# Adnan Ali

**A bit about me:**

I graduated from Imperial College London with a BSc in Mathematics.

I have completed a MSc in the field of Complexity Science at the University Of Warwick.

**Current research:**

Fluctuation phenomena, random processes, noise, and Brownian motion, Fractals; macroscopic aggregates (including diffusion-limited aggregates), Spatiotemporal pattern formation in cellular populations.

For my PhD I have developed a theory which can completely describe the distribution of the fluctuating diverse states of a system. It is based on mapping increasing geometries onto more easily tractable fixed or linear geometries, for which in many applications analytical solutions are available. The statistical properties of the rescaled increasing system at large times are identical to the system in fixed geometry at a specific finite time which is determined by a non-linear time transformation, this isomorphism preserves the local scaling properties of the system.

In our applications we focus on interacting particle systems. Such systems are ubiquitous across nature, real world examples can range from the interactions between traders in a market to the growth of cells in a tumour. A common theme across many of these systems, is that local interactions lead to a global change in the state of the system. Due to the complexity of these systems, currently there exist a gap in our knowledge, where current techniques break down. The idea of my PhD is to quantify the local relationship between particles in order to understand how their interplay affects macroscopic observables. Through an interdisciplinary approach we explain behaviour in these complex systems by using a variety of mathematical techniques to successfully predict how correlations and interactions between agents/particles may lead to a particular behaviour.

**General research interests:**

Statistical mechanics, stochastic processes, stochastic analysis, measure theory and complex systems.

**Publications:**

**Pattern formation through genetic drift at expanding population fronts. Ali, Adnan and Grosskinsky, Stefan (2010), Advances in Complex Systems, vol.13 (No.3).****Reproduction-time statistics and segregation patterns in growing populations, Adnan Ali, Ellák Somfai and Stefan Grosskinsky, Phys. Rev. E 85, 021923 (2012)**

**Selected Bibliography:**

- A.-L. Barabasi and H. E. Stanley, Fractal concepts in surface growth (Cambridge University Press, 1995), 1st ed.
- M. Eden, Proc. Fourth Berkeley Symposium on Math Statistics and Probility. 4, 223 (1961).
- M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986).
- F. Biagini, Y. Hu, B. Øksendal, and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Appli-

cations (Springer, Berlin, 2010).

CONTACT:

Adnan Ali

Centre for Complexity Science

Zeeman Building

University of Warwick

Coventry

CV4 7AL

Email: a dot ali dot 1@warwick.ac.uk