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1 Dedication Dedicated to the memory of Richard Duun. Abstract The Fokker{Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic diierential equation. It pertains to a wide variety of time{dependent systems in which randomness plays a role. In this paper,(More)
The Fokker–Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of time-dependent systems in which randomness plays a role. In this paper, we are concerned with Fokker–Planck equations for which the(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)
  • Victor W.Guillemin, David Kinderlehrer, Marc A.Rieffel, Bhama Srinivasan, Robert E.Greene, David W.McLaughlin +3 others
  • 2015
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)
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)
We prove a contraction in L 1 property for the solutions of a nonlin-ear reaction–diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary solutions we show that the solutions stabilize as t tends to infinity. Moreover, in the special case of linear reaction terms, we(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)