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.

• Earthquake source mechanism: from chemical energy storage to mechanical rupture
• Observational testing of the critical earthquake concepts
• Rupture in disordered systems: critical versus abrupt rupture; role of the heterogeneity; scaling laws and prediction.
• Self-organized criticality: numerical models and theory
• Discrete scale invariance and complex exponents: evidence and theory of log-periodicity in rupture and growth processes, out-of- equilibrium systems; implications for predictions
• Analysis and theory of financial crashes
• String theory of forward rate curves
• Turbulence models of stock market prices

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
sornette@cyclop.ess.ucla.edu