1 / 2

0812204_Boettcher

New Numerical and Theoretical Methods to Analyze Disordered Materials Stefan Boettcher, Emory University, DMR 0812204.

darryl
Download Presentation

0812204_Boettcher

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. New Numerical and Theoretical Methods to Analyze Disordered MaterialsStefan Boettcher, Emory University, DMR 0812204 Further refinements of the Extremal Optimization (EO) heuristic (developed under DMR-#0312510) has allowed us to probe deep into the structure of the complex energy landscape for spin glasses, and many other NP-hard combinatorial problems. As the archetypical model of disorder, spin glasses provide useful benchmarks for algorithmic testing as well as a foundation for many real-world applications, such as for amorphous materials or neural networks. In this figure, simulations of the Sherrington-Kirkpatrick spin glass reproduce the exactly known Parisi energy (blue arrow) to 0.01% accuracy and provide information down to 2nd-order corrections, see JSTAT, P07002(‘10). Five other glassy models are studied there for their thermodynamic properties, finite-size corrections, and extreme-value statistics. Similar studies for the lattice (Edward-Anderson) spin glasses are ongoing.

  2. New Numerical and Theoretical Methods to Analyze Disordered MaterialsStefan Boettcher, Emory University, DMR 0812204 The success of EO for spin glasses has initiated a number of applications with this optimization heuristic by scientists and engineers throughout the world. These range from the efficient design of cooling elements, optimized satellite trajectories, image alignment, molecular structures, etc. As a result, I have been called to disseminate this research as an invited speaker at several conferences, such as “Physics of Algorithms” in Santa Fe (NM), Sept. ‘09, “Application of Network Science” in Denton (TX), Jan. ‘10, or “Computational Interdisciplinary Science” in Brazil, Aug. ‘10. The EO-data (below) lead to a collaboration with Lenka Zdeborova (LANL) that revealed an unexpected commonality between a vast class of NP-hard combinatorial problems on regular graphs, which share the same thermodynamic limit (red line). Glasses with all (ρ=1) or no AF bonds (ρ=0), or any mix in-between, share the same ground-state energy at zero magnetization. This finding unifies, e.g., graph bipartitioning with the max-cut problem, see JSTAT, P02020 (‘10).

More Related