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BCAMSevero Ochoa Award

basque center for applied mathematics

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Molina García, Daniel


PhD Student - (Predoc Severo Ochoa 2015)

Statistical Physics

Mazarredo, 14. 48009 Bilbao Basque Country - Spain


I studied Physics in the University of Granada and I did a Master in Physics and Mathematics at the same university. My Master Thesis was focused on the computational study of a stochastic model known as multi-species voter model to study ecological communities. Currently, I am PhD student in BCAM. The topic of my thesis is Stochastic Processes for Anomalous Diffusion. The director of my thesis is Gianni Pagnini. Anomalous diffusion is the general name to indicate diffusive processes that do not follow the behavior of classical Gaussian diffusion which is also referred to as normal diffusion. Hence, the label anomalous is stated in contrast to normal in order to underline the differences. In Nature, anomalous diffusion has been observed, for example, in turbulent plasma transport, photon diffusion and cell migration. A successful tool is Fractional Calculus and a fractional kinetics follows from equations built on fractional derivatives. Several stochastic approaches have been introduced in literature to explain anomalous diffusion. The proposed PhD project is focused on the generalized grey Brownian motion, which is a parametric class of self- similar stochastic processes with stationary increments that generalizes the fractional Brownian motion, the time-fractional diffusion and the standard Brownian motion. The corresponding master equation is known to be a fractional differential equation in the Erdélyi-Kober sense. In particular, it has been planned to characterize and simulate a large class of self-similar stochastic processes with stationary increments that can model also space-fractional diffusion and space-time fractional diffusion. The project concludes with the experimental validation of at least one of the derived models.

Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)