Professor Henrik Jeldtoft Jensen  -  Complex Systems Science

Department of Mathematics  Imperial College London South Kensington campus London SW7 2AZ  Office: Huxley Building 6M51  Tel: +44 (0) 20 7594 8541 Fax: +44(0) 20 7594 8517 Email: h.jensen@imperial.ac.uk

Why do we do science?   For the same reason as Glenn Gould plays piano:    The purpose of art is not the release of     a momentary ejection of adrenaline but    rather the gradual, lifelong construction of     a state of wonder.                                          Glenn Gould   There are no such things as   applied sciences,   only applications of science.                                           Louis Pasteur     We shall not cease frome exploration   And the end of all our exploration   Will be to arrive where we started   And know the place for the first time.            T S Eliot                                                                                                                                            HJJ08

Oxherding - HJJ08

For me statistical mechanics is about understanding why the whole is different from the sum of the parts: identifying and understanding emergent properties; understanding how the combined effect of simple interactions and many degrees of freedom creates the never ending complexity we observe in our surroundings. Obviously these general questions have to be studied through concrete cases. I am fortunate to work together with a number of graduate students, research assistants and colleagues on research projects including biology, neuroscience and statistical mechanics. The analysis of the emergence of structure in networks is a natural tool in this quest.

Tangled Nature: Evolutionary ecology is a prototype example of dynamics of complex systems. We have developed a simple individual based model which exhibit intermittency and is able to reproduce a range of ecological observables such as the species-area law and typical species abundance distributions.                                                                                                              Click here for an overview poster on the properties of the   Tangled Nature Model. Below are a few preprints           Review to appear in the proceeding of the 2006 ECMTB Dresden meeting           The Tangled nature model with inheritance and constraint: Evolutionary ecology restricted by a conserved resource  and some reprints:            Diversity as a product of interspecial interactions          The species-area relationship and evolutio          Network properties, species abundance and evolution in a model of evolutionary ecology.          Tangled Nature: a model of evolutionary ecology. (J. Theo. Biol.)        Time dependent extinction rate and species abundance in the Tangled Nature model of biological evolution. (Phys. Rev. E.)           The Tangled Nature model as an evolving quasi-species model. (J. Phys. A)

Record dynamics: Intermittency and relaxation is very often encountered in complex systems. In a broad range of cases we have found that log-Poisson record dynamics is a good description of the observed dynamics. This has a number of very strong implications concerning the structure of the phase space as well as many consequences for the macroscopic temporal behaviour.         Evolution in Complex Systems (Complexity).         Intermittency, aging and extremal fluctuations.         Record dynamics and the observed temperature plateau in the magnetic creep-rate of type II superconductors.

Statistical Mechanics of epedemics:              We have studied the fluctuations in sizes of         Measles Outbreak in a Population with Declining Vaccine Uptake  SCIENCE 301, 804 (2003)                 additional material:  click here         and used lattice models in the study        On the critical behaviour of simple epidemics,                                             Proc. Rol. Soc. Lond. B  264, 1639 (1997). pdf

Population dynamics and evolutionary dynamics: Investigations of how the microscopic behaviour of the individuals in a population affects the behaviour of the whole.  Through the eyes of statistical physics, our main emphasis has been on the phase transitions that occur in our model as the population becomes extinct. Of particular interest is our recent study of the nature of the extinction transition in fractal dimensions between one and two. Aside from this largely theoretical approach, we also examine how the model could be used for ecological purposes, particularly in the conservation of species. Allee Effects and Extinction in a Lattice Model. Change in order of phase transition on fractal lattices. Phase transitions in a lattice population model. The clustering in type space and its relation to neutral and non-neutral models. Understanding clustering in type space using field theoretic techniques. Neutral Evolution in a Biological Population as Diffusion in Phenotype Space: Reproduction with Local Mutation but without Selection.

