Complex Systems

Many of today's most complex and important technological problems are inseparably connected to fundamental scientific issues. Successful solutions of these problems will require coordinated efforts by specialists in a remarkably wide range of areas including engineering, the basic sciences and, increasingly, advanced scientific computation. In many cases, insights are best obtained using a spectrum of models, at varying resolution. A good low resolution model captures fundamental principles and behaviors that are retained in more detailed descriptions, while high resolution models are necessary to understand and predict the behaviors of systems in detail. Our group is involved in a broad range of interdisciplinary activities, aimed at capturing and connecting properties of complex systems at varying scales and resolutions. Focus areas include systems biology, ecology, and geophysics.

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.