We present a simple stochastic algorithm for generating multiplicative processes with multiscaling both in space and in time. With this algorithm we are able to reproduce a synthetic signal with the same space and time correlation as the one coming from shell models for turbulence and the one coming from a turbulent velocity field in a quasi-Lagrangian reference frame. Corresponding author: Dr....

1 Istituto per le Applicazioni del Calcolo “M. Picone”, sede di Bari, Consiglio Nazionale delle Ricerche Via G. Amendola 122/D, I-70126 Bari, Italy 2Department of Computer Science, Stanford University, Gates Building 2B, Room 280, Stanford, CA 94305-9025, USA 3Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA 4Department of Electrical Engi...

Daniel B. Work1, Sébastien Blandin1, Olli-Pekka Tossavainen1, Benedetto Piccoli2,3, and Alexandre M. Bayen4 1Systems Engineering, Department of Civil and Environmental Engineering, University of California, Berkeley, 621 Sutardja Dai Hall #1758, Berkeley, CA, USA, 2Istituto per le Applicazioni del Calcolo ‘M. Picone.’ Via dei Taurini 19, Rome, Italy, 3Department of Mathematical Sciences and CCI...

We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we impose our criteria for the vorticity component is at the scaling invariant level. The proof requires a new decomposition of the four nonlinear terms making u...

This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical results that explain the relation between the different definitions. Additionally, results on the orthogonality of the decomposition, a Parsevaltype identity...