Disordered Systems

The Disordered Systems group at King's is at the forefront of research in statistical mechanics of disordered and complex systems.

The group's research concentrates on the development of new methods to tackle both fundamental issues, for example in non-equilibrium systems, and a broad range of applications to complex systems of many interacting units. The latter include mathematical systems biology and quantitative medicine (protein, metabolic and immune networks & network ensembles) with links to the Institute of Mathematical and Molecular Biomedicine as well as links with statistics and informatics in the area of Bayesian statistical inference and machine learning. The group also has a strong profile in soft condensed matter physics (rheology, polydispersity), glasses and driven non-equilibrium systems. Recent work has led to the development of new models to describe natural and social phenomena, such as systemic risk and catastrophic breakdown in complex systems, with applications to finance and the prediction of power outages. Random matrix theory has become an increasingly important area, studied using extensions of methods for sparse networks.

The group runs the MSc Complex Systems Modelling in collaboration with the Financial Mathematics group and the Departments of Informatics and Physics.

For PhD positions within the Disordered Systems group, please submit an application for Applied Research MPhil/PhD.

Members

Fabian Aguirre Lopez

PhD Student

Alessia Annibale

Senior Lecturer in Disordered Systems

Sirio Belga Fedeli

PhD Student

Gioia Boschi

PhD Student

Giorgio Carugno

PhD Student

Yanik-Pascal Foerster

PhD Student

Yan Fyodorov

Chair in Disordered Systems

Luca Gamberi

PhD Student

Christian Hurry

PhD Student

Reimer Kühn

Professor of Statistical Physics

David Lavis

Emeritus Senior Lecturer

Andrea Mambuca

PhD Student

Izaak Neri

Lecturer in Disordered Systems

Mohammed Osman

PhD Student

Gabriele Sicuro

Lecturer in Disordered Systems

Peter Sollich

Professor of Statistical Mechanics

Vito Susca

PhD Student

Giuseppe Torrisi

PhD Student

Rashel Tublin

PhD Student

Evan Tzanis

Research Associate

Pierpaolo Vivo

Reader in Disordered Systems

Disordered Systems Research

The research activities of the group concentrate on the analysis and development of mathematical theories and models with which to describe the statics and dynamics of disordered (or `complex') systems in physics, biology, financial markets, and computer science. Such systems are characterized by microscopic (usually stochastic) dynamic elements with mutual interactions without global regularity but with a significant degree of built-in competition and incompatibility, resulting in the existence of many locally stable states for the system as a whole and a highly non-ergodic `glassy' type of dynamics.

PINs

The definition and generation of good null models to assess the statistical relevance of observed features in protein interaction networks (PIN) is a well known problem in systems biology, where the aim is to understand how the structure of PINs relates to their biological functionality. By using statistical mechanics techniques, Annibale and Coolen recently derived explicit formulae for complex network ensembles with built-in topologies beyond the degrees, as proxies for real networks; provided exact algorithms for generating random graphs from such ensembles; and derived information-theoretic tools to quantify distances between networks. The application of these tools has enabled them and their coworkers to quantify detection biases in PIN data sets and species consistency.

Physical Systems

In the domain of physical systems, the question of how to pack spheres optimally is familiar from everyday examples such as a greengrocer's stack of oranges. But what if the spheres have a range of sizes, as happens for example in colloidal suspensions? Controversy has surrounded this issue, with proposals that the optimal structure could be disordered. Sollich and co-workers have recently provided a definitive answer, combining mathematical theory (polydisperse phase equilibrium calculations) with specialized numerical simulation techniques. The optimal structures are ordered, i.e. crystalline solids, but depending on the density and the spread of particle sizes the system will fractionate: the particles are effectively sorted out into several solid phases, with each containing only a small range of particle sizes.

Universal Glassy Low-Temperature Anomalies

Kuehn has provided the first formulation of a microscopic model to describe the emergence of the universal glassy low-temperature anomalies, including an understanding of the origin of the mysterious so-called quantitative universality -- a problem that had been open since its formulation in the late 80s. He has also given the first proper formulation and analysis of the role of interactions (networks of functional dependencies) on operational and credit risk, including recently an analysis of the influence of credit derivatives on systemic risk.

Sparse Symmetric Random Matrices

A collaboration between group members Kuehn and Perez Castillo and international collaborators also led to a breakthrough in the spectral problem for sparse symmetric random matrices, allowing to efficiently compute spectral densities of such systems in the limit of large matrix size to any desired accuracy -- more than 20 years after a solution to this problem was first attempted.