On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson

The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f_0(v), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of f_0. We prove that for each f_0 there is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0$is unstable. When$f_0$ is perturbed by an area preserving rearrangement, f_0 will always be stable if the continuous spectrum is only of positive signature, where the signature of the continuous spectrum is defined as in previous work. If there is a signature change, then there is a rearrangement of f_0 that is unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is analogous to Krein's theorem for the continuous spectrum. We prove that if a discrete mode embedded in the continuous spectrum is surrounded by the opposite signature there is an infinitesimal perturbation in C^n norm that makes f_0 unstable. If f_0 is stable we prove that the signature of every discrete mode is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36 pages, 12 figure

Local cytokine transcription in naïve and previously infected sheep and lambs following challenge with Teladorsagia circumcincta

<b>Background</b><p></p> The abomasal helminth Teladorsagia circumcincta is one of the most economically important parasites affecting sheep in temperate regions. Infection is particularly detrimental to lambs, in which it can cause pronounced morbidity and severe production losses. Due to the spreading resistance of this parasite to all classes of anthelmintic drugs, teladorsagiosis is having an increasingly severe impact on the sheep industry with significant implications for sheep welfare. Protective immunity develops slowly, wanes rapidly and does not appear to be as effective in young lambs. To investigate the development of immunity to T. circumcincta in sheep and lambs, we used cytokine transcript profiling to examine differences in the abomasal mucosa and gastric lymph node of naïve and previously infected sheep and lambs following challenge.<p></p> <b>Results</b><p></p> The results of these experiments demonstrated that the abomasal mucosa is a major source of cytokines during abomasal helminth infection. A local Th2-type cytokine response was observed in the abomasal mucosa and gastric lymph node of the previously infected sheep and lambs when compared with those of the naïve during the early stages of infection. In contrast, a pro-inflammatory component more was evident in the abomasal mucosa and gastric lymph node of the naïve sheep when compared with those of the previously infected, which was not observed in the lambs.<p></p> <b>Conclusions</b><p></p> The greater levels of Th2-type cytokine transcripts in both the abomasum and gastric lymph node of the previously infected compared with naïve sheep and lambs emphasises the importance of these mechanisms in the immune response to T. circumcincta infection. Younger lambs appear to be able to generate similar Th2-type responses in the abomasum suggesting that the increased morbidity and apparent lack of resistance in younger lambs following continuous or repeated exposure to T. circumcincta is unlikely to be due to a lack of appropriate Th2-type cytokine production

Mode signature and stability for a Hamiltonian model of electron temperature gradient turbulence

Stability properties and mode signature for equilibria of a model of electron temperature gradient (ETG) driven turbulence are investigated by Hamiltonian techniques. After deriving the infinite families of Casimir invariants, associated with the noncanonical Poisson bracket of the model, a sufficient condition for stability is obtained by means of the Energy-Casimir method. Mode signature is then investigated for linear motions about homogeneous equilibria. Depending on the sign of the equilibrium "translated" pressure gradient, stable equilibria can either be energy stable, i.e.\ possess definite linearized perturbation energy (Hamiltonian), or spectrally stable with the existence of negative energy modes (NEMs). The ETG instability is then shown to arise through a Kre\u{\i}n-type bifurcation, due to the merging of a positive and a negative energy mode, corresponding to two modified drift waves admitted by the system. The Hamiltonian of the linearized system is then explicitly transformed into normal form, which unambiguously defines mode signature. In particular, the fast mode turns out to always be a positive energy mode (PEM), whereas the energy of the slow mode can have either positive or negative sign

Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method

The Vlasov-Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation ("lift") of the Vlasov-Maxwell bracket induced by the dynamical reduction of single-particle dynamics is investigated when the reduction is carried out by Lie-transform perturbation methods. The ultimate goal of this work is to derive explicit Hamiltonian formulations for the guiding-center and gyrokinetic Vlasov-Maxwell equations that have important applications in our understanding of turbulent magnetized plasmas. Here, it is shown that the general form of the reduced Vlasov-Maxwell equations possesses a Hamiltonian structure defined in terms of a reduced Hamiltonian functional and a reduced bracket that automatically satisfies the standard bracket properties.Comment: 39 page

Letters between W. J. Kerr and F. M. Morrison

Letters concerning a position in the mathematics department at Utah Agricultural College

A Deep Radio Survey of Abell 2125 III: The Cluster Core - Merging and Stripping

We use radio, near-IR, optical, and X-ray observations to examine dynamic processes in the central region of Abell 2125. In addition to the central triple, including members of both major dynamical subsystems identified from a redshift survey, this region features a galaxy showing strong evidence for ongoing gas stripping during a high-velocity passage through the gas in the cluster core. The disk galaxy C153 exhibits a plume stretching toward the cluster center seen in soft X-rays by Chandra, parts of which are also seen in [O II] emission and near-UV continuum light. HST imaging shows a distorted disk, with star-forming knots asymmetrically distributed and remnant spiral structure possibly defined by dust lanes. The stars and ionized gas in its disk are kinematically decoupled, demonstrating that pressure stripping must be important, and that tidal disruption is not the only mechanism at work. Comparison of the gas properties seen in the X-ray and optical data on the plume highlight significant features of the history of stripped gas in the intracluster medium. The nucleus of C153 also hosts an AGN, shown by the weak and distorted extended radio emission and a radio compact core. The unusual strength of the stripping signatures in this instance is likely related to the high relative velocity of the galaxy with respect to the intracluster medium, during a cluster/cluster merger, and its passage very near the core of the cluster. Another sign of recent dynamical events is diffuse starlight asymmetrically placed about the central triple in a cD envelope. Transient and extreme dynamical events as seen in Abell 2125 may be important drivers of galaxy evolution in the cores of rich clusters.Comment: 36 pages, 16 figures, accepted AJ, paper with full resolution figures is available at http:www.aoc.nrao.edu/~fowen/papers/a2125/a2125paper3.ps.g

CIR Modulation of the X-ray Flux from the O7.5 III(n)((f)) Star xi Persei?

We analyze a 162 ks HETG Chandra observation of the O7.5 III(n)((f)) star xi Per, together with contemporaneous H alpha observations. The X-ray spectrum of this star is similar to other single O stars, and not pathological in any way. Its UV wind lines are known to display cyclical time variability, with a period of 2.086 days, which is thought to be associated with co-rotating interaction regions (CIRs). We examine the Chandra and H alpha data for variability on this time scale. We find that the X-rays vary by about 15% over the course of the observations and that this variability is out of phase with variable absorption on the blue wing of the H alpha profiles (assumed to be a surrogate for the UV absorption associated with CIRs). While not conclusive, both sets of data are consistent with models where the CIRs are either a source of X-rays or modulate them.Comment: Accepted by MNRAS. 9 pages, 9 figure