4th International Conference on Advances in Solidification Processes
8-11th July 2014, Beaumont Estates, Old Windsor, UK

Prof Alain Karma - Northeastern University, USA

Alain Karma
Professor Karma received his PhD degree in Physics from the University of California at Santa Barabara in 1985 and spent the following three years at the California institute of Technology as a Weingart Fellow in Theoretical Physics. He subsequently joined Northeastern University in 1988 where he is presently Professor of Physics and Arts and Sciences Distinguished Professor. He also heads the Center for Interdisciplinary Research on Complex Systems. His two main research thrusts are phase field modeling of materials and nonlinear dynamics in biological systems. He has co-authored 145 journal articles that have received over 14,000 citations and has an h-index of 62. He has received several awards for his work including the Condorcet Chair from École Normale Supérieure (2004), Northeastern University Klein Lectureship (2006), American Physical Society (APS) Fellow (2007), and the TMS Bruce Chalmers Award (2008).

Abstract

Multiscale modeling of dendritic microstructures: bridging the dendrite tip and grain scales

A. Karma, Y. Song and D. Tourret

Physics Department, Northeastern University, Boston, USA

The last two decades has witnessed major progress in quantitative modeling of dendritic microstructures using the phase field method. However, with perhaps the exception of very dilute alloys, this method still falls short of modeling dendritic evolution on a grain scale that is typically several orders of magnitude larger than the dendrite tip scale. To bridge this length scale gap, we have developed a multiscale “dendritic needle network” (DNN) model [1] that rigorously tracks the growth dynamics of the primary, secondary and higher order branches of the dendritic network. Each branch is treated as a thin needle whose instantaneous velocity V and tip radius R are determined by combining a standard solvability condition, which fixes the product R2V, with a solutal flux condition that determines separately the product RV2 and hence R and V independently. This talk will discuss the theoretical underpinnings of the DNN model and present examples of application to equiaxed and columnar growth in two and three dimensions. The results shed new light on the emergence of scaling laws that describe the evolution of the dendritic grain envelope.

References

  1. D. Tourret and A. Karma, Acta Materiala 61, 6474-6491 (2013).