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General Description · Committee is standing · Number of members is four or five · Term is four years · Principal Activities This Editorial Committee is charged with selecting for publication by the AMS books which exposit research-level mathematics of current interest to the mathematical community. These books are frequently suitable as texts for an… (More)
Evolution and trend to equilibrium of a (planar) network of grain boundaries subject to curvature driven growth is established under the assumption that the system is initially close to some equilibrium configuration. Curvature driven growth is the primary mechanism in processing polycrystalline materials to achieve desired texture, ductility, toughness,… (More)
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.
The flashing rachet is the simplest example of diffusion mediated transport as well as the suggested mechanism for a class of protein motors. Here we briefly explain these concepts and give an entropy based argument for existence and uniqueness of a model problem. We also examine the features of the system that lead to transport
In this note we discuss transport properties of weakly coupled parabolic systems of evolution equations. These arise in the study of molecular motors, like conventional kinesin, which are responsible for eukaryotic intracellular transport. It falls under the rubric of what we call diffusion mediated transport. Diffusion mediated transport generally concerns… (More)
We construct weak global in time solutions to the classical Keller-Segel system describing cell movement by chemotaxis in two dimensions when the total mass is below the established critical value. Our construction takes advantage of the fact that the Keller-Segel system can be realized as a gradient flow in a suitable functional product space. This allows… (More)