DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension D(s)=2. In kinematic simulations the exponent gamma in Richardson's law and the fractal dimension D(s) are related by gamma=6/D(s). The Richardson constant is found to be an increasing function of the number density of str...

We prove that, after removing a zero Hausdorff dimension exceptional set of parameters, all self-similar measures on the line have power decay Fourier transform at infinity. In homogeneous case, when contraction ratios are equal, this is essentially due to Erdős and Kahane. non-homogeneous case difficulty we overcome apparent lack convolution structure.

We study diffusion in heterogeneous multifractal continuous media that are characterized by the second-order dimension of the multifractal spectrum D2, while the fractal dimension of order 0, D0, is equal to the embedding Euclidean dimension 2. We find that the mean anomalous and fracton dimensions, d(w) and d(s), are equal to those of homogeneous media showing that, on average, the key paramet...

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to new non-trivial constraints. This fact has been used to conjecture that the resulting models correspond to the spatially hom...

A conjecture of Liggett [9] concerning the regime of weak survival for the contact process on a homogeneous tree is proved. The conjecture is shown to imply that the Hausdorff dimension of the limit set of such a contact process is no larger than half the Hausdorff dimension of the space of ends of the tree. The conjecture is also shown to imply that at the boundary between weak survival and st...

A quantum cellular automaton (QCA) is a discrete dynamical system with exactly unitary local evolution. Failure to find homogenous scalar QCAs in one dimension led to consideration of only “approximately unitary” CAs—until recently, when we proved both a No-go Lemma in one dimension and then showed how it may be evaded. In this note we extend the one dimensional result to prove the absence of n...