David Kinderlehrer

Professor
Ph.D., University of California, Berkeley

Office: Wean Hall 7208
Phone: (412) 268-5729
E-mail: davidk@andrew.cmu.edu

Research

How do the systems we find in nature evolve and why? Some of the most challenging of these involve interactions among many communicating length and time scales and, even when equations for their motion have been written down on paper, little is understood about their nature. They may be only metastable, for example, hovering for long periods away from equilibrium. They may involve complicated microstructure that can only be interpreted through some coarse graining devices. We find them everywhere, in both material and biological environments. At this moment we are studying complex features of grain growth (http://mimp.mems.cmu.edu/) and fluctuation driven transport in soft systems, like protein motors and liquid crystals. Below are both some older references and some new ones. We know the secret code of rocks (and metals too)! By the way, have a weakness for Las Vegas? Try Heath, Kinderlehrer and Kowalczyk cited below. Most often, I find myself in the company of colleagues who are not mathematicians. We are learning together what we could not do in our native disciplines: new science. Mathematics can say something about the world. Want to help? Come to Carnegie Mellon!

Here is a movie clip, of grain growth, the evolution of polycrystalline interfaces, by our group, joint work with Shlomo Ta'asan and Maria Emelianenko, Eva Eggeling, and Guillermo Leiva. Download in .avi (Windows), .m4v (iPod movie) or Quicktime format.

Selected Publications (see also this list of recent preprints and the Center for Nonlinear Analysis preprint series)

Barmak, K., W. E. Archibald, A. D. Rollett, S. Ta'asan, D. Kinderlehrer, 2004 Grain Boundary Properties and Grain Growth: Al Foils, Al Films, Mater. Res. Symp. Proc. 819, N6.6, 1-12

Chipot, M., Hastings, S., and Kinderlehrer, D. 2004 Transport in a molecular motor system, M2AN 38.6, 1011-1034

Chipot, M. and Kinderlehrer, D. 1988, Equilibrium Configurations of Crystals," Arch. Rat. Mech. Anal. 103: 237-277.

Chipot, M., Kinderlehrer, D., and Kowalczyk, M., 2003, A variational principle for molecular motors Meccanica 38, 505-513

Hardt, R., Kinderlehrer, D., and Lin, F.-H. 1988 Stable defects of minimizers of constrained variational problems, Ann. Inst. H. Poincari: Analyse Nonliniaire 5, 297-322

Heath, D., Kinderlehrer, D., and Kowalczyk, M., 2002, Discrete and continuous rachets: from coin toss to molecular motor, Disc. and Cont. Dyn. Systems B, 2, 153-167.

James, R.D. and Kinderlehrer, D., 1993, Theory of Magnetostriction with Application to TbxDy1-xFe2, Phil. Mag.B 68: 237-274.

Jordan, R., Kinderlehrer, D., and Otto, F. 1998 The variational formulation of the Fokker-Planck Equation, SIAM J. Math Anal. 29.1, 1-17

Kinderlehrer, D., Livshits, I., Rohrer, G.S., Ta'asan, S., and Yu, P. 2004 Mesoscale evolution of the grain boundary character distribution, Recrystallization and Grain Growth, Materials Science Forum vols 467-470, 1063-1068

Kinderlehrer, D., Livshits, I., Manolache, F., Rollett, A. D., and Ta'asan, S., 2001, An approach to the mesoscale simulation of grain growth, Influences of interface and dislocation behavior on microstructure evolution, (Aindow, M. et al., eds), Mat. Res. Soc. Symp. Proc. 652, Y1.5.

Kinderlehrer, D. and Kowalczyk, M., 2002, Diffusion mediated transport and the flashing rachet, Arch. Rat. Mech. Anal. 161, 149-179.

Kinderlehrer, D. and Tudorascu, A. Transport via mass transport 2006 Discrete and Continuous Dynamical Systems- Series B, 6.2, 311-338

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