Using Dynamic Quantum Clustering to Analyze Structure of Hierarchically Heterogeneous Samples at the Nanoscale Allison Hume Mentor: Marvin Weinstein

Problem: Interface of materials Sample data: Roman pottery – Red and Black colors are from different iron oxides Similar problems: – Lithium-ion batteries – Catalyst breakdown

Data X-ray Absorption Near Edge Structure (XANES) for each pixel: 30nm resolution Large field of view: half a million data points Can DQC be used for this data? Spectrum of a pixel Florian Meirer, ProtoSig1_a1_Clustering_Analysis_report_v2

Singular Value Decomposition Original Curve

Singular Value Decomposition Curve Reconstructed from first N Components N = 5

Singular Value Decomposition Curve Reconstructed from first N Components N = 30

Singular Value Decomposition N = 70 Curve Reconstructed from first N Components

Singular Value Decomposition N = 146 Curve Reconstructed from first N Components

DQC: Modeling the Data Each data point is a 5-dimensional Gaussian Data set is sum of Gaussians: M. Weinstein, D. Horn. Dynamic quantum clustering: a method for visual exploration of structures in data. Physical Review E 2009 (80)

DQC: a QM Problem Composite function is ground state of Hamiltonian Define potential according to time- independent Schrodinger equation: M. Weinstein, D. Horn. Dynamic quantum clustering: a method for visual exploration of structures in data. Physical Review E 2009 (80)

Clustering Process:

Data collapses into clumps and strands

Clustering Process: Data collapses into clumps and strands

Clustering Process: Some strands collapse to points, others remain

Clustering Process: Some strands collapse to points, others remain

Clustering Process: Separation continues

Clustering Process: Separation continues

Clustering Process: Separation continues

Identifying Clusters

Recreate the Picture F. Meirer, Y. Liu, A. Mehta. Mineralogy and morphology at nanoscale in hierarchically heterogeneous materials. June 24, 2011.

Spectra Iron phases Hercynite phases Hematite

Importance of Sub-clustering Sub-clusters of blue show big difference in shape – revealing the existence of Iron

Conclusion

Special Thanks to: Marvin Weinstein Apurva Mehta David Horn Florian Meirer Yijin Liu DOE & SLAC Steve Rock & SULI Program

DQC vs. Gradient Descent D. Horn, A. Gottlieb. Algorithm for Data Clustering in Pattern Recognition Problems Based on Quantum Mechanics. Physical Review Letters 2001 (88)