61 research outputs found
Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
In this paper we study a parametric class of stochastic processes to model
both fast and slow anomalous diffusion. This class, called generalized grey
Brownian motion (ggBm), is made up off self-similar with stationary increments
processes (H-sssi) and depends on two real parameters alpha in (0,2) and beta
in (0,1]. It includes fractional Brownian motion when alpha in (0,2) and
beta=1, and time-fractional diffusion stochastic processes when alpha=beta in
(0,1). The latters have marginal probability density function governed by
time-fractional diffusion equations of order beta. The ggBm is defined through
the explicit construction of the underline probability space. However, in this
paper we show that it is possible to define it in an unspecified probability
space. For this purpose, we write down explicitly all the finite dimensional
probability density functions. Moreover, we provide different ggBm
characterizations. The role of the M-Wright function, which is related to the
fundamental solution of the time-fractional diffusion equation, emerges as a
natural generalization of the Gaussian distribution. Furthermore, we show that
ggBm can be represented in terms of the product of a random variable, which is
related to the M-Wright function, and an independent fractional Brownian
motion. This representation highlights the -{\bf sssi} nature of the ggBm
and provides a way to study and simulate the trajectories. For this purpose, we
developed a random walk model based on a finite difference approximation of a
partial integro-differenital equation of fractional type.Comment: 25 pages, 9 figure
Bernstein Processes Associated with a Markov Process
Abstract. A general description of Bernstein processes, a class of diffusion processes, relevant to the probabilistic counterpart of quantum theory known as Euclidean Quantum Mechanics, is given. It is compatible with finite or infinite dimensional state spaces and singular interactions. Although the rela-tions with statistical physics concepts (Gibbs measure, entropy,...) is stressed here, recent developments requiring Feynmanâs quantum mechanical tools (ac-tion functional, path integrals, Noetherâs Theorem,...) are also mentioned and suggest new research directions, especially in the geometrical structure of our approach. This is a review of various recent developments regarding the construction and properties of Bernstein processes, a class of diffusions originally introduced for the purpose of Euclidean Quantum Mechanics (EQM), a probabilistic analogue o
Improved intact peptide and protein quantitation by LCâMS: Battling the deleterious effects of analyte adsorption
Electron spin polarization in field emission: calculation of the effects due to external fields
Eckstein W, MĂŒller N. Electron spin polarization in field emission: calculation of the effects due to external fields. Applied Physics, A: Materials Science and Processing. 1975;6(1):71-77.In field emission experiments with spin polarized electrons a magnetic field is superposed on the electric emission field to define the preferred spin direction. The motion of the polarization vector in these fields was calculated for rays emanating from individual points of the emitter by integrating the equation of motion and taking into account relativistic terms. There is a slight shift of the polarization vector from its initial direction. If the initial polarization is aligned with the magnetic field and the emission tip is sufficiently well centred in the magnetic field, the tilting of the polarization vector for a beam of electrons starting not too far from the tip apex is less than 10
Classical equations of motion of magnetic monopole with an intrinsic electric dipole moment
Canonical transformations of Dirac's equation to even forms. Expansion in terms of the external fields
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