Gunnar Pruessner

Senior Lecturer in Mathematical Physics
Senior Tutor Mathematics
  • Department of Mathematics
  • Room No: 657
  • Telephone No.: +44 (0)20 759 48534
  • E-Mail Address: g DOT pruessner AT imperial DOT ac DOT uk
    my @physics.org address is no longer in use
  • Office hours: Mon 10am-11am, Wed 12noon-1pm, Fri 2pm-3pm
    [Please email beforehand.]
Full address: Gunnar Pruessner
Department of Mathematics
Imperial College London
180 Queen's Gate
London SW7 2AZ
Photo of Gunnar

Complex Systems Dynamics Meeting Series

Senior Tutor

Teaching

Publications

Students:

Seng Cheang (PhD, Synchronisation)
Gary Willis (PhD, Wetting)
Christopher Rochester (PhD, Electrolytes in pores)

Research Interests and Projects:

The field theory of SOC

Ever since Bak, Tang and Wiesenfeld conceived Self-Organised Criticality (SOC) 25 years ago, its most fundamental features have remained a mystery: How does Self-Organised Criticality work? Why do these systems organise themselves to a critical point? How can we estimate their universal features? The most powerful tool of statistical mechanics, the renormalisation group, could not be deployed effectively, as the systems displaying SOC are not easy to cast in the language of field theory. It turns out this can be done for the Manna Model and the resulting field theory allows us to understand how SOC comes about. Above the upper critical dimension, the underlying mean-field theory can be extracted and solved in closed form. Non-trivial results for universal quantities can be compared to numerics, and predictions for exponents below the upper critical dimensions become accessible through renormalised field theory.
Some of the technical difficulties of the field theory of SOC, such as fermionicity versus carrying capacity, multiple species (some of which resting), boundary conditions and finite size scaling, can be studied in the field theory of the Wiener sausage, that I have introduced more recently.

Synchronisation by time delay

Synchronisation is a very widespread phenomenon observed in flashing fireflies, applauding audiences and the neuronal network of the brain. Hitherto, one major branch of research has focussed on the exchange of instantaneous, sudden pulses which are exchanged when an oscillator reaches a threshold, triggering sudden, discontinuous relaxations. A second branch focussed on smooth interaction that vanishes in the synchronised state, best known as the Kuramoto Model. We changed this setup, studying smooth, continuous interaction that never disappears. At first, very basic considerations suggest that such a system cannot synchronise. Numerics, however, seems to suggest otherwise. It turns out that this clash is caused by an effective time delay built into the numerics: Time delay causes synchronisation on a time scale that is inversely proportional to the time lag.

Borderlines in ecotones and the contact process in ecological systems

Borderlines, such as tree lines, appear frequently in ecological systems. Does the structure of such borderlines give away the universality class of the underlying microscopic dynamics? With a suitable definition, the borderlines become a trivial percolation phenomenon. It would be highly desirable to detect the contact process, which has an enormously large universality class, yet has proved difficult to find so far. Can one identify observables and predict their properties, which could be used to detect the contact process in natural systems? Can one measure and characterise the role of correlations? Assuming that the contact process is at work in population dynamics, what effect has the range of interaction on its critical point?

Thermodynamic Properties of Grain Boundaries

Many of the interesting mechanical and electrical properties of titanates are due to intergranular films, i.e. the interfaces between grains. The aim is to develop a density functional theory for these systems, rather than doing first principles calculations or simulations. In particular, such a theory should be able to predict the thickness of the interface as a function of the misorientation of the adjoining crystalline lattices, as well as indicate the onset of a wetting transition. Moreover, a connection can be made to phase field models of these systems.

Self-Organised Criticality

Some non-equilibrium systems seem to develop into a state that lacks characteristic spatial or temporal scales. This behaviour has been dubbed "Self-Organised Criticality". Keeping in mind that scale invariance is usually only found at a critical point of second order phase transitions, the aim is to find the necessary and sufficient conditions for the occurence of this very surprising phenomenon. These questions can be addressed either numerically or analytically. The link to absorbing states phase transitions is of particular interest.

Field theory of growth with and without disorder

The single most powerful tool of the statistical mechanics of phase transitions is field theory. While equilibrium models have been studied extensively using this mathematical technique, non-equilibrium phenomena and those with (quenched) disorder are far less understood. Non-equilibrium phase transitions into an absorbing state, their field-theoretic particularities and their theoretical basis (such as the apropriate ensemble) are studied using scaling arguments and field theoretic RG, both supported by numerics.

Non-perturbative renormalisation group

In recent years the non-perturbative renormalisation group has gained some momentum and has been applied successfully to a number of hitherto rather elusive problems, in particular non-equilibrium systems. Yet, its foundations and restrictions (in particular regarding symmetries, such as causality) remain somewhat unclear, but can be studied using exactly solvable or well understood models.

Percolation

Using a novel algorithm to study percolation numerically, it was possible to calculate with very high precision various crossing, spanning and wrapping probabilities in two-dimensional lattices of unprecedented size.