228 research outputs found
A note on maximal estimates for stochastic convolutions
In stochastic partial differential equations it is important to have pathwise
regularity properties of stochastic convolutions. In this note we present a new
sufficient condition for the pathwise continuity of stochastic convolutions in
Banach spaces.Comment: Minor correction
Anomalous diffusion in polymers: long-time behaviour
We study the Dirichlet boundary value problem for viscoelastic diffusion in
polymers. We show that its weak solutions generate a dissipative semiflow. We
construct the minimal trajectory attractor and the global attractor for this
problem.Comment: 13 page
Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
We use the zero-temperature random-field Ising model to study hysteretic
behavior at first-order phase transitions. Sweeping the external field through
zero, the model exhibits hysteresis, the return-point memory effect, and
avalanche fluctuations. There is a critical value of disorder at which a jump
in the magnetization (corresponding to an infinite avalanche) first occurs. We
study the universal behavior at this critical point using mean-field theory,
and also present preliminary results of numerical simulations in three
dimensions.Comment: 12 pages plus 2 appended figures, plain TeX, CU-MSC-747
A Brownian motion version of the directed polymer problem
Consider a Brownian particle in three dimensions in a random environment. The environment is determined by a potential random in space and time. It is shown that at small noise the large-time behavior of the particle is diffusive. The diffusion constant depends on the environment. This work generalizes previous results for random walk in a random environment. In these results the diffusion constant does not depend on the environment.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45170/1/10955_2005_Article_BF02179650.pd
Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach
We study the zero temperature random field Ising model as a model for noise
and avalanches in hysteretic systems. Tuning the amount of disorder in the
system, we find an ordinary critical point with avalanches on all length
scales. Using a mapping to the pure Ising model, we Borel sum the
expansion to for the correlation length exponent. We sketch a
new method for directly calculating avalanche exponents, which we perform to
. Numerical exponents in 3, 4, and 5 dimensions are in good
agreement with the analytical predictions.Comment: 134 pages in REVTEX, plus 21 figures. The first two figures can be
obtained from the references quoted in their respective figure captions, the
remaining 19 figures are supplied separately in uuencoded forma
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