Given a network of N nodes and L links, with each link having a failure probability of p, how can one measure and calculate the probability of failure of the linkage between two randomly chosen nodes. This is a problem addressed and developed recently by mathematicians for simple network and the theories are the domination theory and the theory of signature. Here we will investigate this problem using simple topology, on rings, bands, and two-dimensional patterns. Applicant is expected to know how to do numerical simulation and has some background in statistical physics.

The applicant is expected to know how to do numerical simulation and has some background in statistical physics.

Data analysis and analytical calculation using some mathematics in statistics will be conducted.

1 To learn the mathematics of reliability

2 To apply numerical techniques to test analytical calculations

Complexity of the project involves

1 Since the number of possible network with given N and L can be enormous, one has to find a meaningful subset that is mathematically interesting and at

the same time has real applications. Implications to science and engineering can be important as network is a very common descriptor for complex

systems.

2 Rigorous analysis of the evolution dynamics