DYNAMICS AND NETWORKS GROUP

Dynet is a research group that is concerned with developing mathematical and computational techniques to understand various aspects of dynamics and networks.

Historically, dynamics is the branch of physics that deals with changes in the world. Originally, it refers to classical dynamics which studies the relationship between force and motion based on Newtonian mechanics, how certain types of forces causes certain types of and changes in motion of certain types of matter. Classical electrodynamics is the application of Newtonian mechanics to motion of bodies with electric charge and the forces between them. With the discovery quantum physics, quantum dynamics was also born. Relativistic quantum mechanics of charged particles is also called quantum electrodynamics.

We take a more encompassing notion of the term dynamics. We aim to study quantities or systems of quantities that changes in time and space, or spatiotemporal dynamics. Mathematically, we will use techniques in ordinary and partial differential equations as well as those in discrete dynamical systems (difference equations, etc.) to analyze such systems. It could be changes in certain proteins in a cell or tissue, fluctuations in physical properties of the environment, ebb and flow of population of certain species in a given ecosystem, or variations in certain factors that describe a person or a society.

In studying the dynamics of complex systems, understanding of the general and particular aspects of networks is important. Thus, we may also use existing knowledge about networks to improve our understanding of the system we are studying. Consequently, we may also contribute to the existing literature about particular networks or in graph theory in general.

Our research is interdisciplinary as we employ many techniques developed in different areas such as mathematics, computer science, physics, biology, chemistry, psychology, sociology, economics, and other fields. Our motivation is to contribute deeper knowledge and insights about change and networks, with applications as side results but not the focus.

There are at least four (4) categories of group members: Regular Faculty Members, Regular Student Members, Apprentice, Observers.

• Regular Faculty Member – A faculty member who is committed to mentor student members in research in the field of dynamics and networks

• Regular Student Member – A student who has apprenticed in the group for one year and is actively pursuing a research in the field of dynamics and networks

• Apprentice – A student who wants to be a regular member, must attend the weekly meetings of the group, and must give at least one show-and-tell presentation

• Observers – A faculty member or student who is interested but has not yet decided to be a regular member of the group, must attend the weekly meetings of the group

• Weekly show-and-tell meetings

• Research meetings between student members and their respective mentors

• Development of solutions to a research problem

• Writing publications

• Finding funding sources for on-going or planned research activities