16,345 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
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
Perturbation theory for the effective diffusion constant in a medium of random scatterer
We develop perturbation theory and physically motivated resummations of the
perturbation theory for the problem of a tracer particle diffusing in a random
media. The random media contains point scatterers of density uniformly
distributed through out the material. The tracer is a Langevin particle
subjected to the quenched random force generated by the scatterers. Via our
perturbative analysis we determine when the random potential can be
approximated by a Gaussian random potential. We also develop a self-similar
renormalisation group approach based on thinning out the scatterers, this
scheme is similar to that used with success for diffusion in Gaussian random
potentials and agrees with known exact results. To assess the accuracy of this
approximation scheme its predictions are confronted with results obtained by
numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style
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
Experimental and analytical study of thermal acoustic oscillations
The thermal acoustic oscillations (TAO) data base was expanded by running a large number of tubes over a wide range of parameters known to affect the TAO phenomenon. These parameters include tube length, wall thickness, diameter, material, insertion length and length-to-diameter ratio. Emphasis was placed on getting good boiloff data. A large quantity of data was obtained, reduced, correlated and analyzed and is presented. Also presented are comparisons with previous types of correlations. These comparisons show that the boiloff data did not correlate with intensity. The data did correlate in the form used by Rott, that is boiloff versus TAO pressure squared times frequency to the one-half power. However, this latter correlation required a different set of correlation constants, slope and intercept, for each tube tested
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
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
Thermal Casimir drag in fluctuating classical fields
A uniformly moving inclusion which locally suppresses the fluctuations of a
classical thermally excited field is shown to experience a drag force which
depends on the dynamics of the field. It is shown that in a number of cases the
linear friction coefficient is dominated by short distance fluctuations and
takes a very simple form. Examples where this drag can occur are for stiff
objects, such as proteins, nonspecifically bound to more flexible ones such as
polymers and membranes.Comment: 4 pages RevTex, 2 figure
Continuum Derrida Approach to Drift and Diffusivity in Random Media
By means of rather general arguments, based on an approach due to Derrida
that makes use of samples of finite size, we analyse the effective diffusivity
and drift tensors in certain types of random medium in which the motion of the
particles is controlled by molecular diffusion and a local flow field with
known statistical properties. The power of the Derrida method is that it uses
the equilibrium probability distribution, that exists for each {\em finite}
sample, to compute asymptotic behaviour at large times in the {\em infinite}
medium. In certain cases, where this equilibrium situation is associated with a
vanishing microcurrent, our results demonstrate the equality of the
renormalization processes for the effective drift and diffusivity tensors. This
establishes, for those cases, a Ward identity previously verified only to
two-loop order in perturbation theory in certain models. The technique can be
applied also to media in which the diffusivity exhibits spatial fluctuations.
We derive a simple relationship between the effective diffusivity in this case
and that for an associated gradient drift problem that provides an interesting
constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8
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