialized into
reproductive (germ) and vegetative (soma) functions, such as motility, implies
both costs and benefits, the analysis of which involves the physics of
buoyancy, diffusion, and mixing. In this talk, I discuss recent results on this
transition in a model lineage: the volvocine green
algae. Particle Imaging Velocimetry of fluid flows
generated by these organisms show that they exist in the regime of very large Peclet numbers, where the scaling of nutrient uptake rates
with organism size is highly nontrivial. In concert with metabolic studies of deflagellated colonies, investigations of phenotypic
plasticity under nutrientdeprived conditions, and theoretical studies of
transport in the highPeclet number regime, we find
that flagellagenerated fluid flows enhance the nutrient uptake rate per cell,
and thereby provide a driving force for evolutionary transitions to multicellularity. Thus, there is a link between motility,
mixing, and multicellularity. ********************************** Chemically
Powered Nanodimers Raymond Kapral Molecular
motors play important roles in transport in biological systems. These molecular
machines are powered by chemical energy and operate in the regime of low
Reynolds number hydrodynamics. Recently a class of simple inorganic molecular
motors has been constructed and studied experimentally [1,2].
These motors are bimetallic rods, one end of which is chemically active. The
talk will describe simple mesoscopic models for the
motion of such nanomotors. The motor consists of two
linked spheres, one of which catalyzes the conversion between two chemical
species. The chemical species interact differently with the two spheres in the dimer. The nanodimer motor is
solvated by a molecules treated at a mesoscopic level
whose evolution is governed by multiparticle collision dynamics. The dynamics
conserves mass, momentum and energy so that coupling between the nanomotor and the hydrodynamic modes of the solvent is
treated correctly. The simulations allow one to explore the mechanisms of the
chemically powered motion and the effects of fluctuations on the motor
dynamics. *
Work in collaboration with Gunnar Rueckner. [1]
W. F. Paxton, et al., "Catalytic Nanomotors:
Autonomous Movement of Striped Nanorods", J. Am.
Chem. Soc. (JACS), 126 (41), 13424 (2004). [2] S. FournierBidoz, et al. "Synthetic
SelfPropelled Nanorotors", Chem. Commun., (4), 441 (2005). ********************************** A new hypothesis towards the onset of cardiac
fibrillation Kyoung J. Lee Ventricular
fibrillation (VF) is one of the most deadly cardiac arrhythmia during which
different parts of the ventricle beat asynchronously. A
growing body of evidence shows that rotating spiral waves (or reentries) are a
precursor to VF: Selforganized spiral waves in heart tissue are
lifethreatening because their fast rotation frequency (510 Hz) drives an
abnormally rapid contraction known as ventricular tachycardia (VT), which
subsequently becomes unstable and decays to VF. Another, equally important,
precursor of VF is “alternans,” a beattobeat
temporal alternation in the sequence of heart beats. Our
recent in vitro studies have shown that these two phenomena can coexist as a
form of period2 oscillatory reentry having line defects. Thus the underlying
mechanism for VF very likely stems from the instability of this unusual spiral
reentry. Here, I will discuss some important recent findings
and future directions. ********************************** Nonlinear
relaxation dynamics in elastic networks and design principles of molecular
machines Alexander S. Mikhailov Analyzing
nonlinear conformational relaxation dynamics in elastic networks corresponding
to two classical motor proteins, we find that they respond by welldefined
internal mechanical motions to various initial deformations and that these
motions are robust against external perturbations. We show that this behavior
is not characteristic for random elastic networks. However, special network
architectures with such properties can be designed by evolutionary optimization
methods. Using them, an example of an artificial elastic network, operating as
a cyclic machine powered by ligand binding, is
constructed. ********************************** Pinning
and depinning for localized waves in heterogeneous
media Yasumasa Nishiura Particlelike
(spatially localized) dissipative patterns arise in many fields such as
chemical reaction, gasdischarge system, liquid crystal, binary convection, and
morphogenesis. A typical model system treated here is a threecomponent
reaction diffusion system of oneactivatortwoinhibitor type. We discuss about
the dynamics of moving particles in heterogeneous media, especially we are
interested in the case in which traveling pulses or spots encounter
heterogeneities of bump type. A variety of dynamics are produced such as
penetration, annihilation, rebound, splitting, and relaxing to an ordered
pattern, i.e., pinning. It turns out that global bifurcation such as heteroclinic one and a basin switching controlled by the
unstable manifolds of saddless called scattors play a crucial role for the transition from
pinning to depinning. We also discuss a
wavegenerator created near the jump of heterogeneity. A dynamical system view
point obtained here is basic for the understanding of the collective behavior
of many particles in heterogeneous media. ********************************** Reactiondiffusionmechanics
systems A.V. Panfilov Mechanoelectric feedback is a complex concept that
has been studied in the clinical community for over a century, and may have arrhythmogenic consequences. Mathematical modelling is a useful tool to study cardiac arrhythmogenesis, however most electrophysiological
simulation studies have not accounted for the mechanical function of the heart.
