epshteyn (at) math.utah.edu)
Welcome Back Meeting
Speaker: Masashi Mizuno, Department of Mathematics, Nihon University, Japan
Title: Grain boundary motion with time-dependent misorientation and mobility effects
Abstract: In my talk, I will present a model of grain boundary motion with time-dependent misorientation and mobility effects. Dynamics of grain boundaries play an important role in defining the materials properties of polycrystals. The model, considered in the talk, is given by the system of partial differential equations, and is derived using energetic variational principle. Next, I will present the analysis of the model for the grain boundary motion. The key ingredient of the analysis is the so-called monotonicity formula of Huisken's type. Moreover, to treat the time-dependent mobility, we use the modified Gauss kernel to the monotonicity formula.
Speaker: Tom Alberts, Department of Mathematics, University of Utah
Title: Random Matrix Theory for Homogenization of Composites on Graphs
Abstract: I will discuss the random matrix theory behind two-component random resistor networks on general graphs. This involves random submatrices of the graph's Gamma projection operator, with the particular realization of the submatrix determined by the disorder of the conductances. Certain combinations of graph symmetries together with different models for the random conductances lead to exactly computable spectral statistics. Our recent results lead to exact spectral statistics for the uniform spanning tree model on a diamond hierarchical lattice. Joint work with Ken Golden, Elena Cherkaev, Ben Murphy, Han Le.
Speaker: Andrejs Treibergs, Department of Mathematics, University of Utah
Title: Compatibility Conditions for Discrete Planar Structures
Abstract: The nonlinear and linearized equations for the state of a planar material with prescribed strain are overdetermined PDE's. To be solvable, the strains must satisfy the necessary compatibility conditions. Approximations of the material by discrete network satisfy overdetermined algebraic equations whose compatibility conditions are less well understood. For generic networks, the number of compatibility conditions is given by the Maxwell number which is a measure of the resilience of a network to damage. It can be easily computed for triangulated networks. We will give a geometric description for the compatibility conditions, discuss which networks are generic, explain why the discrete problems approximate the continuous ones and consider boundary integrals over regions satisfying the compatibility conditions.
Speaker: Graeme Milton, Department of Mathematics, University of Utah
October 29. Note day is Tuesday and Time is 3pm - 4pm. Room
is LCB 225.
Speaker: Jeffrey Rickman, Department of Materials Science and Engineering, Lehigh University
Speaker (Invited by Graeme Milton): Yekaterina Epshteyn, Department of Mathematics, University of Utah
Speaker: Junshan Lin, Department of Mathematics, Auburn University
epshteyn (at) math.utah.edu).
Past lectures: Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.