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Application of Morse Theory to Analysis of Rayleigh-Taylor Topology (open access)

Application of Morse Theory to Analysis of Rayleigh-Taylor Topology

We present a novel Morse Theory approach for the analysis of the complex topology of the Rayleigh-Taylor mixing layer. We automatically extract bubble structures at multiple scales and identify the resolution of interest. Quantitative analysis of bubble counts over time highlights distinct mixing trends for a high-resolution Direct Numerical Simulation (DNS) [1].
Date: January 24, 2007
Creator: Miller, P L; Bremer, P T; Cabot, W H; Cook, A W; Laney, D E; Mascarenhas, A A et al.
System: The UNT Digital Library
Bubble Counts for Rayleigh-Taylor Instability Using Image Analysis (open access)

Bubble Counts for Rayleigh-Taylor Instability Using Image Analysis

We describe the use of image analysis to count bubbles in 3-D, large-scale, LES [1] and DNS [2] of the Rayleigh-Taylor instability. We analyze these massive datasets by first converting the 3-D data to 2-D, then counting the bubbles in the 2-D data. Our plots for the bubble count indicate there are four distinct regimes in the process of the mixing of the two fluids. We also show that our results are relatively insensitive to the choice of parameters in our analysis algorithms.
Date: January 24, 2007
Creator: Miller, P L; Gezahegne, A G; Cook, A W; Cabot, W H & Kamath, C
System: The UNT Digital Library
A Camera for Coherent Diffractive Imaging and Holography With a Soft-X-Ray Free Electron Laser (open access)

A Camera for Coherent Diffractive Imaging and Holography With a Soft-X-Ray Free Electron Laser

We describe a camera to record coherent scattering patterns with a soft-X-ray free-electron laser. The camera consists of a laterally-graded multilayer mirror which reflects the diffraction pattern onto a CCD detector. The mirror acts as a bandpass filter both for wavelength and angle, which isolates the desired scattering pattern from non-sample scattering or incoherent emission from the sample. The mirror also solves the particular problem of the extreme intensity of the FEL pulses, which are focused to greater than 10{sup 14} W/cm{sup 2}. The strong undiffracted pulse passes through a hole in the mirror and propagates on to a beam dump at a distance behind the instrument rather than interacting with a beamstop placed near the CCD. The camera concept is extendable for the full range of the fundamental wavelength of the FLASH FEL (i.e. between 6 nm and 60 nm) and into the water window. We have fabricated and tested various multilayer mirrors for wavelengths of 32 nm, 16 nm, 13.5 nm, and 4.5 nm. At the shorter wavelengths mirror roughness must be minimized to reduce scattering from the mirror. We have recorded over 30,000 diffraction patterns at the FLASH free-electron laser with no observable mirror damage or degradation …
Date: September 24, 2007
Creator: Bajt, S.; Chapman, H. N.; Spiller, E.; Alameda, J.; Woods, B.; Frank, M. et al.
System: The UNT Digital Library
CANCELLED EMT and back again: does cellular plasticity fuel neoplastic progression? (open access)

CANCELLED EMT and back again: does cellular plasticity fuel neoplastic progression?

Epithelial-mesenchymal transition (EMT) is a cellular transdifferentiation program that facilitates organ morphogenesis and tissue remodeling in physiological processes such as embryonic development and wound healing. However, a similar phenotypic conversion is also detected in fibrotic diseases and neoplasia, in which it is associated with disease progression. EMT in cancer epithelial cells often appears to be an incomplete and bi-directional process. Here we discuss the phenomenon of EMT as it pertains to tumor development, focusing on exceptions to the commonly held rule that EMT promotes invasion and metastasis. We also highlight the role of the Ras-controlled signaling mediators, ERK1, ERK2 and PI3-kinase, as microenvironmental responsive regulators of EMT.
Date: February 24, 2007
Creator: Turley, Eva A.; Veiseh, Mandana; Radisky, Derek C. & Bissell, MinaJ.
System: The UNT Digital Library
A Cell-Based Approach for the Biosynthesis/Screening of Cyclic Peptide Libraries against Bacterial Toxins (open access)

A Cell-Based Approach for the Biosynthesis/Screening of Cyclic Peptide Libraries against Bacterial Toxins