Modelling in creativity and music cognition using a complexity science approach: We explore patterns in brain activity that are a result of a musician's playing. The focus in particular is to elucidate what happens when creative leaps and ingenuity occur during this playing - EEG recordings are analysed. Together with Conductor Richard Dickens and J Bhattacharya, Goldsmith.

Brain scales          We analyse the spatial and temporal scales of the brain by use of fMRI.

 
Additional interests: Kids, books, music, philosophy, painting,.... 
 
 

List of publications:    Click here to see Publication List                                         HJJ08

Some lectures:     Emergence of network structure in Models of Collective     Evolutionary Dynamics     Slides  (4.5MB)     On the relation between painting and mathematics.      Slides (39.1MB)    Tangled Nature: a model of evolutionary ecology.      Slides  (2.9MB)     Dynamics of complex systems: The record dynamics.     Slides  (2.2MB)      Subtle relations:       prime numbers, complex functions, energy levels and Riemann.       Slides  (1.0MB)    Self-Organised Criticality:what does it mean and is it important.      Slides (1.1MB)     Godel's  Proof.     An introduction to the back ground, the structure of the proof and its consequences.    Slides (1.0MB)

 
 

Some selected publications:
 

Complex systems:  Self-Organized Criticality, H.J. Jensen, Cambridge University Press. 1998.           Buy online from  Cambridge University Press or from  Amazon.com   Anisotropy and universality: the Oslo model, the rice pile experiment  and the quenched Edwards-Wilkinson equation,         G. Pruessner and H.J. Jensen, Phys. Rev. Lett. 91, 244303 (2003). pdf    A solvable non-conservative model of Self-Organised Criticality,          G. Pruessner and H.J. Jensen, Europhys. Lett. 58, 250 (2002). pdf    Universal fluctuations in correlated systems,        S.T. Bramwell, K. Christensen, J.-Y. Fortin, P.C.W. Holdsworth,         H.J. Jensen, S. Lise, J. Lopez, M. Nicodemi, J.-F. Pinton, M. Sellito,        Phys. Rev. Lett. 84 , 3744 (2000).  pdf

Biology: Emergence of species and punctuated equilibrium in the Tangled Nature model of biological evolution.         H.J. Jensen, Physica A: 340,  697-704 (2004). pdf Darwinian selection in a locally unstable Boolean Network.         D. Eriksson and H.J. Jensen, J Stat. Mech.: Theor. Exp. P09001 (2004).pdf   Nonequlibrium Roughening transition in a Simple Model of Fungal Growth in 1+1 Dimensions,      J.M. Lopez and H.J. Jensen, Phys. Rev. Lett. 81 , 1734 (1998). pdf   A Genric Model of Morphological Changes in Growing Colonies of Fungi,      J.M. Lopez and H.J. Jensen,  Phys. Rev. E. 65, 021903 (2002). pdf

Vortex dynamics:     Time dependent phenomena in transport properties and I-V characteristics of a model for driven vortex matter.          M. Nicodemi and H.J. Jensen, J. Phys.: Cond. Mat. 16, 6789 (2004). pdf Creep of superconducting vortices in the limit of vanishing temperature A finger print off equilibrium dynamcs,      M. Nicodemi and H.J. Jensen,  Phys. Rev. Lett. 86, 4378 (2001). pdf Aging and memory phenomena in magnetic and transport properties of vortex matter,      M. Nicodemi and H.J. Jensen, J. Phys. A 34, 8425 (2001). pdf Off equilibrium glassy properties of vortex creep in superconductors,        H.J. Jensen and M. Nicodemi, Europhysics Lett. 54, 566 (2001). pdf

Other topics: Mathematics and painting.        H.J. Jensen, Interdisciplinary Science Review 27, 45 (2002). pdf Turner                              Mathematical Moddeling of Species formation.         K. Christensen and H.J. Jensen, Science Progress 83, 93 (2000).  pdf                                                                    HJJ03