Basque Center for Applied Mathematics – BCAM offers a Postdoctoral Fellowship position in Special Functions and Random Walks to work with Dr. Gianni Pagnini at Statistical Physics research line inside the Generalized Master Equation for the Continuous-Time Random Walk. The proposed research project is focused on the derivation of the Generalized Master Equation (GME) for the Continuous-Time Random Walk (CTRW) as published in literature, e.g., [1,2], and on its specific determination for fractional diffusion [3]. Actually, the GME depends on a kernel function that is explicitly given in terms of the jumps and waiting-times distributions of the CTRW. Surprisingly, a systematic study concerning the features of the CTRW, the kernel of the GME and the resulting walker’s distribution is not provided, yet. The aim of the research is to fill this literature gap in the view of the many applications of the CTRW and in particular because of the recent regime-transitions (exponential-to-fractional-to-Gaussian) observed in anomalous diffusion processes.

[1] Klafter J and Silbey R 1980 Phys. Rev. Lett. 44 55–58
[2] Klafter J, Blumen A and Shlesinger M F 1987 Phys. Rev. A 35 3081–3085
[3] Hilfer R and Anton L 1995 Phys. Rev. E 51 R848–R851

Deadline: 29th April 2022
More info and applications at: http://www.bcamath.org/en/research/job/ic2022-03-postdoctoral-fellowship-in-special-functions-and-random-walks

Requirements: Applicants must have their PhD completed before the contract starts.

Skills:
• Good interpersonal skills.
• A proven track record in quality research, as evidenced by research publications in top scientific journals and conferences.
• Demonstrated ability to work independently and as part of a collaborative research team.
• Ability to present and publish research outcomes in spoken (talks) and written (papers) form.
• Ability to effectively communicate and present research ideas to researchers and stakeholders with different backgrounds.
• Fluency in spoken and written English.

The preferred candidate will have:
• Strong background in special functions and integral transforms.
• Background in fractional calculus and fractional modelling.
• Knowledge in statistics and probability.
• Good programming skills in Mathematica and/or Maple and/or MathLab.
• Interest and disposition to work in interdisciplinary groups.