David Kinderlehrer

Alumni Professor of Mathematical Sciences and Professor of Materials Science and Engineering
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)!  Glance at the 200 word summary Microstructure meets Boltzmann  for 11-CNA-001.  By the way, have a weakness for Las Vegas? Try Heath, Kinderlehrer and Kowalczyk. 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, Katayun Barmak, Maria Emelianenko, Eva Eggeling, Yekaterina Epshteyn and Richard Sharp. 

Recent CNA Publications

• 11-CNA-001, An Entropy Based Theory of the Grain Boundary Character Distribution , Katayun Barmak, E. Eggeling, Maria Emelianenko, Yekaterina Epshteyn, David Kinderlehrer, Richard Sharp, Shlomo Ta'asan, (download paper)

• 10-CNA-014, Critical Events, Entropy, and the Grain Boundary Character Distribution , Katayun Barmak, E. Eggeling, Maria Emelianenko, Yekaterina Epshteyn, David Kinderlehrer, Richard Sharp, (download paper)

• 10-CNA-013, Predictive Theory for the Grain Boundary Character Distribution , Katayun Barmak, E. Eggeling, Maria Emelianenko, Yekaterina Epshteyn, David Kinderlehrer, Richard Sharp, Shlomo Ta'asan, (download paper)

• 10-CNA-012, Grain Growth and the Puzzle of its Stagnation in Thin Films: A Detailed Comparison of Experiments and Simulations , Katayun Barmak, Kevin Coffey, E. Eggeling, David Kinderlehrer, Scott Roberts, Anthony D. Rollett, Richard Sharp, Terry Shyu, Tik Sun , Shlomo Ta'asan, Bo Yao, (download paper)

• 08-CNA-015, Contraction in $L^{1}$ and large time behavior for a system arising in chemical reactions and molecular motors , Michel Chipot, Danielle Hilhorst, David Kinderlehrer, Michał Ołech, (download paper)

• 08-CNA-002, The Janossy effect and hybrid variational principles , David Kinderlehrer, Michal Kowalczyk, (download paper)

• 07-CNA-005, On a Statistic Theory of Critical Events in Microstructural Evolution , Katayun Barmak, Maria Emelianenko, Dmitry Golovaty, David Kinderlehrer, Shlomo Ta'asan, (download paper)

• 07-CNA-002, Diffusion Mediated Transport with a Look at Motor Proteins , Stuart Hastings, David Kinderlehrer, Bryce McLeod, (download paper)

• 06-CNA-013, Diffused Mediated Transport in Multiple State Systems , Stuart Hastings, David Kinderlehrer, Bryce McLeod, (download paper)

• 06-CNA-011, Texture Evolution Via Continuous Time Random Walk Theory , Maria Emelianenko, Dmitry Golovaty, David Kinderlehrer, Shlomo Ta'asan, (download paper)

All CNA Publications

Selected Publications (see also 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