Here we introduce the concept of a contracting excitable medium in order to
study the basic effects of mechanical deformations on reentrant cardiac
arrhythmias. We illustrate the electromechanical model formulation using
results from a specific implementation that combines a modified AlievPanfilov 1996 ventricular excitation model with the
nonlinear stress equilibrium equations that govern tissue mechanics. The AlievPanfilov model has been used previously to study
various types of propagation using 2D and 3D representations of cardiac tissue,
and anatomically accurate models of the heart. The model reproduces most of the
regimes important for understanding reentrant electrical activity, such as
stationary rotation of spiral waves, meandering of spiral waves and spiral wave
break up. We have extended the AlievPanfilov model
to include an approximation of the actively developed stress during contraction
to investigate the effects of mechanical deformation on cardiac excitation and
the various types of spiral wave activity. Passive mechanical properties are
defined using an isotropic, homogeneous MooneyRivlin
constitutive law. Propagating waves of excitation initiate tissue contraction
by generating active stresses that add to the passive axial stress components.
The coupled electromechanical model is solved using a hybrid approach that
incorporates finite difference and nonhomogeneous
finite element techniques for the electrical activity and tissue mechanics,
respectively. We
study the effects of mechanical activity on different regimes of wave
propagation in cardiac tissue. We show that for some parameter values, mechanoelectric feedback can induce automaticity
in an array of otherwise nonoscillatory cardiac cells, and illustrate the spatiotemporal dynamics of these pacemakers. We also
demonstrate the significant effects of mechanoelectric
feedback on reentrant wave dynamics. We found that contraction can induce
drift of an otherwise stationary rotating spiral wave. This drift settles to an
attractor that can be located either at the center or periphery of the tissue,
depending on its excitability. Finally, we observed that in some cases mechanoelectric feedback can induce breakup of a single
reentrant wave into complex fibrillatory patterns. We
conclude that tissue mechanics significantly contributes to the dynamics of
cardiac electrical activity, and that a coupled electromechanicalmechanoelectric feedback framework should be adopted for
future electrophysiological modelling studies. ********************************** Stochastic
MultiAgents and Motion of Simple Objects L. SchimanskyGeier
& W. Ebeling In
the lecture we introduce equations of motion of particles which convert energy
into motion by negative friction. If including furtheron
random forces which act on the particles these active Brownian particles may
describe the motion of simple organisms which results in a diffusional
motion of the particles. External forces as well as chemotactical
interactions may be included into the description for the purpose to decribe more complex situtations.
We present several typical situations and corresponding attractors of particles
in external fields and if interacting. A
few animals have prefered turning angles along their
random motion. This attribute is modeled by forces acting perpendicularly to
the motion which yield a drastic reduction of the diffusion coefficient
compared to the situation of free motion. A biological reason for this
restricted motion is seen in an enhanced foodconsumption of these animals
compared to the case of free diffusion. ********************************** Collective
Behavior in Excitable Media: Interacting ParticleLike Waves Kenneth Showalter* We
describe studies of interacting particlelike waves in the photosensitive BelousovZhabotinsky reaction. Unstable waves are
stabilized by global feedback that affects the overall excitability of the
medium, and the motion of these waves is controlled by imposing excitability
gradients that are regulated by a secondary feedback loop. Waves interact via a
LennardJones potential in which there are attractive
forces at long distances and repulsive forces at short distances. Processional
motion is the most common behavior, where waves align with one another to
varying degrees depending on the strength of the potential. Rotational motion
is also observed, which may occur for the same parameters as processional
motion depending on initial conditions. We also discuss other modes of behavior
and an analysis of the wave interaction in terms of the gradient of the
potential. *
In collaboration with Mark Tinsley and Aaron Steele. ********************************** Continuous
phase transition in collective motion: experiments and models Tamas Vicsek* Detailed
investigations on the nature of the phase transition in the scalar noise model
(SNM) of collective motion will be presented. Our results confirm the original
findings, i.e., that the disorderorder transition in the SNM is a continuous,
second order phase transition for small particle velocities (v < 0.1).
