Keyword Suggestions

NN1.01 - A Theory and Challenges for Coarsening in Microstructure 
December 1, 2014   8:30am - 9:00am

Cellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. The grain boundary character distribution (GBCD) is an empirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misorientation and normal. During the coarsening, or growth, process, an initially random grain boundary arrangement reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, if the given energy density depends only on lattice misorientation, then the steady state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest non-random distributions, corresponding to independent trials with respect to the energy. Why does such simplicity emerge from such complexity?

Here we describe an entropy based theory which suggests that the evolution of the GBCD satisfies a Fokker-Planck Equation, an equation whose stationary state is a Boltzmann distribution. The properties of the evolving network that characterize the GBCD must be identified and appropriately upscaled or `coarse-grained'. This entails identifying the evolution of the statistic in terms of the recently discovered Monge-Kantorovich-Wasserstein implicit scheme. The undetermined diffusion coefficient or temperature parameter is found by means of a convex optimization problem reminiscent of large deviation theory.
Joint work with K. Barmak (Columbia), M. Emelianenko (George Mason). Y. Epshteyn (Utah), R. Sharp (Globys), and S. Ta'asan (CMU)

Average Rating: (No Ratings)
  Was great, surpassed expectations, and I would recommend this
  Was good, met expectations, and I would recommend this
  Was okay, met most expectations
  Was okay but did not meet expectations
  Was bad and I would not recommend this

Performance Enhancement of Pentacene Based Organic Field-Effect Transistor through DNA Interlayer
Semiconducting Polymer-Dipeptide Nanostructures by Ultrasonically-Assisted Self-Assembling
DNA as a Molecular Wire: Distance and Sequence Dependence
Structure-Property Relationship in Biologically-Derived Eumelanin Cathodes Electrochemical Energy Storage
Artificial Physical and Chemical Awareness (proprioception) from Polymeric Motors