6,962 research outputs found
Quantum States Allowing Minimum Uncertainty Product of angular position and momentum
We provide necessary and sufficient conditions for states to have an
arbitrarily small uncertainty product of the azimuthal angle and its
canonical moment . We illustrate our results with analytical examples
Plasticity in current-driven vortex lattices
We present a theoretical analysis of recent experiments on current-driven
vortex dynamics in the Corbino disk geometry. This geometry introduces
controlled spatial gradients in the driving force and allows the study of the
onset of plasticity and tearing in clean vortex lattices. We describe plastic
slip in terms of the stress-driven unbinding of dislocation pairs, which in
turn contribute to the relaxation of the shear, yielding a nonlinear response.
The steady state density of free dislocations induced by the applied stress is
calculated as a function of the applied current and temperature. A criterion
for the onset of plasticity at a radial location in the disk yields a
temperature-dependent critical current that is in qualitative agreement with
experiments.Comment: 11 pages, 4 figure
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
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
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
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
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