However, for large velocities (v > 0.3) we find a strong anisotropy in the
particle diffusion in contrast to the isotropic diffusion for small velocities.
The interplay between the anisotropic diffusion and the periodic boundary
conditions leads to an artificial symmetry breaking of the solutions
(directionally quantized density waves) and, a consequence, to a first order
transition like behavior. Our
preliminary results suggest that the situation is the same if flocking takes
place in three dimensions. We
also investigated the transition experimentally, by recording the swarminglike
collective migration of a large number of keratocytes
(tissue cells obtained from the scales of goldfish) using longterm videomicroscopy. By increasing the overall density of the
migrating cells, we were able to demonstrate a kinetic phase transition from a
disordered into an ordered state. Near the critical density a complex picture
emerges with interacting clusters of cells moving in groups. Motivated
by these experiments we have constructed a flocking model that exhibits a
continuous transition to the ordered phase, while assuming only shortrange
interactions and no explicit information about the knowledge of the direction
of motion of the neighbours. Placing the cells into microfabricated arenas we obsereved
a spectacular whirling pattern of motion which we could reproduce in the
simulations as well. *
In collaboration with I. Daruka, B. Gonci, Zs. Juranyi, M. Nagy ********************************** The
ticking of a circadian clock Pieter Rein ten Wolde In
a recent series of groundbreaking experiments, Nakajima et al. [Science 308, 414415
(2005)] showed that the three cyanobacterial clock
proteins KaiA, KaiB, and KaiC are sufficient in vitro to generate circadian phosphorylation of KaiC. Here, we
present a mathematical model of the Kai system. At its heart is the assumption
that KaiC can exist in two conformational states, one
favoring phosphorylation and the other dephosphorylation. Eachindividual
KaiC hexamer then has a
propensity to be phosphorylated in a cyclic manner.
To generate macroscopic oscillations, however, the phosphorylation
cycles of the different hexamers must be
synchronized. We propose a novel synchronisation
mechanism based on differential affinity: KaiA
stimulates KaiC phosphorylation,
but the limited supply of KaiA dimers
binds preferentially to those KaiC hexamers that are falling behind in the oscillation. KaiB sequesters KaiA and
stabilizes the dephosphorylating KaiC
state. We show that our model can reproduce a wide range of published data,
including the observed insensitivity of the oscillation period to variations in
temperature, and that it makes nontrivial predictions about the effects of
varying the concentrations of the Kai proteins. POSTER
ABSTRACTS Pulse
dynamics in a threecomponent system Peter van
Heijster, Arjen Doelman & Tasso J. Kaper We
investigate various types of pulse solutions in a certain singularly perturbed,
bistable, three component, reactiondiffusion system,
that has a natural twocomponent limit. Using geometric singular perturbation
theory and the Evans function approach, we study the existence, stability and
bifurcations of standing pulses, travelling pulses
and doublepulse solutions. ********************************** Clusters
and Loops in a ReactionAdvectionDiffusion System Yasuaki Kobayashi We
construct a phenomenological model describing aggregated spots and a loop
structure. Our model is based on the GrayScott model which is supplemented by
a global coupling term and advection terms. One of the species makes a field
proportional to its concentration, which induces the advection. By numerically
investigating the model, we show that the system has a transition from
aggregated spots to a loop which wanders around chaotically or reaches a
stationary state. We also show the reduced equation of motion of spots in which
the advection term can be interpreted as a longrange attractive force.
