Robert J. Gelinas

Sensitivity analysis of ordinary differential equation systems—A direct method

Given a system of time dependent ordinary differential equations, dotyi = fi(c1, c2, …, y1, y2, …, t), where ck are rate parameters, we simultaneously solve for both yi and a set of sensitivity functions, ϱyiϱck, over all times t. These partial derivatives measure the sensitivity of the solution with respect to changes in the parameters ck. Often these parameters are not accurately known. An example is given from atmospheric chemical kinetics using constant as well as time varying (diurnal) rate parameters. For the purposes of this paper, our calculations considered both first- and second-order contributions to Δy with respect to Δc. It is found that second-order sensitivity terms can be highly significant, but tend to be too costly for present widespread application.

Stiff systems of kinetic equations—A practitioner's view☆

Abstract An ever increasing number of current problems in applied science are described by sets of kinetic equations which may suffer from the difficulty known as stiffness when numerical solution of the equations is attempted. In this article the common causes and effects of stiffness are examined from a general users point of view. Generally available measures for alleviating this type of difficulty are indicated. A specialized routine designed specifically for stiff systems (in that it enacts the measures which are discussed herein) is applied to a kinetic model of photochemical smog. Performance of the specialized routine is compared to a standard Adams predictor-corrector method as well as to the results obtained by another standard kinetics code which was originally applied to this model problem. Finally, the admissibility of quasi-steady state assumptions on selected components in this system model is examined.

QUANTUM THEORETICAL DEDUCTION OF RADIATIVE TRANSFER EQUATIONS IN THE SPECTRAL LINE REGIME.

Abstract Radiative transfer equations appropriate to low-temperature astrophysical systems, as well as to other radiating systems, are deduced nonphenomenologically from quantum theoretical foundations. Initially, attention is directed to the formulation of a logically consistent theoretical framework in which finite lifetime effects (as manifest by spectral line shapes of nonzero width) emerge systematically into the structure of radiative transfer equations. Subsequently, we consider reductions to the familiar Plancks Law and the Einstein coefficients as viewed in the context of kinetic equations. Nonequilibrium considerations are also briefly discussed.

A Conceptual Model and Remediation Strategy for Volatile Organic Compounds in Groundwater in Unconsolidated Sediments: A Lawrence Livermore National Laboratory Case Study

Field data collected during the first 7 years of pump-and-treat remediation of groundwater containing volatile organic compounds (VOCs) at the Lawrence Livermore National Laboratory (LLNL) Superfund Site in Livermore, California, indicate that groundwater contaminant plumes at this site can be divided into two distinct parts: source areas and distal areas. In source areas, located in the immediate vicinity of the contaminant releases, the contaminants are distributed in relatively high concentrations throughout the vadose zone and below the water table in both fine-grained and coarse-grained sediments. In distal portions of the plume, downgradient of the source areas, the contaminants: 1) are primarily limited to coarse-grained zones, 2) are usually orders of magnitude lower in concentration than in the source areas, and 3) have slightly diffused into the bordering aquitards but should not significantly affect the approach to or achievement of cleanup goals. The cleanup strategy for this distribution of contaminants calls for the hydraulic isolation of the source area followed by aggressive remediation of both the source and distal areas of the plume as needed to achieve remediation objectives most efficiently. In contrast to some of the currently perceived limitations of pump-and-treat remediation, our data and analyses indicate that distal portions of contaminant plumes can be expeditiously remediated, perhaps in less time than it took the contaminants to be transported to their preremediation locations.

The Moving Finite Element Method: Strong Shock and Penetration Applications

The present work on the moving finite element (MFE) method has been motivated by those challenging problems in non-equilibrium physics which involve the central topics of this workshop: (i) codes; (ii) physical basis and engineering model formulation; (iii) numerical ODE and PDE solution methods; and (iv) large-scale computing hardware and software. In this article, primary emphasis is directed toward problems in blast wave hydrodynamics and in penetration mechanics (although other applications could include radiation transport, plasmas, laser interactions, structural response, combustion, etc.) which have the following common features: such transient non-equilibrium systems can be sufficiently far from equilibrium that their macroscopic properties are strongly coupled to their microscale dissipation processes; one or more shocks/traveling waveforms may propagate and interact at disparate rates; and extremely high levels of resolution (which are frequently out of the reach of fixed node PDE methods) are required in numerous portions of the problem domain.

Thermo‐optical modeling of flashlamp‐pumped Zig‐Zag labs

This article describes the thermo‐optical mechanics of wave front phase distortions in flashlamp‐pumped, convectively cooled zig‐zag slabs. We identify, from both computations and laboratory measurements, the causes of beam phase distortions that are frequently observed in output beams from zig‐zag slabs.

Calculations of dynamic stresses in the envelopes of pulsed Xe flashlamps

We have modeled dynamic stresses in the envelopes of pulsed xenon flashlamps, treating stresses produced by three different sources: the heating of the envelope by the plasma; the pressure rise of the xenon gas; and magnetic forces, due to currents flowing in nearby lamps. The heat-induced stresses were calculated by the finite element method, using uniform heating rates for the inside surface of the envelope that were inferred from flashlamp radiant efficiency measurements. Pressure-induced stresses were calculated analytically, using empirical relationships for temperature and pressure in terms of current density. Magnetically-induced stresses were also calculated analytically, for flashlamps packed parallel to each other in linear arrays.