Available methods for developing and screening small drug-like molecules able to knockout toxins or pathogenic microorganisms have some limitations. In order to be useful, these new methods must provide high-throughput analysis and identify specific binders in a short period of time. To meet this need, we are developing an approach that uses living cells to generate libraries of small biomolecules, which are then screened inside the cell for activity. Our group is using this new, combined approach to find highly specific ligands capable of disabling anthrax Lethal Factor (LF) as proof of principle. Key to our approach is the development of a method for the biosynthesis of libraries of cyclic peptides, and an efficient screening process that can be carried out inside the cell.
Date: October 24, 2007
Creator: Camarero, J. A.; Kimura, R.; Woo, Y.; Cantor, J. & Steenblock, E.
System: The UNT Digital Library
Chemometric and Statistical Analyses of ToF-SIMS Spectra of Increasingly Complex Biological Samples (open access)

Chemometric and Statistical Analyses of ToF-SIMS Spectra of Increasingly Complex Biological Samples

Characterizing and classifying molecular variation within biological samples is critical for determining fundamental mechanisms of biological processes that will lead to new insights including improved disease understanding. Towards these ends, time-of-flight secondary ion mass spectrometry (ToF-SIMS) was used to examine increasingly complex samples of biological relevance, including monosaccharide isomers, pure proteins, complex protein mixtures, and mouse embryo tissues. The complex mass spectral data sets produced were analyzed using five common statistical and chemometric multivariate analysis techniques: principal component analysis (PCA), linear discriminant analysis (LDA), partial least squares discriminant analysis (PLSDA), soft independent modeling of class analogy (SIMCA), and decision tree analysis by recursive partitioning. PCA was found to be a valuable first step in multivariate analysis, providing insight both into the relative groupings of samples and into the molecular basis for those groupings. For the monosaccharides, pure proteins and protein mixture samples, all of LDA, PLSDA, and SIMCA were found to produce excellent classification given a sufficient number of compound variables calculated. For the mouse embryo tissues, however, SIMCA did not produce as accurate a classification. The decision tree analysis was found to be the least successful for all the data sets, providing neither as accurate a classification nor chemical …
Date: October 24, 2007
Creator: Berman, E. S.; Wu, L.; Fortson, S. L.; Nelson, D. O.; Kulp, K. S. & Wu, K. J.
System: The UNT Digital Library
Complexation of U(VI) with 1-Hydroxyethane-1,1-diphosphonicAcid (HEDPA) in Acidic to Basic Solutions (open access)

Complexation of U(VI) with 1-Hydroxyethane-1,1-diphosphonicAcid (HEDPA) in Acidic to Basic Solutions

Complexation of U(VI) with 1-hydroxyethane-1,1-diphosphonic acid (HEDPA) in acidic to basic solutions has been studied with multiple techniques. A number of 1:1 (UO{sub 2}H{sub 3}L), 1:2 (UO{sub 2}H{sub j}L{sub 2} where j = 4, 3, 2, 1, 0 and -1) and 2:2 ((UO{sub 2}){sub 2}H{sub j}L{sub 2} where j = 1, 0 and -1) complexes form, but the 1:2 complexes are the major species in a wide pH range. Thermodynamic parameters (formation constants, enthalpy and entropy of complexation) were determined by potentiometry and calorimetry. Data indicate that the complexation of U(VI) with HEDPA is exothermic, favored by the enthalpy of complexation. This is in contrast to the complexation of U(VI) with dicarboxylic acids in which the enthalpy term usually is unfavorable. Results from electrospray ionization mass spectrometry (ESI-MS) and {sup 31}P NMR have confirmed the presence of 1:1, 1:2 and 2:2 U(VI)-HEDPA complexes.
Date: January 24, 2007
Creator: Reed, W. A.; Rao, L.; Zanonato, P.; Garnov, A.; Powell, B. A. & Nash, K. L.
System: The UNT Digital Library
Deinococcus geothermalis: The Pool of Extreme Radiation Resistance Genes Shrinks (open access)

