On the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes

We analyze the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes, and specifically how they modify the Poissonian switching-time statistics. After addressing simple cases such as diffusion in a channel, and the switching statistics in the presence of a polarization potential, we thoroughly study Poisson-Kac diffusion in fractal domains. Diffusion in fractal spaces highlights neatly how the modification in the switching-time statistics associated with reflections against a complex and fractal boundary induces new emergent features of Poisson-Kac diffusion leading to a transition from a regular behavior at shorter timescales to emerging anomalous diffusion properties controlled by walk dimensionality of the fractal set

Markovian nature, completeness, regularity and correlation properties of Generalized Poisson-Kac processes

We analyze some basic issues associated with Generalized Poisson-Kac (GPK) stochastic processes, starting from the extended notion of the Markovian condition. The extended Markovian nature of GPK processes is established, and the implications of this property derived: the associated adjoint formalism for GPK processes is developed essentially in an analogous way as for the Fokker-Planck operator associated with Langevin equations driven by Wiener processes. Subsequently, the regularity of trajectories is addressed: the occurrence of fractality in the realizations of GPK is a long-term emergent property, and its implication in thermodynamics is discussed. The concept of completeness in the stochastic description of GPK is also introduced. Finally, some observations on the role of correlation properties of noise sources and their influence on the dynamic properties of transport phenomena are addressed, using a Wiener model for comparison

Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part II Irreversibility, Norms and Entropies

In this second part, we analyze the dissipation properties of Generalized Poisson-Kac (GPK) processes, considering the decay of suitable $L^2$-norms and the definition of entropy functions. In both cases, consistent energy dissipation and entropy functions depend on the whole system of primitive statistical variables, the partial probability density functions $\{ p_\alpha({\bf x},t) \}_{\alpha=1}^N$, while the corresponding energy dissipation and entropy functions based on the overall probability density $p({\bf x},t)$ do not satisfy monotonicity requirements as a function of time. Examples from chaotic advection (standard map coupled to stochastic GPK processes) illustrate this phenomenon. Some complementary physical issues are also addressed: the ergodicity breaking in the presence of attractive potentials, and the use of GPK perturbations to mollify stochastic field equations

Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part I Basic theory

This article introduces the notion of Generalized Poisson-Kac (GPK) processes which generalize the class of "telegrapher's noise dynamics" introduced by Marc Kac in 1974, usingPoissonian stochastic perturbations. In GPK processes the stochastic perturbation acts as a switching amongst a set of stochastic velocity vectors controlled by a Markov-chain dynamics. GPK processes possess trajectory regularity (almost everywhere) and asymptotic Kac limit, namely the convergence towards Brownian motion (and to stochastic dynamics driven by Wiener perturbations), which characterizes also the long-term/long-distance properties of these processes. In this article we introduce the structural properties of GPK processes, leaving all the physical implications to part II and part III

Coronal mass ejections from the same active region cluster: Two different perspectives

The cluster formed by active regions (ARs) NOAA 11121 and 11123, approximately located on the solar central meridian on 11 November 2010, is of great scientific interest. This complex was the site of violent flux emergence and the source of a series of Earth-directed events on the same day. The onset of the events was nearly simultaneously observed by the Atmospheric Imaging Assembly (AIA) telescope aboard the Solar Dynamics Observatory (SDO) and the Extreme-Ultraviolet Imagers (EUVI) on the Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI) suite of telescopes onboard the Solar-Terrestrial Relations Observatory (STEREO) twin spacecraft. The progression of these events in the low corona was tracked by the Large Angle Spectroscopic Coronagraphs (LASCO) onboard the Solar and Heliospheric Observatory (SOHO) and the SECCHI/COR coronagraphs on STEREO. SDO and SOHO imagers provided data from the Earth's perspective, whilst the STEREO twin instruments procured images from the orthogonal directions. This spatial configuration of spacecraft allowed optimum simultaneous observations of the AR cluster and the coronal mass ejections that originated in it. Quadrature coronal observations provided by STEREO revealed a notably large amount of ejective events compared to those detected from Earth's perspective. Furthermore, joint observations by SDO/AIA and STEREO/SECCHI EUVI of the source region indicate that all events classified by GOES as X-ray flares had an ejective coronal counterpart in quadrature observations. These results have direct impact on current space weather forecasting because of the probable missing alarms when there is a lack of solar observations in a view direction perpendicular to the Sun-Earth line.Comment: Solar Physics - Accepted for publication 2015-Apr-25 v2: Corrected metadat

Brand Equity Evolution: a System Dynamics Model

One of the greatest challenges in brand management lies in monitoring brand equity over time. This paper aimsto present a simulation model able to represent this evolution. The model was drawn on brand equity concepts developed by Aaker and Joachimsthaler (2000), using the system dynamics methodology. The use ofcomputational dynamic models aims to create new sources of information able to sensitize academics and managers alike to the dynamic implications of their brand management. As a result, an easily implementable model was generated, capable of executing continuous scenario simulations by surveying casual relations among the variables that explain brand equity. Moreover, the existence of a number of system modeling tools will allow extensive application of the concepts used in this study in practical situations, both in professional and educational setting