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 $\xi (3,3)$ describing the asymptotic decay of the probability of non-intersection between two packs of three independent planar Brownian motions each is $(73-2 \sqrt {73}) / 12$. More generally, the values of $\xi (w_1, >..., w_k)$ and \tx (w_1', ..., w_k') are determined for all $k \ge 2$, $w_1, w_2\ge 1$, $w_3, ...,w_k\in[0,\infty)$ and all $w_1',...,w_k'\in[0,\infty)$. 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

Brownian Super-exponents

We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new exponential process is often merely a supermartingale even in cases where the original process is a martingale. We determine a necessary and sufficient condition for the transform to be a martingale process. The condition links expected values of the transformed stochastic exponential to the distribution function of certain time-integrals.Comment: 10 page

Depinning exponents of the driven long-range elastic string

We perform a high-precision calculation of the critical exponents for the long-range elastic string driven through quenched disorder at the depinning transition, at zero temperature. Large-scale simulations are used to avoid finite-size effects and to enable high precision. The roughness, growth, and velocity exponents are calculated independently, and the dynamic and correlation length exponents are derived. The critical exponents satisfy known scaling relations and agree well with analytical predictions.Comment: 6 pages, 5 figure