Deinococcus geothermalis: The Pool of Extreme Radiation Resistance Genes Shrinks

Bacteria of the genus Deinococcus are extremely resistant to ionizing radiation (IR), ultraviolet light (UV) and desiccation. The mesophile Deinococcus radiodurans was the first member of this group whose genome was completely sequenced. Analysis of the genome sequence of D. radiodurans, however, failed to identify unique DNA repair systems. To further delineate the genes underlying the resistance phenotypes, we report the whole-genome sequence of a second Deinococcus species, the thermophile Deinococcus geothermalis, which at itsoptimal growth temperature is as resistant to IR, UV and desiccation as D. radiodurans, and a comparative analysis of the two Deinococcus genomes. Many D. radiodurans genes previously implicated in resistance, but for which no sensitive phenotype was observed upon disruption, are absent in D. geothermalis. In contrast, most D. radiodurans genes whose mutants displayed a radiation-sensitive phenotype in D. radiodurans are conserved in D. geothermalis. Supporting the existence of a Deinococcus radiation response regulon, a common palindromic DNA motif was identified in a conserved set of genes associated with resistance, and a dedicated transcriptional regulator was predicted. We present the case that these two species evolved essentially the same diverse set of gene families, and that the extreme stress-resistance phenotypes of the Deinococcus lineage emerged …
Date: July 24, 2007
Creator: Makarova, Kira S.; Omelchenko, Marina V.; Gaidamakova, Elena K.; Matrosova, Vera Y.; Vasilenko, Alexander; Zhai, Min et al.
System: The UNT Digital Library
Diffusion of H in Pd Ag Alloys (423 to 523 K) (open access)

Diffusion of H in Pd Ag Alloys (423 to 523 K)

None
Date: May 24, 2007
Creator: Shanahan, Kirk; Flanagan, Ted B. & Da Wang, Da
System: The UNT Digital Library
Does complex absorption behavior leading to conditioning and damage in KDP/DKDP reflect the electronic structure of initiators? (open access)

Does complex absorption behavior leading to conditioning and damage in KDP/DKDP reflect the electronic structure of initiators?

Currently, most of our thinking about the defects responsible for initiating laser damage considers them as featureless absorbers. However, an increasing body of evidence, particularly involving multi-wavelength irradiation, suggests electronic structure of damage initiators is important in determining both initiation and conditioning behaviors in KDP. The effective absorption coefficient of energy under multi-wavelength irradiation cannot be accounted for by a structureless absorber, but is consistent with an initiator with a multi-level structure. We outline the evidence and assess the ability of such a simple multi-level model to explain these and other experimentally observed behaviors.
Date: October 24, 2007
Creator: Feit, M D; DeMange, P P; Negres, R A; Rubenchik, A M & Demos, S G
System: The UNT Digital Library
The E158 Experiment (open access)

The E158 Experiment

We have carried out a precision of the parity-violating asymmetry A{sub PV} in the scattering of longitudinally polarized electrons off electrons in a liquid hydrogen target. The measurement was performed with the 50 GeV beam line at SLAC. The final result with the full data set collected in three production runs is A{sub PV} = -131 {+-}14 (stat) {+-} 10 (syst) parts per billion. The result leads to new limits on possible contact interactions at the TeV scale. We discuss future prospects for more precise measurements.
Date: October 24, 2007
Creator: Kumar, Krishna S.
System: The UNT Digital Library
Energy dependence of jet transport parameter and parton saturationin quark-gluon plasma (open access)

Energy dependence of jet transport parameter and parton saturationin quark-gluon plasma

We study the evolution and saturation of the gluondistribution function in the quark-gluon plasma as probed by apropagating parton and its effect on the computation of jet quenching ortransport parameter $\hat q $. For thermal partons, the saturation scale$Q2_s$ is found to be proportional to the Debye screening mass $\mu_D2$.For hard probes, evolution at small $x=Q2_s/6ET$ leads to jet energydependence of hat q. We study this dependence for both a conformal gaugetheory in weak and strong coupling limit and for (pure gluon) QCD. Theenergy dependence can be used to extract the shear viscosity $\eta$ ofthe medium since $\eta$ can be related to the transport parameter forthermal partons in a transport description. We also derive upper boundson the transport parameter for both energetic and thermal partons. Thelater leads to a lower bound on shear viscosity-to-entropy density ratiowhich is consistent with the conjectured lower bound $\eta/s\geq 1/4\pi$.Implications on the study of jet quenching at RHIC and LHC and the bulkproperties of the dense matter are discussed.
Date: June 24, 2007
Creator: Casalderrey-Solana, Jorge & Wang, Xin-Nian
System: The UNT Digital Library
Entropy of near-extremal black holes in AdS5 (open access)

