Existence of Spherical Initial Data with Unit Mass, Zero Energy, and Virial less than - 1/2 for the Relativistic Vlasov-Poisson Equation with Attractive Coupling

In a recent paper, Kiessling and Tahvildar-Zadeh proved that any classical solution of the relativistic Vlasov-Poisson equation with attractive coupling launched by spherically symmetric initial data with zero total energy and virial less than or equal to -1/2 will blow up in finite time. They left open whether such data exist. Subsequently, the question was raised whether any such data exist at all. In fact, the simplest conceivable ansatz, a nearly uniform ball of material centered at the origin with momenta directed inward, must have virial strictly larger than -1/2! In this brief note, we settle this issue by constructing two classes of such initial data

On Linear Landau Damping for Relativistic Plasmas via Gevrey Regularity

We examine the phenomenon of Landau Damping in relativistic plasmas via a study of the relativistic Vlasov-Poisson system (both on the torus and on $\mathbb{R}^3$) linearized around a sufficiently nice, spatially uniform kinetic equilibrium. We find that exponential decay of spatial Fourier modes is impossible under modest symmetry assumptions. However, by assuming the equilibrium and initial data are sufficiently regular functions of velocity for a given wavevector (in particular that they exhibit a kind of Gevrey regularity), we show that it is possible for the mode associated to this wavevector to decay sub-exponentially if its magnitude exceeds a certain critical size. We also give a heuristic argument why one should not expect such rapid decay for modes with wavevectors below this threshold.Comment: Accepted for publication in J. Diff. Eqns. April 201

Landau Damping in Relativistic Plasmas

We examine the phenomenon of Landau Damping in relativistic plasmas via a study of the relativistic Vlasov-Poisson system (rVP) on the torus for initial data sufficiently close to a spatially uniform steady state. We find that if the steady state is regular enough (essentially in a Gevrey class of degree in a specified range) and that the deviation of the initial data from this steady state is small enough in a certain norm, the evolution of the system is such that its spatial density approaches a uniform constant value sub-exponentially fast (i.e. like $\exp(-C|t|^{\overline{\nu}})$ for $\overline{\nu} \in (0,1)$). We take as \emph{a priori} assumptions that solutions launched by such initial data exist for all times (by no means guaranteed with rVP, but reasonable since we are close to a spatially uniform state) and that the various norms in question are continuous in time (which should be a consequence of an abstract version of the Cauchy-Kovalevskaya Theorem). In addition, we must assume a kind of "reverse Poincar\'e inequality" on the Fourier transform of the solution. In spirit, this assumption amounts to the requirement that there exists $0<\varkappa<1$ so that the mass in the annulus $\varkappa \le |v| < 1$ for the solution launched by the initial data is uniformly small for all $t$.Comment: 88 pages, 3 figure

Optimal Lβ\mathfrak{L}^{\beta}-Control for the Global Cauchy Problem of the Relativistic Vlasov-Poisson System

Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum space, vanishes on characteristics with vanishing angular momentum, and for $\beta \ge 3/2$ has $\mathfrak{L}^{\beta}$-norm strictly below a positive, critical value $\mathcal{C}_{\beta}$. Everything else being equal, data leading to finite time blow-up can be found with $\mathfrak{L}^{\beta}$-norm surpassing $\mathcal{C}_{\beta}$ for any $\beta >1$, with $\mathcal{C}_{\beta}>0$ if and only if $\beta\geq 3/2$. In their paper, the critical value for $\beta = {3}/{2}$ is calculated explicitly while the value for all other $\beta$ is merely characterized as the infimum of a functional over an appropriate function space. In this work, the existence of minimizers is established, and the exact expression of $\mathcal{C}_{\beta}$ is calculated in terms of the famous Lane-Emden functions. Numerical computations of the $\mathcal{C}_{\beta}$ are presented along with some elementary asymptotics near the critical exponent ${3}/{2}$.Comment: 24 pages, 2 figures Refereed and accepted for publication in Transport Theory and Statistical Physic

Organoplatinum: Some Reaction Modes

The thermal decomposition of organoplatinum(ll) complexes of the type cis-L2PtAr2 and (biL)PtAr2 [Ar =C6H5, 4-Me-C6H4; L = Ph3P, (4-Me-C6H4)3P, Ph2MeP; biL = Ph2PCH2PPh2 (dpm), Ph2PC2H4PPh2 (dpe), Me2PC2H4PMe2 (dmpe)] has been studied. In the condensed phase, the thermolyses have been examined by thermal analytical techniques (DSC and simultaneous TGA/DTA) and by product analysis (GLC). The results indicate that the complexes undergo thermal disruption via a predominant primary route which involves concerted reductive elimination of the platinum-bound aryl ligands as biaryl. This process is intramolecular, and no intermolecular exchange of aryls occurs prior to, or during, decomposition. Secondary reactions which produce quantities of arene and biaryl originating from the arylphosphine ligands, and whose operation is concurrent with, but essentially independent of, the primary reductive elimination, are also observed. These data are interpreted in terms of slower reactions (subsequent to the primary process) of the species L2Pto or (biL)Pto , involving aryl- or hydride-transfer to platinum, by oxidative insertion into P-C or C-H bonds, and ultimate reductive eliminations. Although their identities remain uncertain,analysis of the glassy, red-brown decomposition residues provides more evidence for these propositions. In the presence of an added equimolar amount of the appropriate phosphine, primary concerted reductive elimination of biaryl is facilitated. The effect is most marked for complexes of dpm in presence of free ligand. This general observation is in qualitative agreement with previous predictions and is discussed in terms of nucleophilic attack at Pt(ll) by a phosphorus donor. Secondary reactions are largely, if not altogether suppressed, and this is attributable to the diminished tendency of Pt(0) to undergo the oxidative insertion sequences in higher coordination number phospbine complexes. An exception is (dpm)2Pt(0) which appears to decompose under the conditions of its formation. In this case, an additional secondary process involves rupture of the P-C-P bridge, presumably again by oxidative insertion of Pt(0) into P-C (the first such example with P-alkyl). When a phosphine different to that already present is added, there is some evidence that exchange may occur prior to the Pt-C scission processes. The thermal decomposition of these systems was, additionally, followed in toluene solution. Product analyses served to corroborate the mechanistic conclusions drawn from the condensed-phase data. Primary, concerted, intramolecular reductive elimination is followed by the same slower secondary processes. Kinetic studies showed that the primary elimination is first-order in platinum complex and that, again, reductive elimination is facilitated by the presence of free phosphine. Only the complexes cis-(Ph3P)2PtAr2 displayed sufficient lability to be extensively studied under these conditions. Such activation parameters as were determined for these systems suggested that the enhanced lability of the 4-tolylplatinum species compared with its phenyl-analogue, and that of either system in the presence of Ph3P (relative to the complex alone) may be largely due to entropy effects, interpretations of which are discussed