Relation to a similar transition observed in a recent gas discharge experiment
is discussed. ********************************** Transport
in a periodic velocity field without attractors Felix Müller
& Lutz SchimanskyGeier We
consider the transport of overdamped particles in a twodimensional periodic
velocity field. This field possesses extended lines of fixed points where the
deterministic motion stops. Additive noise makes the lines penetrable and
results in an oscillatory motion along tori. We
characterize the stochastic motion by the probability distribution density, the
stationary mean velocity and mean times of escape from bounded domains. For
intermediate noise intensities the fluctuations enhance the transport of the
particles compared to the deterministic case. A fast dichotomic
modulation of asymmetry enhances fluxes. ********************************** Nucleation,
Drift, and Decay of Phase Bubbles in Period2 Oscillatory Wave Trains JinSung Park, SungJae Woo, Okyu Kwon, Tae Yun Kim, and Kyoung J. Lee Abstract:
We report experimental observations of phase bubbles, simply closed boundaries
between domains oscillating $2\pi$ out of phase, associated with period2
oscillatory traveling waves in a BelousovZhabotinsky
reactiondiffusion system. These phase bubbles nucleate unpredictably and
spontaneously through a fast localized phase slip in the traveling waves, drift
away from the spiral core in an oscillatory fashion, and gradually shrink to
disappear. Their oscillatory drift in the radial direction is an attribute of
Doppler effect, while their lateral shrinkage is an
attribute of the local curvature. Similar phenomenon is also captured in a simple, threespecies reactiondiffusion model that support
period2 oscillatory wave trains. ********************************** Intercellular Calcium
Communications in Cultured Networks of Glia JinSung Park, Byeong
Ha Jeong, Joon Hoan Kim, Cheol Hong Min, and Kyoung J. Lee Abstract:
A series of recent studies augments the role of glia
as regulatory agents of neuronal activity, undertaking active roles in brain
computation. Intercellular and extracellular calcium
kinetics are believed to be an important mediator for
the interplay among neurons and glia. In mature
neuronglia coculture systems, populations of
neurons often exhibit globally synchronized fast 'calcium spikes' that are
accompanied by electrical bursts of action potentials. The glia in the same culture system do
often show slower calcium wave activities that possibly modulate the neuronal
activity. We examine the property of these slowly propagating calcium waves in
pure glia networks under various pharmacological
conditions and with different extrinsic stimulations. We find that there are at
least two distinct modes of propagation: (1) calcium puffs  circular wave
fronts (which are initiated by localized sources) that propagate for some
distance and extinguish by themselves and (2) small irregular wavelets that
often emerge in the wake of some dominant pacemaker waves to last for quite
some time circulating along local recurrent networks. We investigate on the spatiotemporal dynamics of cytosolic
calcium levels for concentration changes of extracellular
calcium and magnesium. As the concentration of extracellular
calcium ion becomes lower, calcium waves begin to generate at a number of puff
sites and their propagating ranges are also more increased. As well, a long
range correlation of these glial calcium dynamics is
obviously increased by periodic stimulus through local electrical pulse. ********************************** Selfpropelled
particles: from individual to collective behavior Fernando Peruani,
Luis G. Morelli, Andreas Deutsch, and Markus Baer We
study general aspects of noninteracting selfpropelled particles (SPPs) with fluctuations in the speed and the direction of
motion in two dimensions. We consider the case in which fluctuations in the
speed are not correlated to fluctuations in the direction of motion, and assume
that both processes can be described by independent characteristic timescales.
We investigate two different angular dynamics which correspond to persistent
and directed random walks and show the occurrence of a complex transient that
exhibits a series of alternating regimes of motion. We also show additive
corrections to the diffusion coefficient. The characteristic timescales are
also exposed in the velocity autocorrelation, which is a sum of exponential
forms [1]. Inspired
by the motion of anisotropic selfpropelled objects as myxobacteria
[2], we apply the obtained results for noninteracting SPPs
to understand orientational ordering and clustering
in a simple model of SPPs that interact locally by a
liquidcrystal alignment mechanism. It is observed through extensive
simulations that the behavior of the system at high and low densities is
remarkably different. In particular, we show that at low density orientational order emerges from the interplay between
local orientation and cluster formation, whose dynamics is explained in terms
of a reaction equation approach [3]. [1] F. Peruani and L. G. Morelli, to appear in Phys. Rev. Lett. [2] F. Peruani, A. Deutsch, and
M. Baer, Phys. Rev. E, 74, 030904(R) (2006). [3] F. Peruani, A. Deutsch, and
M. Baer (in preparation). ********************************** Beyond
the KellerSegel Model – Microscopic Description of Chemotactic Bacteria Pawel Romanczuk, Udo Erdmann & Lutz SchimanskyGeier Complex
