24,129 research outputs found
Renormalization of Drift and Diffusivity in Random Gradient Flows
We investigate the relationship between the effective diffusivity and
effective drift of a particle moving in a random medium. The velocity of the
particle combines a white noise diffusion process with a local drift term that
depends linearly on the gradient of a gaussian random field with homogeneous
statistics. The theoretical analysis is confirmed by numerical simulation. For
the purely isotropic case the simulation, which measures the effective drift
directly in a constant gradient background field, confirms the result
previously obtained theoretically, that the effective diffusivity and effective
drift are renormalized by the same factor from their local values. For this
isotropic case we provide an intuitive explanation, based on a {\it spatial}
average of local drift, for the renormalization of the effective drift
parameter relative to its local value. We also investigate situations in which
the isotropy is broken by the tensorial relationship of the local drift to the
gradient of the random field. We find that the numerical simulation confirms a
relatively simple renormalization group calculation for the effective
diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep
Effective diffusion constant in a two dimensional medium of charged point scatterers
We obtain exact results for the effective diffusion constant of a two
dimensional Langevin tracer particle in the force field generated by charged
point scatterers with quenched positions. We show that if the point scatterers
have a screened Coulomb (Yukawa) potential and are uniformly and independently
distributed then the effective diffusion constant obeys the
Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained
for pure Coulomb scatterers frozen in an equilibrium configuration of the same
temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure
Spin-Dependent Neutralino-Nucleus Scattering for Nuclei
We perform nuclear shell model calculations of the neutralino-nucleus cross
section for several nuclei in the A = 127 region. Each of the four nuclei
considered is a primary target in a direct dark matter detection experiment.
The calculations are valid for all relevant values of the momentum transfer.
Our calculations are performed in the model space
using extremely large bases, allowing us to include all relevant correlations.
We also study the dependence of the nuclear response upon the assumed nuclear
Hamiltonian and find it to be small. We find good agreement with the observed
magnetic moment as well as other obervables for the four nuclei considered:
^{127}I, ^{129,131}Xe, and ^{125}Te.Comment: 23 pages + 7 postscript figures. LaTeX uses RevTe
Path integrals for stiff polymers applied to membrane physics
Path integrals similar to those describing stiff polymers arise in the
Helfrich model for membranes. We show how these types of path integrals can be
evaluated and apply our results to study the thermodynamics of a minority
stripe phase in a bulk membrane. The fluctuation induced contribution to the
line tension between the stripe and the bulk phase is computed, as well as the
effective interaction between the two phases in the tensionless case where the
two phases have differing bending rigidities.Comment: 11 pages RevTex, 4 figure
Some observations on the renormalization of membrane rigidity by long-range interactions
We consider the renormalization of the bending and Gaussian rigidity of model
membranes induced by long-range interactions between the components making up
the membrane. In particular we analyze the effect of a finite membrane
thickness on the renormalization of the bending and Gaussian rigidity by
long-range interactions. Particular attention is paid to the case where the
interactions are of a van der Waals type.Comment: 11 pages RexTex, no figure
Dynamical transition for a particle in a squared Gaussian potential
We study the problem of a Brownian particle diffusing in finite dimensions in
a potential given by where is Gaussian random field.
Exact results for the diffusion constant in the high temperature phase are
given in one and two dimensions and it is shown to vanish in a power-law
fashion at the dynamical transition temperature. Our results are confronted
with numerical simulations where the Gaussian field is constructed, in a
standard way, as a sum over random Fourier modes. We show that when the number
of Fourier modes is finite the low temperature diffusion constant becomes
non-zero and has an Arrhenius form. Thus we have a simple model with a fully
understood finite size scaling theory for the dynamical transition. In addition
we analyse the nature of the anomalous diffusion in the low temperature regime
and show that the anomalous exponent agrees with that predicted by a trap
model.Comment: 18 pages, 4 figures .eps, JPA styl
Diffusion of active tracers in fluctuating fields
The problem of a particle diffusion in a fluctuating scalar field is studied.
In contrast to most studies of advection diffusion in random fields we analyze
the case where the particle position is also coupled to the dynamics of the
field. Physical realizations of this problem are numerous and range from the
diffusion of proteins in fluctuating membranes and the diffusion of localized
magnetic fields in spin systems. We present exact results for the diffusion
constant of particles diffusing in dynamical Gaussian fields in the adiabatic
limit where the field evolution is much faster than the particle diffusion. In
addition we compute the diffusion constant perturbatively, in the weak coupling
limit where the interaction of the particle with the field is small, using a
Kubo-type relation. Finally we construct a simple toy model which can be solved
exactly.Comment: 13 pages, 1 figur
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