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Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems. 1991 Mathematics… (More)

- David Kinderlehrer, YOUNG MEASURES, Pablo Pedregal
- 2015

- Stuart Hastings, David Kinderlehrer, John Bryce McLeod
- SIAM J. Math. Analysis
- 2007

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical motion. Nanoscale motors like kinesins tow organelles and other cargo on microtubules or filaments, have a role separating the mitotic spindle during the cell cycle, and perform many other functions. The simplest description gives rise… (More)

We establish a new and intriguing connection between the FokkerPlanck equation with gradient drift term and an associated free energy functional. Namely, we demonstrate that such a Fokker-Planck equation may be interpreted as a gradient flux, or a steepest descent, of a free energy functional with respect to a certain metric. This is accomplished through… (More)

- MICHEL CHIPOT, DAVID KINDERLEHRER, MICHAL KOWALCZYK, PIERO VILLAGGIO
- 2002

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical motion. Muscle myosin has been known since the mid nineteenth century and its role in muscle contraction demonstrated by A. F. Huxley and H. E. Huxley in the 1950's. Kinesins and their role in intracellular transport were discovered… (More)

A mesoscale, variational simulation of grain growth in two-dimensions has been used to explore the effects of grain boundary properties on the grain boundary character distribution. Anisotropy in the grain boundary energy has a stronger influence on the grain boundary character distribution than anisotropy in the grain boundary mobility. As grain growth… (More)

- David Kinderlehrer, Irene Livshits, Shlomo Ta'asan
- SIAM J. Scientific Computing
- 2006

Most technologically useful materials arise as polycrystalline microstructures, composed of a myriad of small crystallites, called grains, separated by their interfaces, called grain boundaries. The orientations and arrangements of the grains and their network of boundaries are implicated in many properties across wide scales, for example, functional… (More)

The resolution of transport equations is shown to be intimately related to the Monge-Kantorovich optimal mass transportation theory. Existence results for linear systems of transport equations in divergence form are given at the end of the paper.

- Katayun Barmak, Wayne E. Archibald, Anthony D. Rollett, Shlomo Ta’asan, David Kinderlehrer
- 2004

Relative grain boundary energy as a function of misorientation angle has been measured in cube-oriented, i.e., <100> fiber-textured, 120 μm-thick Al foil using orientation imaging microscopy and a statistical multiscale method. The energies of low-angle boundaries increase with misorientation angle, in good agreement with the Read-Shockley model. The… (More)

Diffusion mediated transport is a phenomenon in which a unidirectional motion of particles is achieved as a result of two opposing tendencies: diffusion, which spreads the particles uniformly through the medium and transport, which concentrates the particles at some special sites. The flashing ratchet version of the Brownian motor, a simple model for… (More)