Entropy of near-extremal black holes in AdS5

We construct the microstates of near-extremal black holes in AdS_5 x S5 as gases of defects distributed in heavy BPS operators in the dual SU(N) Yang-Mills theory. These defects describe open strings on spherical D3-branes in the S5, and we show that they dominate the entropy by directly enumerating them and comparing the results with a partition sum calculation. We display new decoupling limits in which the field theory of the lightest open strings on the D-branes becomes dual to a near-horizon region of the black hole geometry. In the single-charge black hole we find evidence for an infrared duality between SU(N) Yang-Mills theories that exchanges the rank of the gauge group with an R-charge. In the two-charge case (where pairs of branes intersect on a line), the decoupled geometry includes an AdS_3 factor with a two-dimensional CFT dual. The degeneracy in this CFT accounts for the black hole entropy. In the three-charge case (where triples of branes intersect at a point), the decoupled geometry contains an AdS_2 factor. Below a certain critical mass, the two-charge system displays solutions with naked timelike singularities even though they do not violate a BPS bound. We suggest a string theoretic resolution of these …
Date: July 24, 2007
Creator: Simon, Joan; Balasubramanian, Vijay; de Boer, Jan; Jejjala, Vishnu & Simon, Joan
System: The UNT Digital Library
Evidence for Strong Tantalum-to-Boron Dative Interactions in (silox)3Ta(BH3) and (silox)3Ta(ɳ2-B,CI-BCI2Ph) (silox = tBu3SiO)1 (open access)

Evidence for Strong Tantalum-to-Boron Dative Interactions in (silox)3Ta(BH3) and (silox)3Ta(ɳ2-B,CI-BCI2Ph) (silox = tBu3SiO)1

This article discusses strong tantalum-to-boron dative interactions in (silox)3Ta(BH3) and (silox)3Ta(ɳ2-B,CI-BCI2Ph) (silox = tBu3SiO)1.
Date: January 24, 2007
Creator: Bonanno, Jeffrey B.; Henry, Thomas P.; Wolczanski, Peter T.; Pierpont, Aaron W. & Cundari, Thomas R., 1964-
System: The UNT Digital Library
Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei (open access)

Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei

Clear evidence for symplectic symmetry in low-lying states of {sup 12}C and {sup 16}O is reported. Eigenstates of {sup 12}C and {sup 16}O, determined within the framework of the no-core shell model using the JISP16 NN realistic interaction, typically project at the 85-90% level onto a few of the most deformed symplectic basis states that span only a small fraction of the full model space. The results are nearly independent of whether the bare or renormalized effective interactions are used in the analysis. The outcome confirms Elliott's SU(3) model which underpins the symplectic scheme, and above all, points to the relevance of a symplectic no-core shell model that can reproduce experimental B(E2) values without effective charges as well as deformed spatial modes associated with clustering phenomena in nuclei.
Date: April 24, 2007
Creator: Dytrych, Tomas; Sviratcheva, Kristina D.; Bahri, Chairul; Draayer, Jerry P. & Vary, James P.
System: The UNT Digital Library
Examples of the Zeroth Theorem of the History of Science (open access)

Examples of the Zeroth Theorem of the History of Science

The zeroth theorem of the history of science, enunciated byE. P. Fischer, states that a discovery (rule,regularity, insight) namedafter someone (often) did not originate with that person. I present fiveexamples from physics: the Lorentz condition partial muAmu = 0 definingthe Lorentz gauge of the electromagnetic potentials; the Dirac deltafunction, delta(x); the Schumann resonances of the earth-ionospherecavity; the Weizsacker-Williams method of virtual quanta; the BMTequation of spin dynamics. I give illustrated thumbnail sketches of boththe true and reputed discoverers and quote from their "discovery"publications.
Date: August 24, 2007
Creator: Jackson, J.D.
System: The UNT Digital Library
FLOW ANALYSIS OF DIFFUSER-GETTER-DIFFUSER SYSTEMS (open access)

