Vittoria Sposini received her Bachelor’s degree in Physics at the University of Perugia (Italy) in 2014. In 2016 she obtained a Master’s degree in Physics at the University of Bologna. During this period, she spent two-months internship at Basque Center for Applied Mathematics – BCAM in Statistical Physics group, headed by Dr. Gianni Pagnini.
After that, for her Doctoral work, she joined the group of Prof. Ralf Metzler at the University of Potsdam (Germany) and thanks to the tight link with the group of Dr. Pagnini in BCAM she carried out her PhD research between Potsdam and Bilbao, including a nine-month research internship at BCAM.
Her PhD thesis, The random diffusivity approach for diffusion in heterogeneous systems, has been supervised by Dr. Gianni Pagnini (BCAM) and Prof. Ralf Metzler (University of Potsdam).
The thesis defence will take place on Wednesday, December 16th at 15:00 at the University of Potsdam, Germany.
On behalf of all BCAM members, we would like to wish Vittoria the best of luck in her upcoming thesis defense.
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.