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© Centre for Modeling & Simulation, Savitribai Phule Pune University
| Savitribai Phule Pune University |
Networks is a widely studied topic in various fields like food web, regulatory networks, neural networks, information network and so on. It has received widespread attention and though it is a modern topic, few books have been published on it.
We plan to investigate different spatially extended dynamical systems defined on various underlying networks. We will mainly study deterministic systems like cellular automata (CA) models and coupled map lattice (CML) models. These models have been useful in studying various natural phenomena from pattern formation to immunology. One of our major aims is to explore the nature of various dynamical phases and find out the characteristics of transitions between them. We will also inspect and compare stochastic dynamical models for the same. Finding the nature of phase transition and its universality class is a computationally intensive problem. While for equilibrium models like the Ising or the XY model there are some studies on this question, nonequilibrium systems on networks are relatively less studied.
The specific problems we would like to address are (for example):
(A) Are small world networks just interpolations between
regular and random networks or something more?
(B) Are scale free networks with a large degree exponent similar to
Erdos-Renyi (ER) networks? If so, what is the exponent?
(C) Dynamically, is there a serious difference between
static configuration networks and networks generated
by growth when they have a similar degree distribution?
(D) Universality classes of phase transitions in certain
stochastic systems are well known and in some cases
understood. Are phase transitions in spatially
extended dynamical systems in the same universality class
of stochastic systems?
Obviously, networks is a hot area and newer questions could emerge in the course of research.
Prerequisites for the Candidate: M. Sc. in Physics, Chemistry, Mathematics or Statistics with an overall good academic record. Knowledge of any computer language is desirable. If the candidate does not already know any programming language, we expect him to pick up a language quickly. We plan to work on some well framed problems that will involve intensive and systematic computation.