FLOW ANALYSIS OF DIFFUSER-GETTER-DIFFUSER SYSTEMS

Tritium clean-up systems typically deploy gas processing technologies between stages of palladium-silver (Pd/Ag) diffusers/permeators. The number of diffusers positioned before and after a gas clean-up process to obtain optimal system performance will vary with feed gas inert composition. A simple method to analyze optimal diffuser configuration is presented. The method assumes equilibrium across the Pd/Ag tubes and system flows are limited by diffuser vacuum pump speeds preceding or following the clean-up process. A plot of system feed as a function of inert feed gas composition for various diffuser configuration allows selection of a diffuser configuration for maximum throughput based on feed gas composition.
Date: July 24, 2007
Creator: Klein, J & Dave W. Howard, D
System: The UNT Digital Library
FLUOR HANFORD (FH) MAKES CLEANUP A REALITY IN NEARLY 11 YEARS AT HANFORD (open access)

FLUOR HANFORD (FH) MAKES CLEANUP A REALITY IN NEARLY 11 YEARS AT HANFORD

For nearly 11 years, Fluor Hanford has been busy cleaning up the legacy of nuclear weapons production at one of the Department of Energy's (DOE'S) major sites in the United States. As prime nuclear waste cleanup contractor at the vast Hanford Site in southeastern Washington state, Fluor Hanford has changed the face of cleanup. Fluor beginning on October 1, 1996, Hanford Site cleanup was primarily a ''paper exercise.'' The Tri-Party Agreement, officially called the Hanford Federal Facility Agreement and Consent Order - the edict governing cleanup among the DOE, U.S. Environmental Protection Agency (EPA) and Washington state - was just seven years old. Milestones mandated in the agreement up until then had required mainly waste characterization, reporting, and planning, with actual waste remediation activities off in the future. Real work, accessing waste ''in the field'' - or more literally in huge underground tanks, decaying spent fuel POO{approx}{approx}S, groundwater, hundreds of contaminated facilities, solid waste burial grounds, and liquid waste disposal sites -began in earnest under Fluor Hanford. The fruits of labors initiated, completed and/or underway by Fluor Hanford can today be seen across the site. Spent nuclear fuel is buttoned up in secure, dry containers stored away from regional water …
Date: May 24, 2007
Creator: Gerber, M. S.
System: The UNT Digital Library
Frontier Hed Science Accessible on NIF (open access)

Frontier Hed Science Accessible on NIF

With the advent of high-energy-density (HED) experimental facilities, such as high-energy lasers and fast Z-pinch pulsed-power facilities, millimeter-scale quantities of matter can be placed in extreme states of density, temperature, and/or velocity. With the commissioning of the NIF laser facility in the very near future, regimes experimentally accessible will be pushed to even higher densities and pressures. This is enabling the emergence of a new class of experimental science, wherein the properties of matter and the processes that occur under the most extreme physical conditions can be examined in the laboratory. Areas particularly suitable to laboratory astrophysics include the study of opacities relevant to stellar interiors, equations of state relevant to planetary interiors, strong shock-driven nonlinear hydrodynamics and radiative dynamics relevant to supernova explosions and subsequent evolution, protostellar jets and high Mach number flows, radiatively driven molecular clouds, nonlinear photoevaporation front dynamics, and photoionized plasmas relevant to accretion disks around compact objects such as black holes and neutron stars. In the area of materials science and condensed matter physics, material properties such as phase, elastic coefficients such as shear modulus, Peierls stress, and transport coefficients such as thermal diffusivity can be accessed at considerably higher densities and pressure than any …
Date: September 24, 2007
Creator: Remington, B. A.; Ho, D. D. & Ilinskij, A.
System: The UNT Digital Library
Genome of Methylobacillus flagellatus, Molecular Basis for Obligate Methylotrophy, and Polyphyletic Origin of Methylotrophy (open access)

Genome of Methylobacillus flagellatus, Molecular Basis for Obligate Methylotrophy, and Polyphyletic Origin of Methylotrophy

