Two‐dimensional dispersion analyses of finite element approximations to the shallow water equations

Dispersion analysis of discrete solutions to the shallow water equations has been extensively used as a tool to define the relationships between frequency and wave number and to determine if an algorithm leads to a dual wave number response and near 2Δx oscillations. In this paper, we explore the application of two‐dimensional dispersion analysis to cluster based and Galerkin finite element‐based discretizations of the primitive shallow water equations and the generalized wave continuity equation (GWCE) reformulation of the harmonic shallow water equations on a number of grid configurations. It is demonstrated that for various algorithms and grid configurations, contradictions exist between the results of one‐dimensional and two‐dimensional dispersion analysis as a result of subtle changes in the mass matrix. Numerical experiments indicate that the two‐dimensional dispersion analysis correctly predicts the existence and onset of near 2Δx noise in the solution. Copyright © 2004 John Wiley & Sons, Ltd.     

Photolytic dechlorination of 4-chlorophenol in O2-saturated aqueous solutions in the absence of photocatalysts or additives using ArF (193 nm) and KrF (248 nm) excimer lasers

One of the toxic products from chlorine bleaching of wood pulp is 4-chlorophenol (4-CP). Detoxification of such compounds usually requires their dechlorination. The present study involves a fairly detailed comparison of the attempt and success of the photolytic dechlorination of 4-CP in O₂-saturated aqueous solutions using ArF^* (193 nm) and KrF^* (248 nm) excimer laser radiation at higher (1.1 × 10⁻² M) and lower (4.5 × 10⁻⁴ M) starting substrate concentrations and comparisons of quantum yield (φ), product distributions, etc.

At the higher starting substrate concentration (1.1 × 10⁻² M) the average initial quantum yields, i.e. early in the reaction process, for the disappearance of 4-CP (φ ≈2 0.30) and for the generation of chloride ions (φ ≈2 0.25) were about the same for both 193 and 248 nm radiation. However, when the number of photons absorbed (n) became greater than about 3 × 10²⁰, more chloride ions (higher φ) were generated with the 193 nm radiation than with the 248 nm radiation. Oligomers were the major products for both wavelengths of radiation, but the quantity of oligomers generated was greater using the 193 nm radiation. At 248 nm a significant amount of hydroquinone was generated, whereas hydroquinone was not detected with the 193 nm radiation. In addition, a significant amount of 4-chlorocatechol was generated during the direct photolysis of 4-CP using either wavelength of radiation. This is a new result for the photolysis of 4-CP at a wavelength longer than 193 nm in the absence of added H₂O₂.

At the lower starting substrate concentration (4.5 × 10⁻⁴ M) the average initial quantum yields for the disappearance of 4-CP (φ ≈2 0.55) and for the generation of chloride ions (φ ≈2 0.45) were both much greater using the 193 nm radiation than with the 248 nm radiation and 0.10 respectively). At 193 nm oligomers were still the major products generated, but the fraction of oligomeric products generated was less than the fraction at the higher substrate concentration. This is consistent with the fact that at the lower substrate concentration a significant amount of hydroquinone was generated at 193 nm, whereas it was not detected at this wavelength for the higher substrate concentration. During the 248 nm photolysis of 4-CP at this lower starting substrate concentration, hydroquinone was the only major product generated in these experiments. Oligomers were not observed at this lower substrate concentration using 248 nm radiation, whereas oligomers were generated at the higher substrate concentration.

The results demonstrate the utility of using an excimer laser for the photolytic dechlorination of 4-CP without added photocatalysts or additives. It is also possible to suggest a number of explanations, given in the text, which are consistent with our findings.     

Infinite-interval nonlinear approximations

Uniform nonlinear approximation on an infinite interval is studied. This study was motivated by a specific nonlinear approximation problem arising in the construction of a stiff ordinary differential equation system solver. General results include characterization, uniqueness, and discretization theorems, as well as a computational algorithm for this problem.     

Development of arc ion sources for heavy ion fusion

An overview of the development of arc ion sources for heavy ion fusion is presented. Two approaches to heavy ion fusion (HIF)-the RF linac-storage ring approach and the induction linac approach-are described. RF linac schemes require low emittance and moderate current levels, because the beam is accumulated in storage rings before being focused on target. The induction linac approach requires low emittance and high current, because this is a single-pass approach to HIF and one wishes to limit the number of beams in the machine. The RF scheme generally uses long pulse sources together with a buncher of RFQ. The induction linac approach requires sources in the microsecond pulse length range, with good optics being maintained during the pulse. Emphasis is on the induction linac approach pursued at the Lawrence Berkeley Laboratory     

Layered Synthetic Microstructures (LSM): Reflecting media for X-ray optic elements and diffracting structures for the study of condensed matter

During the past two decades techniques for synthesis of superlattices, Layered Synthetic Microstructures (LSM) in the following, have been developed to a sufficiently high level for the product structures to be used as reflecting media in x-ray optics. Additionally, since this application requires high absolute reflectivity, LSMs may be used in both traditional and unique ways to study condensed matter. A short review of synthesis processes will be given as background, with emphasis on process parameters important in LSM deposition. A short review of the reflectivity/wavelength relationship over the spectral range 1 to 500 Å is then given. Experimental results for simple planar LSM structures are then discussed with emphasis on the effects of structural imperfections and engineered variations such as those necessary to construct LSM Fabry-Perot etalons. Results for experiments in which LSMs were used as reflecting/diffracting structures for evanescent and standing wave fluorescent scattering studies will be presented and the implications of these results discussed.     

