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- Statistical physics modeling of earthquakes
- Earthquake source mechanism: from chemical energy storage to mechanical rupture
- Observational testing of the critical earthquake concepts
- Rupture in heterogeneous systems: critical versus abrupt rupture; role of the heterogeneity; scaling laws and prediction.
- Models of self-organization, self-organized criticality and crisis: 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
- Theoretical finance (Derivatives, portfolios, interest rates)
- Analysis and theory of financial crashes
- String theory of forward rate curves
- Turbulence cascade 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: The earthquake source problem is characterized by the complexity coming from repeated interactions between
many elemens. The one-earthquake or one-fault problem is usually thought to be relatively well-understood 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).
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. 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 across 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 signaling the global nature of the maturing process.
Scientific Prediction of
Catastrophes: A New Approach
essay selected as one of the
ten finalist to the James S. McDonnell,
Centennial Fellowships (november
1998) |
| | 1977-81, Ecole Normale Superieure (ENS Ulm, Paris) in Physical Sciences
M.S., 1981, Ecole Normale Superieure (ENS Ulm, Paris, France)
Ph.D., 1985, University of Nice, France |
