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At least 55 records · Page 3

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition” [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An atomic orbital-based formulation of the complete active space self-consistent field method on graphical processing units

Despite its importance, state-of-the-art algorithms for performing complete active space self-consistent field (CASSCF) computations have lagged far behind those for single reference methods. We develop an algorithm for the CASSCF orbital optimization that uses sparsity in the atomic orbital (AO) basis set to increase the applicability of CASSCF. Our implementation of this algorithm uses graphical processing units (GPUs) and has allowed us to perform CASSCF computations on molecular systems containing more than one thousand atoms. Additionally, we have implemented analytic gradients of the CASSCF energy; the gradients also benefit from GPU acceleration as well as sparsity in the AO basis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An atomic orbital-based formulation of analytical gradients and nonadiabatic coupling vector elements for the state-averaged complete active space self-consistent field method on graphical processing units

We recently presented an algorithm for state-averaged complete active space self-consistent field (SA-CASSCF) orbital optimization that capitalizes on sparsity in the atomic orbital basis set to reduce the scaling of computational effort with respect to molecular size. Here, we extend those algorithms to calculate the analytic gradient and nonadiabatic coupling vectors for SA-CASSCF. Combining the low computational scaling with acceleration from graphical processing units allows us to perform SA-CASSCF geometry optimizations for molecules with more than 1000 atoms. The new approach will make minimal energy conical intersection searches and nonadiabatic dynamics routine for molecular systems with O(10{sup 2}) atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability

The magnetic-Rayleigh–Taylor (MRT) instability is a ubiquitous phenomenon that occurs in magnetically-driven Z-pinch implosions. It is important to understand this instability since it can decrease the performance of such implosions. In this work, I present a theoretical model for the weakly nonlinear MRT instability. I obtain such a model by asymptotically expanding an action principle, whose Lagrangian leads to the fully nonlinear MRT equations. After introducing a suitable choice of coordinates, I show that the theory can be cast as a Hamiltonian system, whose Hamiltonian is calculated up to the sixth order in a perturbation parameter. The resulting theory captures the harmonic generation of MRT modes. It is shown that the amplitude at which the linear magnetic-Rayleigh–Taylor instability exponential growth saturates depends on the stabilization effect of the magnetic-field tension. Overall, the theory provides an intuitive interpretation of the weakly nonlinear MRT instability and provides a systematic approach for studying this instability in more complex settings.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

HSCT Assessment Calculations with the AER 2-D Model: Sensitivities to Transport Formulation, PSC Formulation, Interannual Temperature Variation

The summary are: (1) Some chemical differences in background atmosphere are surprisingly large (NOY). (2) Differences in model transport explain a majority of the intertnodel differences in the absence of PSCs. (3) With PSCS, large differences exist in predicted O3 depletion between models with the same transport. (4) AER/LLNL model calculates more O3 depletion in NH than LLNL. (5) AER/GSFC model cannot match calculated O3 depletion of GSFC model in SH. and (6) Results sensitive to interannual temperature variations (at least in NH).

Weisenstein, Debra K.↗

Formulation and Characterization of Waste Glasses with Varying Processing Temperature

This report documents the preliminary results of glass formulation and characterization accomplished within the finished scope of the EM-31 technology development tasks for WP-4 and WP-5, including WP-4.1.2: Glass Formulation for Next Generation Melter, WP-5.1.2.3: Systematic Glass Studies, and WP-5.1.2.4: Glass Formulation for Specific Wastes. This report also presents the suggested studies for eventual restart of these tasks. The initial glass formulation efforts for the cold crucible induction melter (CCIM), operating at {approx}1200 C, with selected HLW (AZ-101) and LAW (AN-105) successfully developed glasses with significant increase of waste loading compared to that is likely to be achieved based on expected reference WTP formulations. Three glasses formulated for AZ-101HLW and one glass for AN-105 LAW were selected for the initial CCIM demonstration melter tests. Melter tests were not performed within the finished scope of the WP-4.1.2 task. Glass formulations for CCIM were expanded to cover additional HLWs that have high potential to successfully demonstrate the unique advantages of the CCIM technologies based on projected composition of Hanford wastes. However, only the preliminary scoping tests were completed with selected wastes within the finished scope. Advanced glass formulations for the reference WTP melter, operating at {approx}1200 C, were initiated with selected specific wastes to determine the estimated maximum waste loading. The incomplete results from these initial formulation efforts are summarized. For systematic glass studies, a test matrix of 32 high-aluminum glasses was completed based on a new method developed in this study.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A novel matching formulation for startup costs in unit commitment

Here we present a novel formulation for startup cost computation in the unit commitment problem (UC). Both our proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. Our proposed formulation is tested empirically against existing formulations on large-scale UC instances drawn from real-world data. While requiring more variables than the current state-of-the-art formulation, our proposed formulation requires fewer constraints, and is empirically demonstrated to be as tight as a perfect formulation for startup costs. This tightening can reduce the computational burden in comparison to existing formulations, especially for UC instances with large reserve margins and high penetration levels of renewables.

97 MATHEMATICS AND COMPUTING↗