In many settings, differential equation models do not always provide adequate fidelity to the continuum phenomena being modeled. This occurs in diverse areas such as crack nucleation and propagation in solids, charge transport in semiconductors, subsurface and polymer flows, and animal migration in ecological systems, just to name a few. A common feature in these and other settings is that interactions can occur at a distance and not just in infinitesimal neighborhoods as is the case for differential equation models. The summer school focuses on the continuum modeling, analysis, simulation, and numerical analysis of settings that feature such nonlocal interaction.

Although the universe of continuum nonlocal models is large, two approaches have gained popularity due to their wide applicability. On one hand, we have fractional derivative models that can be used to describe many non-Fickian diffusion processes that are observed in practice. Both spatial and temporal fractional derivative models are used for this purpose. On the other hand, we find integral equation models that can treat problems such as those in solid mechanics, which cannot be modeled using fractional derivatives. These integral equation models can be viewed as generalizations of fractional derivative models and can be treated through the use of a nonlocal vector calculus.

The general aim of the school is for students to become familiar with these two approaches. In both cases, the lectures cover models arising in applications, the mathematical analysis of the models, algorithms for obtaining approximate solutions, and the numerical analysis of those algorithms. In addition, the close connection between some of the models discussed and stochastic processes is also a subject of interest.

Attendance to the Summer School is free of charge but registration through our online system is required.
To register, follow this link and click on Registration.