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

Hierarchical social modularity in gorillas

Modern human societies show hierarchical social modularity (HSM) in which lower-order social units like nuclear families are nested inside increasingly larger units. It has been argued that this HSM evolved independently and after the chimpanzee–human split due to greater recognition of, and bonding between, dispersed kin. We used network modularity analysis and hierarchical clustering to quantify community structure within two western lowland gorilla populations. In both communities, we detected two hierarchically nested tiers of social structure which have not been previously quantified. Both tiers map closely to human social tiers. Genetic data from one population suggested that, as in humans, social unit membership was kin structured. The sizes of gorilla social units also showed the kind of consistent scaling ratio between social tiers observed in humans, baboons, toothed whales, and elephants. These results indicate that the hierarchical social organization observed in humans may have evolved far earlier than previously asserted and may not be a product of the social brain evolution unique to the hominin lineage

A discontinuous Galerkin method for the Vlasov-Poisson system

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates associated system's approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86 figure

Passivation of pigment particles for thermal control coatings

The preparation of a matrix of 48 samples consisting of pigments and pigmented paints is described. The results obtained from testing these samples by electron spin resonance and by in situ spectral reflectance measurements in space simulation tests are presented. Conclusions and recommendations for further research are given