Emil Popescu

A Note on Feller Semigroups

We present an integral representation of the operators which form a Feller semigroup using a result of P. Courrège.

Fractional Cauchy Problem with Applications to Anomalous Diffusion

Starting from the Cauchy problem associated with a Feller semigroup, some expressions of solutions of the fractional Cauchy problem are presented. The fractional Cauchy problem is applied in physics for modeling anomalous diffusion, in which particles spread slower than is predicted by the classical diffusion model.

Multi-scale Modeling of the Interplanetary Magnetic Field

Models for heavy-tailed data with applications to the study of multi-scale behaviour of the interplanetary magnetic field are presented. Numerical aspects are given in the case of the data obtained by Ulysses mission (magnetometer VHM/FGM). This approach yields probabilistic predictions of the dynamics and multiscale behaviour of the interplanetary magnetic field.

Trotter products and reaction-diffusion equations

In this paper, we study a class of generalized diffusion-reaction equations of the form @?u@?t(x,t)=(Au(@?,t))(x)+f(x,u(x,t)), where A is a pseudodifferential operator which generates a Feller semigroup. Using the Trotter product formula we give a corresponding discrete time integro-difference equation for numerical solutions.

Models for Heavy Tailed Data and Applications

An important topic in space research is represented by the study of statistical properties of the interplanetary magnetic field fluctuations, these being closely related to acceleration processes and energy transport in the solar wind. Analysis of the probability distribution functions of the velocity and magnetic field fluctuations has underlined their non‐Gaussian properties on small time scales, and uncorrelated features at large scale. In this paper, numerical solutions of space‐time fractional diffusion equations are used to analyze the presence or absence of heavy tails typically associated with multiscale behavior, in the case of the interplanetary magnetic field data obtained by Ulysses mission.