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# Professor Carl Dettmann

## Professor Carl Dettmann

A.Mus.A (piano), B.Sc.(Hons.), Ph.D.(Physics)

Professor of Applied Mathematics
## Summary

## Biography

## Memberships

### Organisations

### Mathematical Physics

### Probability, Analysis and Dynamics

### Research themes

## Links

## Selected publications

## Recent publications

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A.Mus.A (piano), B.Sc.(Hons.), Ph.D.(Physics)

Office 1.41

Fry Building,

Woodland Road,
BS8 1UG

(See a map)

+44 (0) 117 42 84915

carl.dettmann@

bristol.ac.uk

Dynamical systems, statistical physics, wireless networks.

A more complete description of activities may be found at my home page, http://www.maths.bris.ac.uk/~macpd

**PhD projects**

I am happy to supervise well motivated students who want to work on the above general areas. Two areas of particular interest are:

**Deterministic diffusion **A particle moves according to a deterministic law in an unbounded domain, starting from a random initial condition. How does the displacement depend on time? A good class of such systems to visualise are mathematical billiards: The particle (“billiard ball”) moves in straight lines except for reflections from obstacles. Different shapes lead to dynamical properties from regular to chaotic and including many finer distinctions. The obstacle locations can be deterministic or random. Depending on these factors the diffusion can be anything from normal (Brownian motion) to highly anomalous. See my paper "Diffusion in the Lorentz gas," available from the above website.

**Spatial networks** What happens if you place points randomly in space, link them with a probability that depends on pairwise distance, and study the resulting network? How does this depend on the shape of the domain, the density of points, generalisations such as angular dependence, obstacles, time-dependent locations? These questions are interesting from both a theoretical and practical point of view. One of the main applications is the design of wireless ad-hoc networks, of interest to Toshiba research labs in Bristol. But there are many other kinds of networks with spatial structure that could be considered. See my paper "Random geometric graphs with general connection functions", available from the above website.

For more ideas, please look at other recent publications available from the above website. They are research articles, hence rather technical; please read only to get the general idea, and then contact me to discuss your interests.

Graduate Dean, Faculty of Science, since 2017.

Professor of Applied Mathematics, since 2013.

Fellow of the Institute of Physics, since 2005.

PhD in physics, University of Melbourne, Australia (1995)

BSc (Hons) in physics, University of Melbourne, Australia (1991)

AMusA in piano, AMEB (1988)

- Dettmann, C & Knight, G, 2018, ‘Symmetric motifs in random geometric graphs’.
*Journal of Complex Networks*, vol 6., pp. 95-105 - Dettmann, CP, Marklof, J & Strömbergsson, A, 2017, ‘Universal Hitting Time Statistics for Integrable Flows’.
*Journal of Statistical Physics*, vol 166., pp. 714-749

- Dettmann, C & Roychaudhury, MK, 2019, ‘An algorithm to compute CVTs for finitely generated Cantor distributions’.
*Southeast Asian Bulletin of Mathematics*. - Koufos, K & Dettmann, CP, 2019, ‘The Meta Distribution of the SIR in Linear Motorway VANETs’.
*IEEE Transactions on Communications*. - Rajanna, A & Dettmann, CP, 2019, ‘Adaptive Transmission in Cellular Networks: Fixed-Rate Codes with Power Control vs Physical Layer Rateless Codes.’.
*IEEE Transactions on Wireless Communications*, vol 18., pp. 3005-3018 - Koufos, K & Dettmann, C, 2019, ‘Distribution of Cell Area in Bounded Poisson Voronoi Tessellations with Application to Secure Local Connectivity’.
*Journal of Statistical Physics*. - Koufos, K & Dettmann, C, 2019, ‘Boundaries as an Enhancement Technique for Physical Layer Security’.
*IEEE Transactions on Information Forensics and Security*, vol 14., pp. 61-74 - Koufos, K & Dettmann, C, 2018, ‘Temporal Correlation of Interference and Outage in Mobile Networks over One-Dimensional Finite Regions’.
*IEEE Transactions on Mobile Computing*, vol 17., pp. 475-487 - Dettmann, C, 2018, ‘Isolation and connectivity in random geometric graphs with self-similar intensity measures’.
*Journal of Statistical Physics*, vol 172., pp. 679-700 - Dettmann, C, Georgiou, O & Pratt, P, 2018, ‘Spatial networks with wireless applications’.
*Comptes Rendus Physique*, vol 19., pp. 187-204

View complete publications list in the University of Bristol publications system

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