371 research outputs found
A coalescence model for freely decaying two-dimensional turbulence
We propose a ballistic coalescence model (punctuated-Hamiltonian approach)
mimicking the fusion of vortices in freely decaying two-dimensional turbulence.
A temporal scaling behaviour is reached where the vortex density evolves like
. A mean-field analytical argument yielding the approximation
is shown to slightly overestimate the decay exponent whereas
Molecular Dynamics simulations give , in agreement with
recent laboratory experiments and simulations of Navier-Stokes equation.Comment: 6 pages, 1 figure, to appear in Europhysics Letter
Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
For a specific choice of the diffusion, the parabolic-elliptic
Patlak-Keller-Segel system with non-linear diffusion (also referred to as the
quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold
phenomenon: there is a critical mass such that all the solutions with
initial data of mass smaller or equal to exist globally while the
solution blows up in finite time for a large class of initial data with mass
greater than . Unlike in space dimension 2, finite mass self-similar
blowing-up solutions are shown to exist in space dimension
Numerical renormalization group of vortex aggregation in 2D decaying turbulence: the role of three-body interactions
In this paper, we introduce a numerical renormalization group procedure which
permits long-time simulations of vortex dynamics and coalescence in a 2D
turbulent decaying fluid. The number of vortices decreases as ,
with instead of the value predicted by a na\"{\i}ve
kinetic theory. For short time, we find an effective exponent
consistent with previous simulations and experiments. We show that the mean
square displacement of surviving vortices grows as .
Introducing effective dynamics for two-body and three-body collisions, we
justify that only the latter become relevant at small vortex area coverage. A
kinetic theory consistent with this mechanism leads to . We find that
the theoretical relations between kinetic parameters are all in good agreement
with experiments.Comment: 23 RevTex pages including 7 EPS figures. Submitted to Phys. Rev. E
(Some typos corrected; see also cond-mat/9911032
Topological correlations in soap froths
Correlation in two-dimensional soap froth is analysed with an effective
potential for the first time. Cells with equal number of sides repel (with
linear correlation) while cells with different number of sides attract (with
NON-bilinear) for nearest neighbours, which cannot be explained by the maximum
entropy argument. Also, the analysis indicates that froth is correlated up to
the third shell neighbours at least, contradicting the conventional ideas that
froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure
Analytical results for random walk persistence
In this paper, we present the detailed calculation of the persistence
exponent for a nearly-Markovian Gaussian process , a problem
initially introduced in [Phys. Rev. Lett. 77, 1420 (1996)], describing the
probability that the walker never crosses the origin. New resummed perturbative
and non-perturbative expressions for are obtained, which suggest a
connection with the result of the alternative independent interval
approximation (IIA). The perturbation theory is extended to the calculation of
for non-Gaussian processes, by making a strong connection between the
problem of persistence and the calculation of the energy eigenfunctions of a
quantum mechanical problem. Finally, we give perturbative and non-perturbative
expressions for the persistence exponent , describing the
probability that the process remains bigger than .Comment: 23 pages; accepted for publication to Phys. Rev. E (Dec. 98
Nontrivial Exponent for Simple Diffusion
The diffusion equation \partial_t\phi = \nabla^2\phi is considered, with
initial condition \phi( _x_ ,0) a gaussian random variable with zero mean.
Using a simple approximate theory we show that the probability p_n(t_1,t_2)
that \phi( _x_ ,t) [for a given space point _x_ ] changes sign n times between
t_1 and t_2 has the asymptotic form p_n(t_1,t_2) \sim
[\ln(t_2/t_1)]^n(t_1/t_2)^{-\theta}. The exponent \theta has predicted values
0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with
simulation results.Comment: Minor typos corrected, affecting table of exponents. 4 pages, REVTEX,
1 eps figure. Uses epsf.sty and multicol.st
A precise approximation for directed percolation in d=1+1
We introduce an approximation specific to a continuous model for directed
percolation, which is strictly equivalent to 1+1 dimensional directed bond
percolation. We find that the critical exponent associated to the order
parameter (percolation probability) is beta=(1-1/\sqrt{5})/2=0.276393202..., in
remarkable agreement with the best current numerical estimate beta=0.276486(8).Comment: 4 pages, 3 EPS figures; Submitted to Physical Review Letters v2:
minor typos + 1 major typo in Eq. (30) correcte
Effect of conduction electron interactions on Anderson impurities
The effect of conduction electron interactions for an Anderson impurity is
investigated in one dimension using a scaling approach. The flow diagrams are
obtained by solving the renormalization group equations numerically. It is
found that the Anderson impurity case is different from its counterpart -- the
Kondo impurity case even in the local moment region. The Kondo temperature for
an Anderson impurity shows nonmonotonous behavior, increasing for weak
interactions but decreasing for strong interactions. The implication of the
study to other related impurity models is also discussed.Comment: 10 pages, revtex, 4 figures (the postscript file is included), to
appear in Phys. Rev. B (Rapid Commun.
Spectrum and diffusion for a class of tight-binding models on hypercubes
We propose a class of exactly solvable anisotropic tight-binding models on an
infinite-dimensional hypercube. The energy spectrum is analytically computed
and is shown to be fractal and/or absolutely continuous according to the value
hopping parameters. In both cases, the spectral and diffusion exponents are
derived. The main result is that, even if the spectrum is absolutely
continuous, the diffusion exponent for the wave packet may be anything between
0 and 1 depending upon the class of models.Comment: 5 pages Late
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