Multi-scale modeling
The
earthquake problem is an excellent
example, and has been the focus of the Keck
Program for Interdisciplinary Studies in Seismology and Materials Physics
at UCSB. One of the most fundamental issues in seismology is the dynamics
of rupture in the Earth's crust. If we knew more about the physics of rupture,
we might be able to explain why some earthquakes are small (millimeters
of slip over an area of one square kilometer) and others are huge (meters
of slip over an area of 20,000 square kilometers). A related goal of research
in rupture dynamics is estimating regional hazards. Understanding when
and where an earthquake is likely to occur requires understanding the mechanisms
of earthquake nucleation.
It is not possible to answer these basic questions by seismological observations alone. The best modern theories still rely on untested phenomenological assumptions about the properties of earthquake faults. The underlying constitutive relations --- friction laws, failure criteria, deformation rules, etc. --- are unknown; and even with rough guesses about these relations, we cannot yet predict the behavior of the resulting nonlinear dynamical systems in mathematically reliable ways.
However, this
field is poised for major advances in part because of recent progress in
theoretical and experimental
understanding of materials, especially at UCSB in the areas of friction,
fracture, and deformation, and also because of the extraordinarily rapid,
world-wide growth in computational capabilities. In addition to studying
dynamical models of earthquakes, a major theme of our group has been to
study of analog processes in simpler, more controlled environments, and
incorporation of the results of those investigations into numerical simulations
of seismic phenomena. Our approach involves multiscale studies of materials
under stress. At the microscopic level, we investigate nanometer scale
friction and lubrication. At the mesoscopic level, we study fracture and
stick-slip behavior in granular and amorphous
systems, and develop theories of these nonequilibrium
phenomena in disordered materials. At the macroscopic scale, we develop
new phenomenological descriptions for these processes, and study them in
the context of earthquake simulations and observations.
Click here for publications on multi-scale modeling.