Prairie
Analysis Seminar 2015



Fri
afternoon
Previous Prairie Seminars 
Department of Mathematics
Kansas State University Manhattan, Kansas September 2526, 2015 David KinderlehrerCarnegie Mellon UniversityLecture 1: Introducing mass transport Abstract: Elements of mass transport. Description of solving equations by the implicit scheme  the Jordan, K, Otto problem of convergence, summarizing the flow interchange work of MatthesMcCannSavare’ to the special case of FokkerPlanck. Lecture 2: Evolution of material microstructure and the discovery of the grain boundary character distribution Abstract: Background of the issue. The theory of the grain boundary character distribution. Validation of the theory and perhaps a better dissipation relation. Invited Speakers: Robert McCann University of Toronto Title: The intrinsic dynamics of optimal transport Abstract: The question of which costs admit unique optimizers in the MongeKantorovich problem of optimal transportation between arbitrary probability densities is investigated. For smooth costs and densities on compact manifolds, the only known examples for which the optimal solution is always unique require at least one of the two underlying spaces to be homeomorphic to a sphere. We introduce a (multivalued) dynamics which the transportation cost induces between the target and source space, for which the presence or absence of a sufficiently large set of periodic trajectories plays a role in determining whether or not optimal transport is necessarily unique. This insight allows us to construct smooth costs on a pair of compact manifolds with arbitrary topology, so that the optimal transportation between any pair of probability densities is unique. Yekaterina Epschtein The University of Utah Title: Grain boundary character distribution and mass transport paradigm Abstract: Cellular networks are ubiquitous in nature. Most technologically useful materials arise as polycrystalline microstructures, composed of a myriad of small crystallites, or grains, separated by interfaces, or grain boundaries. The energetics and connectivity of the grain boundaries network plays a crucial role in determining the properties of a material across a wide range of scales. Coarsening, or growth process is influenced ainly by the effort of the system to decrease the interfacial energy subject to spatial constraints. The recently discovered Grain Boundary Character Distribution (GBCD) indicates that the boundary network of a cellular structure, and, more generally, material texture has a natural order. Grain Boundary Character Distribution (GBCD) is a new characterization of the texture which is found to be strongly correlated to the interfacial energy. In this talk GBCD is introduced and investigated by the use of a large scale simulations and mathematical analysis. We present the simplified critical event model and discuss an entropy based theory based on mass transport and a KantorovichRubinsteinWasserstein metric to suggest that, to first approximation, the GBCD behaves like the solution to a FokkerPlanck Equation. This is joint work with K. Barmak, P. Bardsley, E. Eggeling, M. Emelianenko, D.Kinderlehrer, R. Sharp, and S. Ta'asan. Contributed Talks: There will be time allocated for short contributed talks by participants. Priority will be given to graduate students and those in early stages of their careers. Participants interested in given a contributed talk and/or receiving financial support should visit the registration page, or email Marianne Korten. Organizers: Nathan Albin, KSU Estela A. Gavosto, KU Marianne Korten, KSU Charles Moore, WSU Rodolfo H. Torres, KU Contact Information: marianne@math.ksu.edu, lecronjs@math.ksu.edu 
This conference is supported by the National Science
Foundation (NSF) and by the KSU Mathematics Department through the
Isidore and Hilda Dressler Endowment for the Enrichment
of Mathematics. The Prairie Analysis Seminar is a joint project of the Department of Mathematics of Kansas State University and the Department of Mathematics of the University of Kansas. 