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

Use of accelerometry to investigate physical activity in dogs receiving chemotherapy

Objectives: To perform a preliminary study to assess whether single-agent palliative or adjuvant chemotherapy has an impact on objectively measured physical activity in dogs. Methods: Fifteen dogs with neoplasia (treatment group) wore ActiGraph™ accelerometers for 5-day periods before, during and after receiving single-agent adjuvant or palliative chemotherapy. Mean 5-day total physical activity and time spent in three different intensities of activity (sedentary, light-moderate and vigorous) before, during and after receiving chemotherapy were compared to a group of 15 healthy dogs (control group). Results were also compared within the treatment group across time. Results: Prior to chemotherapy, treated dogs tended to be less active than control dogs. Treatment group dogs were slightly more active at restaging than they were prior to treatment but had similar activity levels to control dogs. Marked effects of chemotherapy on physical activity were not detected. Physical activity was slightly lower in treated dogs during chemotherapy when compared to control dogs but there was a slight increase in physical activity of treated dogs during chemotherapy when compared with pretreatment recordings. There was little change in the mean 5-day total physical activity between treated dogs during chemotherapy and at restaging but a mild decrease in time spent sedentary and increase in time spent in light-moderate activity at this comparison of time points. Clinical Significance: Single-agent adjuvant or palliative chemotherapy had minimal impact on physical activity levels in dogs with neoplasia

Evolution from a molecular Rydberg gas to an ultracold plasma in a seeded supersonic expansion of NO

We report the spontaneous formation of a plasma from a gas of cold Rydberg molecules. Double-resonant laser excitation promotes nitric oxide, cooled to 1 K in a seeded supersonic molecular beam, to single Rydberg states extending as deep as 80 cm$^{-1}$ below the lowest ionization threshold. The density of excited molecules in the illuminated volume is as high as 1 x 10$^{13}$ cm$^{-3}$. This population evolves to produce prompt free electrons and a durable cold plasma of electrons and intact NO$^{+}$ ions.Comment: 4 pages (two column) 3 figures; smaller figure files, corrected typo

Effective transport barriers in nontwist systems

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called standard nontwist map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickiness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickiness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents.FAPESPCNPqCAPESMCT/CNEN (Rede Nacional de Fusao)Fundacao AraucariaUS Department of Energy DE-FG05-80ET-53088Physic

Shear wave generation using a spiral electromagnetic acoustic transducer

A spiral electromagnetic acoustic transducer (EMAT) is efficient in eddy current generation and has been used for surface defect inspection using Rayleigh waves or thickness gauging based on plane waves in echo mode. Measured and calculated particle velocities and directivities are presented. It is found that the shear wave is not predominantly a plane wave. It has zero amplitude on the axis of the generation EMAT and has maximum amplitude at the critical angle. The shear wave could be used in the steel industry for both internal and surface defect inspections together with Rayleigh wave

Mesons and Flavor on the Conifold

We explore the addition of fundamental matter to the Klebanov-Witten field theory. We add probe D7-branes to the ${\cal N}=1$ theory obtained from placing D3-branes at the tip of the conifold and compute the meson spectrum for the scalar mesons. In the UV limit of massless quarks we find the exact dimensions of the associated operators, which exhibit a simple scaling in the large-charge limit. For the case of massive quarks we compute the spectrum of scalar mesons numerically.Comment: 19 pages, 3 figures, v2: typos fixe

Superconformal field theories from crystal lattices

We propose a brane configuration for the (2+1)d, $\mathcal{N}=2$ superconformal theories (CFT$_3$) arising from M2-branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M-theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT$_4$. The fundamental fields of the CFT$_3$ are M2-brane discs localized around the intersections, and the super-potential terms are identified with the atoms of the crystal. The model correctly reproduces the complete BPS spectrum of mesons and baryons.Comment: 4 pages, 4 figures, revtex; v2. references added, minor correction

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

Complex Line Bundles over Simplicial Complexes and their Applications

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension