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Relativistic density functional theory in the full potential linear muffin tin orbital method
In this write-up, we have outlined the general methodology for treating relativity in the FP-LMTO method. The Schrodinger equation is insufficient for describing the physics of heavy elements because it leaves out any relativistic effects. Therefore DFT based on the Schrodinger equation is not sufficient for studying heavy materials. It is, however, possible to incorporate all of the effects of relativity in DFT if starting with a reformulation of the Hohenberg-Kohn theorem that proceeds from the Dirac equation, rather than the Schrodinger equation. The corresponding theorem in relativistic density functional theory (RDFT) shows that the ground-state density of the system is a functional of not only the charge density as in Schrodinger-based DFT, but also of the current density. This leads to a more elaborate procedure in practice when solving the Dirac-Kohn-Sham equations, the relativistic analogs of the Kohn-Sham equations.
Residue Specific Characterization of Electrostatics, Conformational Heterogeneity, and Dynamics of Electron Transfer Proteins with Linear and Nonlinear Infrared Spectroscopy. Final Report
The goal of this research project was to further our understanding of biological electron transfer through the development and application of new methods for studying proteins and their complexes with high spatial and temporal detail. The approach was based on incorporation of reporter bonds with distinct vibrational frequencies at specific locations in proteins and their characterization through the interaction of the bonds with pulses of infrared light. The project focused on the proteins plastocyanin (Pc) and cytochrome (cyt) f, two electron transfer partners in photosynthesis. The first thrust of the project was the incorporation of carbon deuterium bonds as non-perturbative probes at a ligand to the copper ion of Pc and their use to detect changes in the bonding due to the number of electrons at the metal and how the bonding changes upon association with cyt f. Toward developing more advanced approaches to characterize proteins, we incorporated a stronger reporter, the cyano group of cyanophenylalanine, at several locations in Pc and measured the frequency dynamics in the absence and presence of cyt f. The acquired data improved the current model for the protein complex. Notably, the data indicated that the majority of the population is involved in a loosely bound complex, providing insight into the nature of the ensembles formed by electron transfer protein complexes that is not available via other approaches. In addition to learning about the protein complex, we made strides toward developing and improving the new experimental approach to study highly dynamic behaviors of proteins.
Beam breakup in a solid state powered linear induction accelerator
It has been proposed to use solid-state pulsed-power modules to power the new Scorpius accelerator. Since this highcurrent accelerator would have 360 gaps (more than five times the number of cells as present radiography LIAs), it is natural to be concerned about the beam-breakup (BBU) instability. Earlier calculations of this effect used a half-scale model of the accelerator to avoid the limitation to 200 gaps in the code. We have now updated the code to accommodate the extraordinary number of gaps in this proposed LIA. The results of these early simulations are presented here. They indicate that BBU can only be suppressed to the same level as in designs powered by conventional pulsed power, if the calculated cell impedance can truly be achieved in practice. The magnetic focusing field required for this is of the same order as the field required for a conventionally powered LIA only if the transverse impedance can indeed be constrained to the values obtained in some simulations of the cell.
The arbitrary-order virtual element method for linear elastodynamics models. Convergence, stability and dispersion-dissipation analysis.
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under $\textit{h}$-refinement in both the energy and the $L^2$ norms, and optimal error estimates under $\textit{p}$-refinement in the energy norm. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semi-discrete and fully-discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.
The virtual element method for linear elastodynamics models: Design, analysis, and implementation
We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the L 2 norm. The performance of the virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally seen in the p-refinement setting.
Extending Petsc's Composable Hierarchically Nested Linear Solvers
The Contributions from the RELACS group at both Rice University and the University at Buffalo in this phase of the PETSc Composable Solvers effort have centered around four main areas: scalable mesh processing, mesh adaptivity, solvers for subsurface flow, and performance modeling. The prominence of mesh processing demonstrates the tight relationship between meshing and discretization on the one hand, and optimal solvers on the other. All optimal solvers that we consider depend on some notion of hierarchy, and we express this using the DMPlex abstraction in PETSc. This relationship demands tight integration between the DM and SNES/TS components in PETSc that is the foundation of much of this work. In addition, interpretation of performance results for scalable solvers necessitates that information from the discretization and solver enter the performance model. Without this, comparing different solvers can be a fruitless exercise. Some major accomplishment of the past three years in these areas include: scalable mesh loading in PETSc on more than 10K cores, integrated mesh adaptivity using both p4est and Pragmatic, scalable multigrid for DG discretizations of subsurface flow, and predictive performance modeling incorporating error estimates.
Effects of HEX-SCW field errors on linear optics and orbit
Abstract not provided.
Quantum Linear Systems Problem [Slides]
Abstract not provided.
Mixed Precision Numerical Linear Algebra (Final Report)
The objective of this subcontract was to identify opportunities for the use of mixed precision within iterative solvers and to explore these opportunities both theoretically and experimentally. All quarterly milestones were achieved. We summarize the achievements each quarter in sections below.
Linearized three-phase optimal power flow models for distribution grids [Slides]
Abstract not provided.
Modeling Temporal Spot Size Evolution on a Linear Induction Accelerator
This is for the IEEE ICOPS 2021 Virtual Conference, scheduled for September 12-16, 2021. Michael Weller will be giving a virtual talk. Website found here: http://ece-events.unm.edu/icops2021/index.html
The EGRET Library Of Unit Commitment and Economic Dispatch Models and Methods For Large-scale Linear OPF.
Abstract not provided.
3D Printed Linear Shaped Charges [Slides]
Abstract not provided.
Task Force Report: ESR Linear Lattice Design
A new layout and optics for the Electron Storage Ring (ESR) have been produced with revised spin rotators in IRs 6 and 8, a redesign of IR10, and a new geometric layout for the ring. In this report, the efforts to produce this lattice are documented, including the motivation for design decisions. This new lattice, version 5.5, will be used as the baseline for future studies.
High power superconducting electron linear accelerators for industrial applications: Technology development and experimental results at Fermilab
Explore the source record for details and available documents.
Innovative applications of block preconditioning and fast linear solvers [Slides]
The goal is to apply principles of linear/nonlinear solvers to lab applications.