Eigenvalues of the Laplacian of a graph

Let G be a finite undirected graph with no loops or multiple edges. We define the Laplacian matrix of G,Δ(G)by Δ_ij= degree of vertex i and Δ_ij-1 if there is an edge between vertex i and vertex j. In this paper we relate the structure of the graph G to the eigenvalues of A(G): in particular we prove that all the eigenvalues of Δ(G) are non-negative, less than or equal to the number of vertices, and less than or equal to twice the maximum vertex degree. Precise conditions for equality are given.     

On the convergence of the multigroup approximations for multidimensional media

Summary In this paper, we investigate the stability, convergence, and consistency properties of steady-state multigroup models for submultiplying media with spatial dimensions greater than one. We define these concepts in a Banach space whose norm measures the collision density integrated over phase space. Stability and consistency occur under the conditions that the maximum fluctuations in the total cross section, and in the expected number of secondary particles arising from each energy level, tend to zero as the energy mesh becomes finer. A concluding example and discussion deal with pathologies of the multigroup model in situations where these fluctuations do not tend to zero as the norms of the energy partitions. The results in this paper complement the time-dependent results of both Belleni-Morante and Busoni for isotropic slabs and of Yang Mingzhu and Zhu Guangtian for bounded, three-dimensional media. This work directly extends the steady-state results of Paul Nelson, Jr. and H. D. Victory, Jr. for slab media to steady-state transport in multidimensional media.This research was partially supported by the Alexander von Humboldt Foundation and by a Faculty Development Leave from Texas Tech University during the academic year 1982–1983. Partial support was also provided in the initial stages of this work by the U.S. National Science Foundation under Grant CPE 8007396.     

Extraction and enrichment of chlorinated phenols from surface waters for the determination by capillary-GC/FTIR-spectroscopy

Summary A method is presented for the separation and substance-specific determination of chlorinated phenols at trace level in surface waters using capillary-GC/FTIR-spectroscopy. Since an injected amount of at least 100 ng is required to obtain well-structured IR spectra, the extraction and enrichment procedure must provide a concentration factor of 10⁴ and simultaneously high recoveries. The separation of the complete range of chlorinated phenols is performed without derivatisation on a SE54 fused silica WCOT column; the degree of decrease in separation efficiency introduced by the FTIRS detection system is discussed. The applicability of an on-column injection technique using a thermodesorption- and cold trap injector with solvent removal is tested, which allows the injection of large volums of concentrate. Proceeding form 1 l water volume and a 10 ppb concentration level the chlorophenols are correctly identified by their IR spectra and the mean recovery is in the 90% range. Furthermore, the possibility is discussed to obtain information on the identity of matrix components based on IR data only.

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Extraktion und Anreicherung chlorierter Phenole aus Oberflächenwasser zur Bestimmung mit Hilfe der Capillar-GC/FTIR-Spektroskopie

Zusammenfassung Eine Methode zur Trennung und substanzspezifischen Erfassung von Chlorphenolen in Wasser im Spurenbereich mittels Capillar-GC/FTIR-Spektroskopie wird beschrieben. Da mindestens 100 ng Substanzmenge zu dosieren sind, um gut strukturierte IR-Spektren zu erhalten, muß die Extraktions- und Anreicherungsmethode einen Konzentrierungsfaktor von 10⁴ bei gleichzeitig hohen Wiederfindungsraten ermöglichen. Eine SE 54-Quarzkapillare wird zur Trennung aller Chlorphenol-Isomeren ohne Derivatisierung verwendet; das Ausmaß der Abnahme an Trennleistung, die durch das FTIRS-Detektionssystem hervorgerufen wird, wird diskutiert. Die Anwendbarkeit eines Thermodesorptions- und Cold-Trap-Injektors zur on-column-Probenaufgabe großer Volumina an Konzentrat mit vorheriger Abtrennung des Lösungsmittels wird untersucht. Ausgehend von 11 Wasserprobe und 10 ppb Konzentrationsniveau werden alle Chlorphenole richtig über ihre IR-Spektren identifiziert; die mittlere Ausbeute liegt bei 90%. Weiterhin wird die Möglichkeit diskutiert, die Identität von Matrixbestandteilen allein aus den IR-Daten zu bestimmen.

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Dedicated to Prof. Dr. Janeschitz-Kriegl on the occasion of his 60th birthday.