This paper proposes a framework based on which innovations in wind power technologies can be evaluated from the standpoint of their contribution to diffusion expansion. The framework helps build up a missing link between the technical literature on innovations and policy-oriented contributions concerned with the diffusion potential of wind power in national energy systems. The ideas are applied...

In a series of papers [1]–[4] we considered parabolic equations for measures on R. Our motivation was a study of the Kolmogorov equations for transition probabilities of diffusion processes. Here we are concerned with similar problems in infinite dimensions. Applications are given to stochastic partial differential equations such as stochastic equations of Navier– Stokes and reaction-diffusion ...

Stochastic methods offer an attractively simple solution to complex transport-controlled problems, and have a wide range of physical, chemical, and biological applications. Stochastic methods do not suffer from the numerical diffusion that plagues grid-based methods, but they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce some ideas and algorithms t...

This paper is dedicated to a brain magnetic resonance images regularization method, preserving grey/white matter edges using rotating smoothing filters. After a preprocessing, the originality of this approach resides in the mixing of ideas coming both from pixel classification which determines roughly if a pixel belongs to a homogenous region or an edge and an anisotropic edge detector which co...

In the beginning we review briefly the evolution of the ideas on the motion of the bodies in our solar system, from Newton’s clockwork Universe to the presently accepted ubiquity of chaotic transport in the asteroid belt. Then we discuss the result of chaotic motion, which is transport in phase space, and we introduce the concept of diffusion of an asteroid in action space. We proceed by review...

New ideas, products, and practices take time to diffuse, a fact that is often attributed to some form of heterogeneity among potential adopters. This paper examines three broad classes of diffusion models -contagion, social influence, and social learning – and shows how to incorporate heterogeneity into each at a high level of generality without losing analytical tractability. Each type of mode...

In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear parabolic partial differential equations. We illustrate the approach with the verification of a conjecture about the long-time behavior of solutions to a cer...

In this paper we study a free boundary problem modeling the growth of tumors. The model uses the conventional ideas of nutrient diffusion and consumption by the cells. We consider the radially symmetric case of this free boundary problem. We apply a spectral numerical method to the system of equations. 2004 Elsevier Inc. All rights reserved.

It is shown that the fundamental solution of a hyperbolic partial differential equation with time delay has a natural probabilistic structure, i.e. is approximately Gaussian, as t → ∞. The proof uses ideas from the DeMoivre proof of the Central Limit Theorem. It follows that solutions of the hyperbolic equation look approximately like solutions of a diffusion equation with constant convection a...

Nonlinear diffusion filtering and wavelet shrinkage are two successfully applied methods for discontinuity preserving denoising of signals and images. Recently, relations between both methods have been established taking into account wavelet shrinkage at one scale. In this paper, we propose a new explicit scheme for nonlinear diffusion which directly incorporates ideas from multiscale Haar wave...