229,568 research outputs found
Explicit predictability and dispersion scaling exponents in fully developed turbulence
We apply a simple method to provide explicit expressions for different
scaling exponents in intermittent fully developed turbulence, that before were
only given through a Legendre transform. This includes predictability exponents
for infinitesimal and non infinitesimal perturbations, Lagrangian velocity
exponents, and dispersion exponents. We obtain also new results concerning
inverse statistics corresponding to exit-time moments.Comment: Physics Letters A (in press
Values of Brownian intersection exponents III: Two-sided exponents
This paper determines values of intersection exponents between packs of
planar Brownian motions in the half-plane and in the plane that were not
derived in our first two papers. For instance, it is proven that the exponent
describing the asymptotic decay of the probability of
non-intersection between two packs of three independent planar Brownian motions
each is . More generally, the values of and \tx (w_1', ..., w_k') are determined for all ,
, and all
. The proof relies on the results derived in our
first two papers and applies the same general methods. We first find the
two-sided exponents for the stochastic Loewner evolution processes in a
half-plane, from which the Brownian intersection exponents are determined via a
universality argument
Critical exponents in zero dimensions
In the vicinity of the onset of an instability, we investigate the effect of
colored multiplicative noise on the scaling of the moments of the unstable mode
amplitude. We introduce a family of zero dimensional models for which we can
calculate the exact value of the critical exponents for all the
moments. The results are obtained through asymptotic expansions that use the
distance to onset as a small parameter. The examined family displays a variety
of behaviors of the critical exponents that includes anomalous exponents:
exponents that differ from the deterministic (mean-field) prediction, and
multiscaling: non-linear dependence of the exponents on the order of the
moment
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