CIRCS - Northeastern University

Solidification Patterns:

One important class of nonequilibrium patterns are those produced naturally and unavoidably by the solidification process, such as the snow-flakes familiar to Bostonians and the dendrites familiar to casting and welding engineers. These structures determine the physical properties (e.g. the tensile strength) and quality of many man made objects. Thus, understanding how they form is practically relevant.

Modeling solidification microstructures quantitatively is rendered extremely difficult by tracking the highly nonlinear evolution of the solid-liquid interface and, moreover, by the fact that the basic lengthscales that control this evolution differ by several orders of magnitude. Surface tension acts on a nanometer scale whereas heat and mass transport by diffusion takes place on a scale of a millimeter. Convective transport can act on even larger scales. The current research in my group focuses on further developing a phase-field approach, inspired from continuum models of phase transitions, in order to cope with both of these difficulties. Using a reformulated asymptotic analysis of the phase-field model and a Monte Carlo treatment of the long range diffusion field, we are just reaching the point of making benchmark predictions of dendritic growth that can be compared directly to low undercooling experiments in three dimensions.

Movie of 3D dendritic growth in an undercooled melt.
(1.5 MB in fli format)

(2.0 MB in fli format)

Movie of 3D scroll filament breakup (1.8 MB in fli format)

Cardiac Dynamics:

"Spiral waves" are characteristic structures of excitable media that have been observed in systems as different as catalytic surface oxidation, the Belousov-Zhabotinsky chemical reaction, aggregating colonies of slime mold, and heart tissue where they are suspected to play an essential role in cardiac arrhythmia and fibrillation. Our current research focuses on studying the generic behavior of two-dimensional spiral waves and three-dimensional scroll waves in isotropic/homogeneous excitable media, and on understanding how this behavior is altered by the architecture of the anisotropic/non-homogeneous heart muscle. The long term partical aim of this research, in terms of human helath, is to render modeling sufficiently realistic and accurate to guide the search for successful antifibrillatory drugs, implented low voltage defibrillators, and improved surgical procedures.

Spiral waves