26,008 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
Calculation of exciton densities in SMMC
We develop a shell-model Monte Carlo (SMMC) method to calculate densities of
states with varying exciton (particle-hole) number. We then apply this method
to the doubly closed-shell nucleus 40Ca in a full 0s-1d-0f-1p shell-model space
and compare our results to those found using approximate analytic expressions
for the partial densities. We find that the effective one-body level density is
reduced by approximately 22% when a residual two-body interaction is included
in the shell model calculation.Comment: 10 pages, 4 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
Tapping Thermodynamics of the One Dimensional Ising Model
We analyse the steady state regime of a one dimensional Ising model under a
tapping dynamics recently introduced by analogy with the dynamics of
mechanically perturbed granular media. The idea that the steady state regime
may be described by a flat measure over metastable states of fixed energy is
tested by comparing various steady state time averaged quantities in extensive
numerical simulations with the corresponding ensemble averages computed
analytically with this flat measure. The agreement between the two averages is
excellent in all the cases examined, showing that a static approach is capable
of predicting certain measurable properties of the steady state regime.Comment: 11 pages, 5 figure
Colocation and role of polyphosphates and alkaline phosphatase in apatite biomineralization of elasmobranch tesserae
AbstractElasmobranchs (e.g. sharks and rays), like all fishes, grow continuously throughout life. Unlike other vertebrates, their skeletons are primarily cartilaginous, comprising a hyaline cartilage-like core, stiffened by a thin outer array of mineralized, abutting and interconnected tiles called tesserae. Tesserae bear active mineralization fronts at all margins and the tesseral layer is thin enough to section without decalcifying, making this a tractable but largely unexamined system for investigating controlled apatite mineralization, while also offering a potential analog for endochondral ossification. The chemical mechanism for tesserae mineralization has not been described, but has been previously attributed to spherical precursors, and alkaline phosphatase (ALP) activity. Here, we use a variety of techniques to elucidate the involvement of phosphorus-containing precursors in the formation of tesserae at their mineralization fronts. Using Raman spectroscopy, fluorescence microscopy and histological methods, we demonstrate that ALP activity is located with inorganic phosphate polymers (polyP) at the tessera–uncalcified cartilage interface, suggesting a potential mechanism for regulated mineralization: inorganic phosphate (Pi) can be cleaved from polyP by ALP, thus making Pi locally available for apatite biomineralization. The application of exogenous ALP to tissue cross-sections resulted in the disappearance of polyP and the appearance of Pi in uncalcified cartilage adjacent to mineralization fronts. We propose that elasmobranch skeletal cells control apatite biomineralization by biochemically controlling polyP and ALP production, placement and activity. Previous identification of polyP and ALP shown previously in mammalian calcifying cartilage supports the hypothesis that this mechanism may be a general regulating feature in the mineralization of vertebrate skeletons
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
Shell Model Monte Carlo Methods
We review quantum Monte Carlo methods for dealing with large shell model
problems. These methods reduce the imaginary-time many-body evolution operator
to a coherent superposition of one-body evolutions in fluctuating one-body
fields; the resultant path integral is evaluated stochastically. We first
discuss the motivation, formalism, and implementation of such Shell Model Monte
Carlo (SMMC) methods. There then follows a sampler of results and insights
obtained from a number of applications. These include the ground state and
thermal properties of {\it pf}-shell nuclei, the thermal and rotational
behavior of rare-earth and -soft nuclei, and the calculation of double
beta-decay matrix elements. Finally, prospects for further progress in such
calculations are discussed
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
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
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