Vittoria Sposini obtuvo su licenciatura en Física en la Universidad de Perugia (Italia) en 2014. En 2016 obtuvo un máster en Física en la Universidad de Bolonia. Durante este período, pasó dos meses de prácticas en el Basque Center for Applied Mathematics – BCAM en el grupo de Física Estadística, dirigido por el Dr. Gianni Pagnini.
Posteriormente, para su trabajo de Doctorado, se incorporó al grupo del Prof. Ralf Metzler en la Universidad de Potsdam (Alemania) y gracias a la estrecha vinculación con el grupo del Dr. Pagnini en BCAM, realizó su investigación doctoral entre Potsdam y Bilbao, incluyendo un periodo investigación de nueve meses en BCAM.
Su tesis doctoral, The random diffusivity approach for diffusion in heterogeneous systems, ha sido supervisada por el Dr. Gianni Pagnini (BCAM) y el Prof. Ralf Metzler (University of Potsdam).
La defensa de la tesis tendrá lugar el miércoles, 16 de diciembre a las 15:00 horas en la Universidad de Potsdam, Alemania.
En nombre de todos los miembros de BCAM, nos gustaría desear a Vittoria la mejor de las suertes en la defensa de su tesis.
PhD thesis Title:
The random diffusivity approach for diffusion in heterogeneous systems
The two hallmark features of Brownian motion are the linear growth ⟨x2(t)⟩ = 2Ddt of the mean squared displacement (MSD) with diffusion coefficient D in d spatial dimensions, and the Gaussian distribution of displacements. With the increasing complexity of the studied systems deviations from these two central properties have been unveiled over the years. Recently, a large variety of systems have been reported in which the MSD exhibits the linear growth in time of Brownian (Fickian) transport, however, the distribution of displacements is pronouncedly non-Gaussian (Brownian yet non-Gaussian, BNG). A similar behaviour is also observed for viscoelastic-type motion where an anomalous trend of the MSD, i.e., ⟨x2(t)⟩ ∼ tα, is combined with a priori unexpected non-Gaussian distributions (anomalous yet non-Gaussian, ANG). This kind of behaviour observed in BNG and ANG diffusions has been related to the presence of heterogeneities in the systems and a common approach has been established to address it, that is, the random diffusivity approach.
This dissertation explores extensively the field of random diffusivity models. Starting from a chronological description of all the main approaches used as an attempt of describing BNG and ANG diffusion, different mathematical methodologies are defined for the resolution and study of these models. The processes that are reported in this work can be classified in three subcategories, i) randomly-scaled Gaussian processes, ii) superstatistical models and iii) diffu- sing diffusivity models, all belonging to the more general class of random diffusivity models. Eventually, the study focuses more on BNG diffusion, which is by now well-established and re- latively well-understood. Nevertheless, many examples are discussed for the description of ANG diffusion, in order to highlight the possible scenarios which are known so far for the study of this class of processes.
The second part of the dissertation deals with the statistical analysis of random diffusivity processes. A general description based on the concept of moment-generating function is initially provided to obtain standard statistical properties of the models. Then, the discussion moves to the study of the power spectral analysis and the first passage statistics for some particular random diffusivity models. A comparison between the results coming from the random diffusivity approach and the ones for standard Brownian motion is discussed. In this way, a deeper physical understanding of the systems described by random diffusivity models is also outlined.
To conclude, a discussion based on the possible origins of the heterogeneity is sketched, with the main goal of inferring which kind of systems can actually be described by the random diffusivity approach.