710 research outputs found
Optimal paths on the road network as directed polymers
We analyze the statistics of the shortest and fastest paths on the road
network between randomly sampled end points. To a good approximation, these
optimal paths are found to be directed in that their lengths (at large scales)
are linearly proportional to the absolute distance between them. This motivates
comparisons to universal features of directed polymers in random media. There
are similarities in scalings of fluctuations in length/time and transverse
wanderings, but also important distinctions in the scaling exponents, likely
due to long-range correlations in geographic and man-made features. At short
scales the optimal paths are not directed due to circuitous excursions governed
by a fat-tailed (power-law) probability distribution.Comment: 5 pages, 7 figure
First Passage Distributions in a Collective Model of Anomalous Diffusion with Tunable Exponent
We consider a model system in which anomalous diffusion is generated by
superposition of underlying linear modes with a broad range of relaxation
times. In the language of Gaussian polymers, our model corresponds to Rouse
(Fourier) modes whose friction coefficients scale as wavenumber to the power
. A single (tagged) monomer then executes subdiffusion over a broad range
of time scales, and its mean square displacement increases as with
. To demonstrate non-trivial aspects of the model, we numerically
study the absorption of the tagged particle in one dimension near an absorbing
boundary or in the interval between two such boundaries. We obtain absorption
probability densities as a function of time, as well as the position-dependent
distribution for unabsorbed particles, at several values of . Each of
these properties has features characterized by exponents that depend on
. Characteristic distributions found for different values of
have similar qualitative features, but are not simply related quantitatively.
Comparison of the motion of translocation coordinate of a polymer moving
through a pore in a membrane with the diffusing tagged monomer with identical
also reveals quantitative differences.Comment: LaTeX, 10 pages, 8 eps figure
Passive Sliders on Growing Surfaces and (anti-)Advection in Burger's Flows
We study the fluctuations of particles sliding on a stochastically growing
surface. This problem can be mapped to motion of passive scalars in a randomly
stirred Burger's flow. Renormalization group studies, simulations, and scaling
arguments in one dimension, suggest a rich set of phenomena: If particles slide
with the avalanche of growth sites (advection with the fluid), they tend to
cluster and follow the surface dynamics. However, for particles sliding against
the avalanche (anti-advection), we find slower diffusion dynamics, and density
fluctuations with no simple relation to the underlying fluid, possibly with
continuously varying exponents.Comment: 4 pages revtex
Renormalization and Hyperscaling for Self-Avoiding Manifold Models
The renormalizability of the self-avoiding manifold (SAM) Edwards model is
established. We use a new short distance multilocal operator product expansion
(MOPE), which extends methods of local field theories to a large class of
models with non-local singular interactions. This validates the direct
renormalization method introduced before, as well as scaling laws. A new
general hyperscaling relation for the configuration exponent gamma is derived.
Manifolds at the Theta-point, and long range Coulomb interactions are briefly
discussed.Comment: 10 pages + 1 figure, TeX + harvmac & epsf (uuencoded file),
SPhT/93-07
Constraints on stable equilibria with fluctuation-induced forces
We examine whether fluctuation-induced forces can lead to stable levitation.
First, we analyze a collection of classical objects at finite temperature that
contain fixed and mobile charges, and show that any arrangement in space is
unstable to small perturbations in position. This extends Earnshaw's theorem
for electrostatics by including thermal fluctuations of internal charges.
Quantum fluctuations of the electromagnetic field are responsible for
Casimir/van der Waals interactions. Neglecting permeabilities, we find that any
equilibrium position of items subject to such forces is also unstable if the
permittivities of all objects are higher or lower than that of the enveloping
medium; the former being the generic case for ordinary materials in vacuum.Comment: 4 pages, 1 figur
Adsorption of polymers on a fluctuating surface
We study the adsorption of polymer chains on a fluctuating surface. Physical
examples are provided by polymer adsorption at the rough interface between two
non-miscible liquids, or on a membrane. In a mean-field approach, we find that
the self--avoiding chains undergo an adsorption transition, accompanied by a
stiffening of the fluctuating surface. In particular, adsorption of polymers on
a membrane induces a surface tension and leads to a strong suppression of
roughness.Comment: REVTEX, 9 pages, no figure
Energy Barriers to Motion of Flux Lines in Random Media
We propose algorithms for determining both lower and upper bounds for the
energy barriers encountered by a flux line in moving through a two-dimensional
random potential. Analytical arguments, supported by numerical simulations,
suggest that these bounds scale with the length of the line as
and , respectively. This provides the first confirmation
of the hypothesis that barriers have the same scaling as the fluctuation in the
free energy. \pacs{PACS numbers: 74.60.Ge, 05.70.Ln, 05.40.+j}Comment: 4 pages Revtex, 2 figures, to appear in PRL 75, 1170 (1995
Phases of Josephson Junction Ladders
We study a Josephson junction ladder in a magnetic field in the absence of
charging effects via a transfer matrix formalism. The eigenvalues of the
transfer matrix are found numerically, giving a determination of the different
phases of the ladder. The spatial periodicity of the ground state exhibits a
devil's staircase as a function of the magnetic flux filling factor . If the
transverse Josephson coupling is varied a continuous superconducting-normal
transition in the transverse direction is observed, analogous to the breakdown
of the KAM trajectories in dynamical systems.Comment: 12 pages with 3 figures, REVTE
Universal and non-universal tails of distribution functions in the directed polymer and KPZ problems
The optimal fluctuation approach is applied to study the most distant
(non-universal) tails of the free-energy distribution function P(F) for an
elastic string (of a large but finite length L) interacting with a quenched
random potential. A further modification of this approach is proposed which
takes into account the renormalization effects and allows one to study the most
close (universal) parts of the tails. The problem is analyzed for different
dimensions of a space in which the polymer is imbedded. In terms the stochastic
growth problem, the same distribution function describes the distribution of
heights in the regime of a non-stationary growth in a situation when an
interface starts to grow from a flat configuration.Comment: 17 pages, 2 figures, the final version, two paragraphs added to the
conclusio
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