This special Physics department colloquium is scheduled for Wednesday 7/13/16 at 2:00 PM in the Kenwood Interdisciplinary Research Complex (KIRC) Room KEN 1140. Coffee and cookies will be available in KEN 3118 (third floor kitchenette located next to the elevators) at 3:00 PM. Anyone is welcome.

Symmetry and the Reconstruction of Particle Structure in an X-ray Free Electron Laser (XFEL)
Sandi Wibowo, PhD Candidate/UWM Dept. of Physics

The problem of determining the structure of a biomolecule, when all the evidence from experiment consists of individual diffraction patterns from random particle orientations, is the central theoretical problem with an XFEL. One of the methods proposed is a calculation over all measured diffraction patterns of the average angular correlations between pairs of points on the diffraction patterns. It is possible to construct from these a matrix B characterized by angular momentum quantum number l, and whose elements are characterized by radii q and q’ of the resolution shells. If matrix B is considered as dot product of vectors, which magnetic quantum number m is the component, singular value of B reveals the number of magnetic quantum numbers in the spherical harmonics expansion. What is shown in this paper is dependency of magnetic quantum number on symmetry can be associated to lowest independent parameter to describe symmetry. At the very least, this determines information about particle symmetry from experiment data, independent of any assumed symmetry. An equally important point is that matrix B provides a means of reconstructing diffraction volume. This can be done by formulating intensity and matrix B as linear equation. Lastly, positivity constraint and optimization method is used to construct diffraction volume and phase is determined from phasing algorithm.