Professor of Geophysics
Models of self-organization, Physics of earthquakes, Rupture in heterogeneous systems, Complex exponents and log-periodicity, Criticality,pattern recognition, Chaos theory, Theoretical finance, Derivatives,Financial crashes.
Complex systems: my main research effort is devoted to the understanding of complex systems, using a multidisciplinary approach in order to tackle the ever growing complexity of the challenges we have to face for instance in seismo-tectonics, mechano-chemistry, geomorphology, meteorology, volcanology and even finance. From a general standpoint, I aim to understand the ubiquitous intermittent and punctuated dynamics (the fact that processes are not smooth but are often marked by brief bursts of activity interrupting long periods of stasis) presented by many dynamical systems in Natural Sciences. In other words, the question is how simple nonlinear behaviors that can act repetitively may lead to the emergence of complex cooperative behaviors. Earthquake source: when I became interested 11 years ago in the earthquake source problem, I was at the time enthused by its ``N-body'' nature, that has made earthquakes quite fashionable in statistical physics this last decade. Indeed, the one-earthquake or one-fault problem is usually thought to be relatively well-understood (even if an ``isolated'' fault has never been observed!) and the excitement emerges when coupling (via long-range elasticity and relaxation processes) many faults presenting highly nonlinear responses (threshold dynamics) in the presence of rock heterogeneity and fault geometrical complexity. This is the vision that led me to propose an analogy between earthquakes deformations and self-organized criticality about a decade ago and to the recognition that earthquake dynamics offer for the solid earth a complexity and richness (and difficulties!) equivalent or even greater to that of hydrodynamic turbulence (usually considered to be one of the most important and difficult unsolved challenges nowadays). A new way: In the last years, my point of view has evolved dramatically. I am still convinced that the dynamics of earthquakes and their space-time structure provide a nice example of self-organizing nonlinear spatio-temporal systems and that this deserves investigations. However, I have come to realize that maybe the biggest challenge of all resides in the so-called ``one-body'' problem, i.e. in the understanding of the single earthquake ``cycle''. This came while I was trying to synthetize the many geological observations and experimental data. It progressively dawned on me that even the supposedly ``simple'' one-earthquake process is not at all understood and that this poses many fundamental questions. This maturation has led me to propose a new way to model earthquakes using the concept that water in the presence of finite localized strain may lead to the phase transformation of pre-existing minerals into other metastable polymorphs of higher free energy density. This new route of ``chemical'' energy storage can be argued in details for the example of the quartz to coesite transformation, based on laboratory and field observations as well as free energy estimations. According to this scenario, under increasing strain, the transformed minerals eventually become unstable, as shown from Landau theory of structural phase transitions, and transform back explosively, creating a slightly supersonic shock wave propagating along the altered fault core leaving a wake of shaking fluidified fragments. As long as the resulting high-frequency waves remain of sufficient amplitude to fluidify the fault core, the fault is unlocked and free to slip under the effect of the tectonic stress, thus releasing the elastic part of the stored energy. Many observations can be rationalized by this theory which offers testable predictions. Furthermore, the evidence, that out-of-equilibrium processes in the presence of water and/or finite strain lead to mineral structures that are excluded on the basis of equilibrium thermodynamic phase diagrams, suggests new developments in the reconstruction of crustal motions and their histories based on ``inversion'' of metamorphic patterns. Crisis: I am involved in the exploration of the possibility to develop an inter-departmental intensive large-scale computer center at UCLA, focused at reaching qualitative insights and simple insightful theoretical models from large scale simulations exploring realistic scenarios of crisis. A crisis is defined as the dramatic and rapid change of a system which is the culmination of a complex preparatory stage. Crises have fundamental societal impacts and range from large natural catastrophes such as earthquakes, volcanic eruptions, hurricanes and tornadoes, landslides,avalanches, lightning strikes, meteorite/asteroid impacts, catastrophic events of environmental degradation, to the failure of engineering structures, crashes in the stock market, social unrest leading to large-scale strikes and upheaval, economic drawdowns on national and global scales, regional power blackouts, traffic gridlock, diseases and epidemics, etc. Such a theme has a unique multidisciplinary flavor that could use the full potential of the scientific excellence found in the departments within UCLA. The outstanding scientific question is how large-scale patterns of catastrophic nature might evolve from a series of interactions on the smallest and increasingly larger scales, where the rules for the interactions are presumed identifiable and known. For instance, a typical report on an industrial catastrophe describes the unprobable interplay between a succession of events. Each event has a small probability and limited impact in itself. However, their juxtaposition and chaining lead inexorably to the observed losses. The common denominator to the various examples of crises is that they emerge from a collective process: the repetitive actions of interactive nonlinear influences on many scales lead to a progressive build-up of large-scale correlations and ultimately to the crisis. In such systems, it has been found that the organization of spatial and temporal correlations do not stem, in general, from a nucleation phase diffusing accross the system. It results rather from a progressive and more global cooperative process occurring over the whole system by repetitive interactions. An instance would be the many occurrences of simultaneous scientific and technical discoveries signalling the global nature of the maturing process. Didier Sornette Professor Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences Box 951567, Los Angeles, CA 90095-1567 tel/fax: (310) 825 2863 fax (IGPP): (310) 206 3051 email@example.com