Along with methane, methanol and methylated amines represent important biogenic atmospheric constituents; thus, not only methanotrophs but also nonmethanotrophic methylotrophs play a significant role in global carbon cycling. The complete genome of a model obligate methanol and methylamine utilizer, Methylobacillus flagellatus (strain KT) was sequenced. The genome is represented by a single circular chromosome of approximately 3 Mbp, potentially encoding a total of 2,766 proteins. Based on genome analysis as well as the results from previous genetic and mutational analyses, methylotrophy is enabled by methanol and methylamine dehydrogenases and their specific electron transport chain components, the tetrahydromethanopterin-linked formaldehyde oxidation pathway and the assimilatory and dissimilatory ribulose monophosphate cycles, and by a formate dehydrogenase. Some of the methylotrophy genes are present in more than one (identical or nonidentical) copy. The obligate dependence on single-carbon compounds appears to be due to the incomplete tricarboxylic acid cycle, as no genes potentially encoding alpha-ketoglutarate, malate, or succinate dehydrogenases are identifiable. The genome of M. flagellatus was compared in terms of methylotrophy functions to the previously sequenced genomes of three methylotrophs, Methylobacterium extorquens (an alphaproteobacterium, 7 Mbp), Methylibium petroleiphilum (a betaproteobacterium, 4 Mbp), and Methylococcus capsulatus (a gammaproteobacterium, 3.3 Mbp). Strikingly, metabolically and/or phylogenetically, the …
Date: July 24, 2007
Creator: Chistoserdova, Ludmila; Lapidus, Alla; Han, Cliff; Goodwin, Lynne; Saunders, Liz; Brettin, Tom et al.
System: The UNT Digital Library
Genome Sequence and Analysis of the Soil Cellulolytic Actinomycete Thermobifida fusca YX (open access)

Genome Sequence and Analysis of the Soil Cellulolytic Actinomycete Thermobifida fusca YX

None
Date: July 24, 2007
Creator: Lykidis, A.; Mavromatis, K.; Ivanova, N.; Anderson, I.; Land, M.; DiBartolo, G. et al.
System: The UNT Digital Library
Genome-wide experimental determination of barriers to horizontal gene transfer (open access)

Genome-wide experimental determination of barriers to horizontal gene transfer

Horizontal gene transfer, in which genetic material is transferred from the genome of one organism to another, has been investigated in microbial species mainly through computational sequence analyses. To address the lack of experimental data, we studied the attempted movement of 246,045 genes from 79 prokaryotic genomes into E. coli and identified genes that consistently fail to transfer. We studied the mechanisms underlying transfer inhibition by placing coding regions from different species under the control of inducible promoters. Their toxicity to the host inhibited transfer regardless of the species of origin and our data suggest that increased gene dosage and associated increased expression is a predominant cause for transfer failure. While these experimental studies examined transfer solely into E. coli, a computational analysis of gene transfer rates across available bacterial and archaeal genomes indicates that the barriers observed in our study are general across the tree of life.
Date: September 24, 2007
Creator: Rubin, Edward; Sorek, Rotem; Zhu, Yiwen; Creevey, Christopher J.; Francino, M. Pilar; Bork, Peer et al.
System: The UNT Digital Library
GLAST LAT And Pulsars: What Do We Learn from Simulations? (open access)

GLAST LAT And Pulsars: What Do We Learn from Simulations?

Gamma-ray pulsars are among the best targets for the Large Area Telescope (LAT) aboard the GLAST mission. The higher sensitivity, time and energy resolution of the LAT will provide data of fundamental importance to understand the physics of these fascinating objects. Powerful tools for studying the LAT capabilities for pulsar science are the simulation programs developed within the GLAST Collaboration. Thanks to these simulations it is possible to produce a detailed distribution of gamma-ray photons in energy and phase that can be folded through the LAT Instrument Response Functions (IRFs). Here we present some of the main interesting results from the simulations developed to study the discovery potential of the LAT. In particular we will focus on the capability of the LAT to discover new radio-loud gamma-ray pulsars, on the discrimination between Polar Cap and Outer Gap models, and on the LAT pulsar sensitivity.
Date: October 24, 2007
Creator: Razzano, Massimiliano; /Pisa U. /INFN, Pisa; Harding, Alice K. & /NASA, Goddard
System: The UNT Digital Library
Gouy Interferometry: Properties of Multicomponent System Omega Graphs (open access)

Gouy Interferometry: Properties of Multicomponent System Omega Graphs

We consider the properties of {Omega} graphs ({Omega} vs f(z)) obtained from Gouy interferometry on multicomponent systems with constant diffusion coefficients. We show that they must have (a) either a maximum or else a minimum between f(z)=0 and f(z)=1 and (b) an inflection point between the f(z) value at the extremum and f(z)=1. Consequently, an {Omega} graph cannot have both positive and negative {Omega} values.
Date: January 24, 2007
Creator: Miller, D. G.
System: The UNT Digital Library