Jacking in Chinook salmon (Oncorhynchus tshawytscha ): environmental and genotypic effects on life history strategy

Jacking in Chinook salmon (Oncorhynchus tshawytscha), is defined as precocious sexual maturation of males after at least 1 year in sea water, and occurring 1 year prior to females of the same cohort. Substantial evidence supports genetic, environmental, and genetic by environmental effects on precocious maturation in Chinook salmon, however the underlying mechanisms remain unclear. Passive integrated transponder tagged fish were followed through fresh and salt water growth to the sexual maturation of the jacks. Growth data was recorded to examine the relationship between size/growth effects in freshwater rearing on subsequent precocious sexual maturation of the jacks. No effect of size/growth in freshwater was detected. Reanalysis of data from a previous study showed an effect of developmental rate on jacking. Sequencing tested the possibility of a relationship between jacking and Major Histocompatibility (MH) genes at the MH class II β 1 locus. One genotype positively affected the likelihood of jacking

Using Open Stack for an Open Cloud Exchange(OCX)

We are developing a new public cloud, the Massachusetts Open Cloud (MOC) based on the model of an Open Cloud eXchange (OCX). We discuss in this paper the vision of an OCX and how we intend to realize it using the OpenStack open-source cloud platform in the MOC. A limited form of an OCX can be achieved today by layering new services on top of OpenStack. We have performed an analysis of OpenStack to determine the changes needed in order to fully realize the OCX model. We describe these proposed changes, which although significant and requiring broad community involvement will provide functionality of value to both existing single-provider clouds as well as future multi-provider ones

Automating testbed documentation and database access using World Wide Web (WWW) tools

A method for providing uniform transparent access to disparate distributed information systems was demonstrated. A prototype testing interface was developed to access documentation and information using publicly available hypermedia tools. The prototype gives testers a uniform, platform-independent user interface to on-line documentation, user manuals, and mission-specific test and operations data. Mosaic was the common user interface, and HTML (Hypertext Markup Language) provided hypertext capability

Rate and extent of losses from top spoilage in alfalfa silages stored in bunker silos

Alfalfa silages were made in pilot- and farm-scale silos, and five sealing treatments were compared. After 90 days, sealing dramatically reduced dry matter (DM) losses at the 5 and 10 inch depths in the farm silos and at the 0 to 12, 12 to 24, and 24 to 36 inch depths in the pilot silos. Extending the storage period to 180 days in pilot silos had no effect on DM losses for sealed or delay-sealed silages, but DM losses for unsealed silages continued to increase at all three depths. Placing a roof over the unsealed, farm-scale silo increased the silage DM content at all three depths, increased storage temperatures at the 10 and 20 inch depths, and reduced DM loss at the 10 inch depth compared to the unsealed silo without a roof. Rainfall was much above normal (16.8 inches during the first 90 days of storage; 11.2 inches the second 90 days) and contributed to huge increases in the moisture content of silage at the lower depths in the unsealed, no roof, pilot- and farm-scale silos. Sealing also increased the nutritive value of the silages at the 5 and 10 inch depths.; Dairy Day, 1994, Kansas State University, Manhattan, KS, 1994

Effects of a Math-enhanced Curriculum and Instructional Approach on the Performance of Secondary Education Students Enrolled in a Year-long Agricultural Power and Technology Course: an Experimental Study

The purpose of this study was to empirically test the posit that students who participated in a contextualized, mathematics-enhanced high school agricultural power and technology curriculum and aligned instructional approach would develop a deeper and more sustained understanding of selected mathematics concepts than those students who participated in the traditional curriculum and instruction. This study included teachers and students from 32 high schools in Oklahoma (16 experimental classrooms; 16 control classrooms). Students were enrolled in an agricultural power and technology course during the 2004-2005 school year. The experimental design employed was a posttest only control group; unit of analysis was the classroom. One-way analysis of variance (ANOVA) and analysis of covariance (ANCOVA) were used to test the study's null hypotheses.Findings and Conclusions: The math-enhanced curriculum and aligned instruction did not significantly affect (p &lt; .05) students' mathematics ability as measured by a traditional test of student math knowledge, by an "authentic" assessment of student ability to use math to solve workplace problems, or by an examination used to determine students' need for math remediation at the post-secondary level. In addition, the experimental group students' technical competence in agricultural power and technology did not diminish as a result of the study's experimental treatment. Thus, the study's null hypotheses were not rejected. However, the measure of students' need for mathematical remediation at the post-secondary level and the traditional test of student math knowledge did reveal results that held practical significance and favored the experimental group students.Department of Agricultural Education, Communications, and Leadershi