1,227 research outputs found
Diffusion-limited aggregation as branched growth
I present a first-principles theory of diffusion-limited aggregation in two
dimensions. A renormalized mean-field approximation gives the form of the
unstable manifold for branch competition, following the method of Halsey and
Leibig [Phys. Rev. A {\bf 46}, 7793 (1992)]. This leads to a result for the
cluster dimensionality, D \approx 1.66, which is close to numerically obtained
values. In addition, the multifractal exponent \tau(3) = D in this theory, in
agreement with a proposed `electrostatic' scaling law.Comment: 13 pages, one figure not included (available by request, by ordinary
mail), Plain Te
Effect of weak disorder in the Fully Frustrated XY model
The critical behaviour of the Fully Frustrated XY model in presence of weak
positional disorder is studied in a square lattice by Monte Carlo methods. The
critical exponent associated to the divergence of the chiral correlation length
is found to be equal to 1.7 already at very small values of disorder.
Furthermore the helicity modulus jump is found larger than the universal value
expected in the XY model.Comment: 8 pages, 4 figures (revtex
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
Effects of BMI on bone loading due to physical activity
The aim of the current study was to compare bone loading due to physical activity between lean and, overweight and obese individuals. Fifteen participants (lower BMI group: BMI<25 kg/m2, n=7; higher BMI group: 25 kg/m2 < BMI < 36.35 kg/m2, n=8) wore a tri-axial accelerometer on one day to collect data for the calculation of bone loading. The International Physical Activity Questionnaire (short form) was used to measure time spent at different physical activity levels. Daily step counts were measured using a pedometer. Differences between groups were compared using independent t-tests. Accelerometer data revealed greater loading dose at the hip in lower BMI participants at a frequency band of 0.1–2 Hz (P=.039, Cohen‘s d =1.27) and 2–4 Hz (P=.044, d =1.24). Lower BMI participants also had a significantly greater step count (P=.023, d =1.55). This corroborated with loading intensity (d ≥ 0.93) and questionnaire (d =0.79) effect sizes to indicate higher BMI participants tended to spend more time in very light, and less time in light and moderate activity. Overall participants with a lower BMI exhibited greater bone loading due to physical activity; participants with a higher BMI may benefit from more light and moderate level activity to maintain bone health.Kellogg’s Compan
Exact Multifractal Exponents for Two-Dimensional Percolation
The harmonic measure (or diffusion field or electrostatic potential) near a
percolation cluster in two dimensions is considered. Its moments, summed over
the accessible external hull, exhibit a multifractal spectrum, which I
calculate exactly. The generalized dimensions D(n) as well as the MF function
f(alpha) are derived from generalized conformal invariance, and are shown to be
identical to those of the harmonic measure on 2D random walks or self-avoiding
walks. An exact application to the anomalous impedance of a rough percolative
electrode is given. The numerical checks are excellent. Another set of exact
and universal multifractal exponents is obtained for n independent
self-avoiding walks anchored at the boundary of a percolation cluster. These
exponents describe the multifractal scaling behavior of the average nth moment
of the probabity for a SAW to escape from the random fractal boundary of a
percolation cluster in two dimensions.Comment: 5 pages, 3 figures (in colors
The branching structure of diffusion-limited aggregates
I analyze the topological structures generated by diffusion-limited
aggregation (DLA), using the recently developed "branched growth model". The
computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good
agreement with the numerically obtained result of B ~ 5.2. In high dimensions,
B -> 3.12; the bifurcation ratio is thus a decreasing function of
dimensionality. This analysis also determines the scaling properties of the
ramification matrix, which describes the hierarchy of branches.Comment: 6 pages, 1 figure, Euro-LaTeX styl
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
Quasiperiodic Modulated-Spring Model
We study the classical vibration problem of a chain with spring constants
which are modulated in a quasiperiodic manner, {\it i. e.}, a model in which
the elastic energy is , where and is an irrational number. For
, it is shown analytically that the spectrum is absolutely
continuous, {\it i.e.}, all the eigen modes are extended. For ,
numerical scaling analysis shows that the spectrum is purely singular
continuous, {\it i.e.}, all the modes are critical.Comment: REV TeX fil
Energetic Instability Unjams Sand and Suspension
Jamming is a phenomenon occurring in systems as diverse as traffic, colloidal
suspensions and granular materials. A theory on the reversible elastic
deformation of jammed states is presented. First, an explicit granular
stress-strain relation is derived that captures many relevant features of sand,
including especially the Coulomb yield surface and a third-order jamming
transition. Then this approach is generalized, and employed to consider jammed
magneto- and electro-rheological fluids, again producing results that compare
well to experiments and simulations.Comment: 9 pages 2 fi
Tip-splitting evolution in the idealized Saffman-Taylor problem
We derive a formula describing the evolution of tip-splittings of
Saffman-Taylor fingers in a Hele-Shaw cell, at zero surface tension
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