spatiotemporal patterns of cell clusters were observed in colonies of chemotactic bacteria such as Escherichia coli or Sallmonella typhimurium. The
production of a potent chemoattractor by the bacteria
themselves as a reaction to certain nutrients is the essential factor for this
pattern formation. Additional collective dynamics, such as collective
translocation and rotation of bacterial clusters were reported from experiments
on bacterial colonies. Motivated
by this observations we suggest a simple model for the description of bacterial
colonies based on the concept of Active Brownian motion. Our model represents
an interesting alternative to the usually employed “pure” reactiondiffusion
equations as it allows us to study the macroscopic pattern formation of the
colony, the mesoscopic dynamics of bacterial
ensembles (swarming), as well as the microscopic dynamics of single cells. We
are able to reproduce the macroscopic behaviour, as
well as the collective types of motion using Active Brownian particles
including chemotaxis and velocity alignment. We
compare analytical results for macroscopic pattern formation obtained from the overdamped limit approximation with numerical simulations
and discuss the microscopic and collective dynamics of our model. ********************************** Selfmoving
droplet powered by chemical energy Yutaka Sumino In
oilwatersurfactant systems, there appears the difference of the chemical potential
of a surfactant in oil and aqueous phases by introducing appropriate initial
distribution of the surfactant. In systems far from equilibrium it is possible
to generate macroscopically ordered self motion from the microscopic flow of a
surfactant through the interface. This conversion is realized by such as
wetting, Marangoni effect, and generation of elastic
phase. These self motions are particularly interesting because they can be
considered as the energy transduction of chemical energy into mechanical energy
in the isothermal condition, whose mechanism is different from conventional
thermal engines. In this presentation, we will present the various selfmotions
of droplets. 1)
We report the emergence of regular spontaneous motion of an oil droplet in the
oilwatersurfactant system, composed of an organic phase with potassium iodide
and iodine and an aqueous phase containing stearyl trimethyl ammonium chloride (STAC). This self motion is
using the change in the wetting condition of the oil droplet and a substrate
[1, 2]. 2)
We will also show the spontaneous motion in a twophase system of an alcohol (pentanol) and water. Here the self motion is induced by the
Marangoni flow generated on airwater interface. It
is found that the spontaneous motion of an alcohol droplet changes markedly
depending on the size of the droplet, and that regular motion is generated for
suitable rage of the volume. Such a trend is discussed in relation to the
instability of certain wave number, which is crucially dependent on the droplet
size [3]. 3)
Finally, we will briefly talk about the spontaneous deformation of an oil
droplet floating on an aqueous phase. It is found that the system is generating
the elastic phase as it approaches its equilibrium. Interestingly, the thickness
of the generated elastic phase becomes spatially inhomogeneous and as a result
the droplet starts to deform like living cells [4]. [1]
Y. Sumino, N. Magome, T. Hamada and K. Yoshikawa,
Phys. Rev. Lett., 94, 068301 (2005) [2]
Y. Sumino, et. al. Phys. Rev.
E, 72, 041603 (2005) [3]
K. Nagai, Y. Sumino, H. Kitahata and K. Yoshikawa,
Phys. Rev. E, 71, 065301 (2005) [4]
Y. Sumino, H. Kitahata, H. Seto
and K. Yoshikawa, submitting ********************************** Velocity
dependence of the phase transition in the Scalar Noise Model of SelfPropelled
Particles in 2D and 3D Balázs Gönci, Máté Nagy & Tamás Vicsek We
study the nature of phase transition of flocking using the scalar noise model
(SNM). We find that the behaviour of the model is similar
in two and threedimensions in many aspects. For small particle velocities (v
<= 0.1, which is an assumption of the original model), a second order,
continuous disorderorder phase transition occurs. Increasing
the particle velocities the phase transition changes to first order. In
addition, for these velocities we found that an artificial symmetry breaking
occurs in the average movement direction of the particles accompanied by the
emergence of density waves, which are caused by the anisotropic diffusion of
particles and the periodic boundary conditions. ********************************** Rheological and
structural properties of active filament solutions Falko Ziebert
& Igor S. Aronson The
rheology and the structure of a semiflexible
biofilament solution, like Factin,
interacting via molecular motors is probed by
molecular dynamics simulations. Oscillatory external shear is used to measure
the storage and loss moduli as a function of motor
activity in a range of frequencies and for low shear rates. The overall effect
of the motor activity on the rheological properties
is interpreted as an increase of the temperature, with the effective
temperature proportional to the density of motors. However, the effect of
motors on the structural properties of the solution, such as the orientation
correlation function, is opposite: the motors drastically increase the
orientation correlation length whereas thermal fluctuations decrease it. [Back] 