1,315 research outputs found
Exact Multifractal Spectra for Arbitrary Laplacian Random Walks
Iterated conformal mappings are used to obtain exact multifractal spectra of
the harmonic measure for arbitrary Laplacian random walks in two dimensions.
Separate spectra are found to describe scaling of the growth measure in time,
of the measure near the growth tip, and of the measure away from the growth
tip. The spectra away from the tip coincide with those of conformally invariant
equilibrium systems with arbitrary central charge , with related
to the particular walk chosen, while the scaling in time and near the tip
cannot be obtained from the equilibrium properties.Comment: 4 pages, 3 figures; references added, minor correction
Multifractal Dimensions for Branched Growth
A recently proposed theory for diffusion-limited aggregation (DLA), which
models this system as a random branched growth process, is reviewed. Like DLA,
this process is stochastic, and ensemble averaging is needed in order to define
multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys.
Rev. A46, 7793 (1992)], annealed average dimensions were computed for this
model. In this paper, we compute the quenched average dimensions, which are
expected to apply to typical members of the ensemble. We develop a perturbative
expansion for the average of the logarithm of the multifractal partition
function; the leading and sub-leading divergent terms in this expansion are
then resummed to all orders. The result is that in the limit where the number
of particles n -> \infty, the quenched and annealed dimensions are {\it
identical}; however, the attainment of this limit requires enormous values of
n. At smaller, more realistic values of n, the apparent quenched dimensions
differ from the annealed dimensions. We interpret these results to mean that
while multifractality as an ensemble property of random branched growth (and
hence of DLA) is quite robust, it subtly fails for typical members of the
ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl
Investigation of the preparation of materials in space. Task 4 - Field management for weightless containerless processing Quarterly progress report, 22 Aug. - 31 Oct. 1969
Weightless containerless processing for space, electromagnetic position control, force measurements and techniques, and hydrodynamic
Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the DLA Model
We show that the fractal growth described by the dielectric breakdown model
exhibits a phase transition in the multifractal spectrum of the growth measure.
The transition takes place because the tip-splitting of branches forms a fixed
angle. This angle is eta dependent but it can be rescaled onto an
``effectively'' universal angle of the DLA branching process. We derive an
analytic rescaling relation which is in agreement with numerical simulations.
The dimension of the clusters decreases linearly with the angle and the growth
becomes non-fractal at an angle close to 74 degrees (which corresponds to eta=
4.0 +- 0.3).Comment: 4 pages, REVTex, 3 figure
Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis
We compare different partitioning schemes for the box-counting algorithm in
the multifractal analysis by computing the singularity spectrum and the
distribution of the box probabilities. As model system we use the Anderson
model of localization in two and three dimensions. We show that a partitioning
scheme which includes unrestricted values of the box size and an average over
all box origins leads to smaller error bounds than the standard method using
only integer ratios of the linear system size and the box size which was found
by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most
reliable results.Comment: 10 pages, 13 figure
On the kinks and dynamical phase transitions of alpha-helix protein chains
Heuristic insights into a physical picture of Davydov's solitonic model of
the one-dimensional protein chain are presented supporting the idea of a
non-equilibrium competition between the Davydov phase and a complementary,
dynamical- `ferroelectric' phase along the chainComment: small latex file with possible glue problems, just go on !, no
figures, small corrections with respect to the published text, follow-up work
to cond-mat/9304034 [PRE 47 (June 1993) R3818
Conformal Mapping on Rough Boundaries I: Applications to harmonic problems
The aim of this study is to analyze the properties of harmonic fields in the
vicinity of rough boundaries where either a constant potential or a zero flux
is imposed, while a constant field is prescribed at an infinite distance from
this boundary. We introduce a conformal mapping technique that is tailored to
this problem in two dimensions. An efficient algorithm is introduced to compute
the conformal map for arbitrarily chosen boundaries. Harmonic fields can then
simply be read from the conformal map. We discuss applications to "equivalent"
smooth interfaces. We study the correlations between the topography and the
field at the surface. Finally we apply the conformal map to the computation of
inhomogeneous harmonic fields such as the derivation of Green function for
localized flux on the surface of a rough boundary
How Sandcastles Fall
Capillary forces significantly affect the stability of sandpiles. We analyze
the stability of sandpiles with such forces, and find that the critical angle
is unchanged in the limit of an infinitely large system; however, this angle is
increased for finite-sized systems. The failure occurs in the bulk of the
sandpile rather than at the surface. This is related to a standard result in
soil mechanics. The increase in the critical angle is determined by the surface
roughness of the particles, and exhibits three regimes as a function of the
added-fluid volume. Our theory is in qualitative agreement with the recent
experimental results of Hornbaker et al., although not with the interpretation
they make of these results.Comment: 4 pages, 2 figures, revte
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Altering phytoplankton growth rates changes their value as food for microzooplankton grazers
When microzooplankton graze phytoplankton prey, the consumed carbon is partitioned into particulates, dissolved organic carbon (DOC), and CO2. Allocation of prey carbon to these various fates has important consequences for marine ecosystem function. A 2-stage continuous culture system was used to investigate carbon allocation by microzooplankton consuming phytoplankton grown in chemostats at controlled, nutrient-limited growth rates. The chemical composition of Dunaliella tertiolecta and Thalassiosira pseudonana cells varied with growth rate. When a constant amount of prey carbon was fed to the dinoflagellate Oxyrrhis marina, the carbon transfer efficiency to particulates (CTE) decreased from 27 +/- 5% when fast-growing T. pseudonana cells were the prey to only 3 +/- 2% when slow-growing cells were the prey. DOC did not increase with decreasing CTE, indicating that an increase in CO2 remineralization caused the lower CTE when the slow-growing cells were consumed. A similar pattern was observed when D. tertiolecta was the prey, but CTE was higher: 42 +/- 15% for fast-growing cells, declining to 17 +/- 6% for slow-growing prey cells. The microzooplankter showed greater neutral lipid accumulation when fed D. tertiolecta; however, its neutral lipid content did not necessarily mirror that of its phytoplankton prey and varied substantially across treatments. These findings demonstrate that microzooplankton respond strongly to food qualities of prey cells that are influenced by growth rate. We conclude that a significant and variable portion of primary production is lost from ecosystems because microzooplankton CTE is strongly influenced by the impacts of nutrient limitation on prey growth rates
Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at without Doubling
Random bond Hamiltonians of the flux state on the square lattice are
investigated. It has a special symmetry and all states are paired except the
ones with zero energy. Because of this, there are always zero-modes. The states
near are described by massless Dirac fermions. For the zero-mode, we can
construct a random lattice fermion without a doubling and quite large systems (
up to ) are treated numerically. We clearly demonstrate that
the zero-mode is given by a critical wave function. Its multifractal behavior
is also compared with the effective field theory.Comment: 4 pages, 2 postscript figure
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