3,925 research outputs found
The Two-Point Function and the Effective Magnetic Field in Diluted Ising Models on the Cayley Tree
Some results on the two-point function and on the analytic structure of the
momenta of the effective fugacity at the origin for a class of diluted
ferromagnetic Ising models on the Cayley tree are presented.Comment: 22 page
Contractile stresses in cohesive cell layers on finite-thickness substrates
Using a minimal model of cells or cohesive cell layers as continuum active
elastic media, we examine the effect of substrate thickness and stiffness on
traction forces exerted by strongly adhering cells. We obtain a simple
expression for the length scale controlling the spatial variation of stresses
in terms of cell and substrate parameters that describes the crossover between
the thin and thick substrate limits. Our model is an important step towards a
unified theoretical description of the dependence of traction forces on cell or
colony size, acto-myosin contractility, substrate depth and stiffness, and
strength of focal adhesions, and makes experimentally testable predictions.Comment: 5 pages, 3 figure
Pattern formation in self-propelled particles with density-dependent motility
We study the behaviour of interacting self-propelled particles, whose
self-propulsion speed decreases with their local density. By combining direct
simulations of the microscopic model with an analysis of the hydrodynamic
equations obtained by explicitly coarse graining the model, we show that
interactions lead generically to the formation of a host of patterns, including
moving clumps, active lanes and asters. This general mechanism could explain
many of the patterns seen in recent experiments and simulations
Translational Correlations in the Vortex Array at the Surface of a Type-II Superconductor
We discuss the statistical mechanics of magnetic flux lines in a
finite-thickness slab of type-II superconductor. The long wavelength properties
of a flux-line liquid in a slab geometry are described by a hydrodynamic free
energy that incorporates the boundary conditions on the flux lines at the
sample's surface as a surface contribution to the free energy. Bulk and surface
weak disorder are modeled via Gaussian impurity potentials. This free energy is
used to evaluate the two-dimensional structure factor of the flux-line tips at
the sample surface. We find that surface interaction always dominates in
determining the decay of translational correlations in the asymptotic
long-wavelength limit. On the other hand, such large length scales have not
been probed by the decoration experiments. Our results indicate that the
translational correlations extracted from the analysis of the Bitter patterns
are indeed representative of behavior of flux lines in the bulk.Comment: 23 pages, 1 figure (not included), harvmac.tex macro needed (e-mail
requests to [email protected] SU-CM-92-01
Models of plastic depinning of driven disordered systems
Two classes of models of driven disordered systems that exhibit
history-dependent dynamics are discussed. The first class incorporates local
inertia in the dynamics via nonmonotonic stress transfer between adjacent
degrees of freedom. The second class allows for proliferation of topological
defects due to the interplay of strong disorder and drive. In mean field theory
both models exhibit a tricritical point as a function of disorder strength. At
weak disorder depinning is continuous and the sliding state is unique. At
strong disorder depinning is discontinuous and hysteretic.Comment: 3 figures, invited talk at StatPhys 2
Spontaneous rotating vortex rings in a parametrically driven polariton fluid
We present the theoretical prediction of spontaneous rotating vortex rings in
a parametrically driven quantum fluid of polaritons -- coherent superpositions
of coupled quantum well excitons and microcavity photons. These rings arise not
only in the absence of any rotating drive, but also in the absence of a
trapping potential, in a model known to map quantitatively to experiments. We
begin by proposing a novel parametric pumping scheme for polaritons, with
circular symmetry and radial currents, and characterize the resulting
nonequilibrium condensate. We show that the system is unstable to spontaneous
breaking of circular symmetry via a modulational instability, following which a
vortex ring with large net angular momentum emerges, rotating in one of two
topologically distinct states. Such rings are robust and carry distinctive
experimental signatures, and so they could find applications in the new
generation of polaritonic devices.Comment: 6 pages, 4 figure
Nematic and Polar order in Active Filament Solutions
Using a microscopic model of interacting polar biofilaments and motor
proteins, we characterize the phase diagram of both homogeneous and
inhomogeneous states in terms of experimental parameters. The polarity of motor
clusters is key in determining the organization of the filaments in homogeneous
isotropic, polarized and nematic states, while motor-induced bundling yields
spatially inhomogeneous structures.Comment: 4 pages. 3 figure
Bridging the microscopic and the hydrodynamic in active filament solutions
Hydrodynamic equations for an isotropic solution of active polar filaments
are derived from a microscopic mean-field model of the forces exchanged between
motors and filaments. We find that a spatial dependence of the motor stepping
rate along the filament is essential to drive bundle formation. A number of
differences arise as compared to hydrodynamics derived (earlier) from a
mesoscopic model where relative filament velocities were obtained on the basis
of symmetry considerations. Due to the anisotropy of filament diffusion, motors
are capable of generating net filament motion relative to the solvent. The
effect of this new term on the stability of the homogeneous state is
investigated.Comment: 7 pages, 2 figures, submitted to Europhys. Let
Rheology of Active Filament Solutions
We study the viscoelasticity of an active solution of polar biofilaments and
motor proteins. Using a molecular model, we derive the constitutive equations
for the stress tensor in the isotropic phase and in phases with liquid
crystalline order. The stress relaxation in the various phases is discussed.
Contractile activity is responsible for a spectacular difference in the
viscoelastic properties on opposite sides of the order-disorder transition.Comment: 4 pages, 1 figur
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