821 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
Crossing the threshold : an analysis of IBRD graduation policy
According to World Bank policy, countries remain eligible to borrow from the International Bank for Reconstruction and Development until they are able to sustain long-term development without further recourse to Bank financing. Graduation from the Bank is not an automatic consequence of reaching a particular income level, but rather is supposed to be based on a determination of whether the country has reached a level of institutional development and capital-market access that enables it to sustain its own development process without recourse to Bank funding. This paper assesses how International Bank for Reconstruction and Development graduation policy operates in practice, investigating what income and non-income factors appear to have influenced graduation decisions in recent decades, based on panel data for 1982 through 2008. Explanatory variables include the per-capita income of the country, as well as measures of institutional development and market access that are cited as criteria by the graduation policy, and other plausible explanatory variables that capture the levels of economic development and vulnerability of the country. The authors find that the observed correlates of Bank graduation are generally consistent with the stated policy. Countries that are wealthier, more creditworthy, more institutionally developed, and less vulnerable to shocks are more likely to have graduated. Predicted probabilities generated by the model correspond closely to the actual graduation and de-graduation experiences of most countries (such as Korea and Trinidad and Tobago), and suggest that Hungary and Latvia may have graduated prematurely -- a prediction consistent with their subsequent return to borrowing from the Bank in the wake of the global financial crisis.Economic Theory&Research,Emerging Markets,Banks&Banking Reform,Labor Policies,Debt Markets
Dynamic roughening and fluctuations of dipolar chains
Nonmagnetic particles in a carrier ferrofluid acquire an effective dipolar
moment when placed in an external magnetic field. This fact leads them to form
chains that will roughen due to Brownian motion when the magnetic field is
decreased. We study this process through experiments, theory and simulations,
three methods that agree on the scaling behavior over 5 orders of magnitude.
The RMS width goes initially as , then as before it
saturates. We show how these results complement existing results on polymer
chains, and how the chain dynamics may be described by a recent non-Markovian
formulation of anomalous diffusion.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
Two-Dimensional Copolymers and Exact Conformal Multifractality
We consider in two dimensions the most general star-shaped copolymer, mixing
random (RW) or self-avoiding walks (SAW) with specific interactions thereof.
Its exact bulk or boundary conformal scaling dimensions in the plane are all
derived from an algebraic structure existing on a random lattice (2D quantum
gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW
are conformal dimensions of certain star copolymers, here calculated exactly as
non rational algebraic numbers. The associated multifractal function f(alpha)
are found to be identical for a random walk or a SAW in 2D. These are the first
examples of exact conformal multifractality in two dimensions.Comment: 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January
199
Current-voltage scaling of a Josephson-junction array at irrational frustration
Numerical simulations of the current-voltage characteristics of an ordered
two-dimensional Josephson junction array at an irrational flux quantum per
plaquette are presented. The results are consistent with an scaling analysis
which assumes a zero temperature vortex glass transition. The thermal
correlation length exponent characterizing this transition is found to be
significantly different from the corresponding value for vortex-glass models in
disordered two-dimensional superconductors. This leads to a current scale where
nonlinearities appear in the current-voltage characteristics decreasing with
temperature roughly as in contrast with the behavior expected
for disordered models.Comment: RevTex 3.0, 12 pages with Latex figures, to appear in Phys. Rev. B
54, Rapid. Com
A Ball in a Groove
We study the static equilibrium of an elastic sphere held in a rigid groove
by gravity and frictional contacts, as determined by contact mechanics. As a
function of the opening angle of the groove and the tilt of the groove with
respect to the vertical, we identify two regimes of static equilibrium for the
ball. In the first of these, at large opening angle or low tilt, the ball rolls
at both contacts as it is loaded. This is an analog of the "elastic" regime in
the mechanics of granular media. At smaller opening angles or larger tilts, the
ball rolls at one contact and slides at the other as it is loaded, analogously
with the "plastic" regime in the mechanics of granular media. In the elastic
regime, the stress indeterminacy is resolved by the underlying kinetics of the
ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps
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
Renormalization Theory of Stochastic Growth
An analytical renormalization group treatment is presented of a model which,
for one value of parameters, is equivalent to diffusion limited aggregation.
The fractal dimension of DLA is computed to be 2-1/2+1/5=1.7. Higher
multifractal exponents are also calculated and found in agreement with
numerical results. It may be possible to use this technique to describe the
dielectric breakdown model as well, which is given by different parameter
values.Comment: 39 pages, LaTeX, 11 figure
Parallel Algorithm and Dynamic Exponent for Diffusion-limited Aggregation
A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described
and analyzed from the perspective of computational complexity. The dynamic
exponent z of the algorithm is defined with respect to the probabilistic
parallel random-access machine (PRAM) model of parallel computation according
to , where L is the cluster size, T is the running time, and the
algorithm uses a number of processors polynomial in L\@. It is argued that
z=D-D_2/2, where D is the fractal dimension and D_2 is the second generalized
dimension. Simulations of DLA are carried out to measure D_2 and to test
scaling assumptions employed in the complexity analysis of the parallel
algorithm. It is plausible that the parallel algorithm attains the minimum
possible value of the dynamic exponent in which case z characterizes the
intrinsic history dependence of DLA.Comment: 24 pages Revtex and 2 figures. A major improvement to the algorithm
and smaller dynamic exponent in this versio
Contemplative Science: An Insider's Prospectus
This chapter describes the potential far‐reaching consequences of contemplative higher education for the fields of science and medicine
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