The dynamics of complex systemsΒΆ

One thing that silicon carbide epitaxy, the chemistry of non-thermal plasmas, and neuromorphic computing have in common is that they are examples of complex systems with many components that are tightly coupled. The description, characterization, and simulation of such systems is something that cuts across an important part of my research.

The way in which I approach the study of such systems is to focus on simple models that can reproduce their behavior, or at least a particular observable. This effort to distill the main characteristics of systems has some important consequences, including:

  • Being able extract conclusions that are as general as possible and go beyond the details of a particular system. This allows us to identify common patterns in seemingly different systems.
  • Deepening our understanding of what matters and what not in the description of a given system. This is important to find more efficient ways to emulate them or simulate their dynamics.

Most of my research in this area has taken place in the context of materials growth, where usually the details of the complex interactions between molecules and the growing materials are not well understood. Consequently, the search for models that can help rationalize experimental results can help us better understand how materials grow and identify the key factors controlling the growth process. This is also behind my recent incursion in additive manufacturing.

Another area of interest is neuromorphic computing, and how the structure of the network and the type of interactions in dynamic systems can be leveraged to carry out computations.

From a mathematical perspective, I am interested in differential, difference, and delay equations, kinetic Monte Carlo simulations, and various stochastic approaches such as Markov chains.

hyperbolic surface

Hyperbolic surface obtained from a combination of short-range attractive and long-range repulsive potentials