The Finite-Volume-Particle Method for Conservation Laws

In the Finite-Volume-Particle Method (FVPM), the weak formulation of a hyperbolic conservation law is discretized by restricting it to a discrete set of test functions. In contrast to the usual Finite-Volume approach, the test functions are not taken as characteristic functions of the control volumes in a spatial grid, but are chosen from a partition of unity with smooth and overlapping partition functions (the particles), which can even move along pre­scribed velocity fields. The information exchange between particles is based on standard numerical flux functions. Geometrical information, similar to the surface area of the cell faces in the Finite-Volume Method and the corresponding normal directions are given as integral quantities of the partition functions. After a brief derivation of the Finite-Volume-Particle Method, this work focuses on the role of the geometric coefficients in the scheme

Stochastic Transition States: Reaction Geometry amidst Noise

Classical transition state theory (TST) is the cornerstone of reaction rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space such that it is crossed once and only once by each transition path

Aggregation Dynamics: Numerical Approximations, Inverse Problems, and Generalized Sensitivity

In this dissertation, we investigate several important mathematical and computational issues that arise when using the Smoluchowski coagulation equation as a model for bacterial aggregation. In particular, we study the accuracy and robustness of numerical simulations and their impact upon related inverse problems. We also study how generalized sensitivity enhances experimental design optimization with an ultimate goal of comparing with experimental data. First, we study the impact of discretization strategy on the accuracy of solution moment. We perform this investigation in anticipation of comparing with different distributions moments reported by specific experimental devices. For multiplicative aggregation kernels, finite volume methods are superior to finite element methods both in accuracy and computational effort. Conversely, for slowly aggregating systems the finite element approach can produce as little error as the finite volume approach and achieves more accuracy approximating the zeroth moment (at a substantially reduced computational cost). A better understanding of bacterial aggregation dynamics could also lead to improvements in the treatment of bacterially mediated, life-threatening human illnesses. Therefore, to reach towards our ultimate goal, we examine the inverse problem of estimating the aggregation rate from experimental data. In this study, we develop a methodology for a software implementation of parameter fitting when solving inverse problems involving the Smoluchowski coagulation equation. Additionally, we make the novel extension of generalized sensitivity functions (GSFs) for ordinary differential equations to GSFs for partial differential equations. We analyze the GSFs in the context of size-structured population models, and specifically analyze the Smoluchowski coagulation equation in order to determine the most relevant time and volume domains for three, distinct aggregation kernels. Finally, we provide evidence that parameter estimation for the Smoluchowski coagulation equation does not require post-gelation data

Acceptance test report MICON software exhaust fan control

This test procedure specifies instructions for acceptance testing of software for exhaust fan control under Project ESPT (Energy Savings Performance Contract). The software controls the operation of two emergency exhaust fans when there is a power failure. This report details the results of acceptance testing for the MICON software upgrades. One of the modifications is that only one of the emergency fans will operate at all times. If the operating fan shuts off or fails, the other fan will start and the operating fan will be stopped

Metamorphism of CO and CO-like chondrites and comparisons with type 3 ordinary chondrites

In order to explore their metamorphic history, thermoluminescence data have been obtained for 10 CO or CO-related chondrites from the Antarctic. Six have TL properties indicating low to intermediate levels of metamorphism, while Lewis Cliff 85332 and three paired meteorites from MacAlpine Hills (87300,87301 and 88107) have unusual TL properties similar to those of the very primitive Colony and Allan Hills A77307 CO-related chondrites. Cathodoluminescence photomosaics of nine well-studied CO chondrites are also presented and compared with similar data for the type 3 ordinary chondrites in which CL properties vary systematically with metamorphism. It is concluded that the CO chondrites, like the ordinary chondrites, form a metamorphic sequence and may be subdivided in an analogous manner using TL, CL and other petrographic and compositional data. Definitions for CO chondrites of the petrologic types 3.0-3.9 are proposed. However, it is stressed that the thermal history of the CO and ordinary chondrites is quite different, the range of equilibration for the CO chondrites is similar to the ordinary chondrites, but the former have not experienced temperatures above those experienced by type 3.5 ordinary chondrites (probably around 600℃). Presumably the CO chondrites spent longer times at lower temperatures. A CL photomosaic of Murchison is also presented, which has two features in common with the type 3.0-3.1 CO and ordinary chondrites; type I chondrules whose mesostases produce yellow CL (due to an unidentified but highly metamorphism-sensitive phase) and fine-grained matrix with red CL due to forsterite. Haloes of matrix material around chondrules and other objects in Murchison are thought to be due to aqueous destruction of those objects, and Fezoning in olivines in chondrules with broad haloes is also throught to be due to aqueous processes