Related papers: Multiscaling in passive scalar advection as stocha…
Combining the stochastic and $\delta N$ formalisms, we derive non perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered…
We study models of quintessence consisting of a number of scalar fields coupled to several dark matter components. In the case of exponential potentials the scaling solutions can be described in terms of a single field. The corresponding…
We review some of the properties of higher-dimensional superstatistical stochastic models. As an example, we analyse the stochastic properties of a superstatistical model of 3-dimensional Lagrangian turbulence, and compare with experimental…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…
Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…
The stationary condition (Hopf equation) for the ($n$+1) point correlation function of a passive scalar advected by turbulent flow is argued to have an approximate $SL(n, R)$ symmetry which provides a starting point for the perturbative…
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution…
The spiraling of adjacent trajectories in chaotic dynamical systems can be characterized by distribution of local angular velocities of rotation of the displacement vector, which is governed by linearized equations of motion. This…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
Natural selection acts on traits at different scales, often with opposing consequences. This article identifies the particular forces that act at each scale and how those forces combine to determine the overall evolutionary outcome. A…
We show that the spontaneous scalarization scenario in scalar-tensor theories is a specific case of a more general phenomenon. The key fact is that the instability causing the spontaneous growth in scalars is due to the nonminimal coupling…
The anomalous scaling behavior of the n-th order correlation functions $F_n$ of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero-modes) of the Kraichnan equation…
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…
In this paper, we investigated the statistical differences between active and passive scalars in isotropic compressible turbulence. In the inertial range, the kinetic energy and scalar have the Kolmogorov spectra, and the Kolmogorov and…
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time.…
It is argued that in the case of a smooth transition across a (dilaton-driven) curvature bounce the growing mode of the vector fluctuations matches continuously with a decaying mode at later times. Analytical examples of this observation…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically.…