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

Temperature gradient and electric field driven electrostatic instabilities

The stability of electrostatic waves to thermodynamic and electric potential gradients was investigated. It is shown that thermodynamic gradients drive instabilities even when the internal electric field vanishes. Skewing of the distribution function is not included in the dielectric

Exactly Conservative Integrators

Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.Comment: 30 pages, postscript (1.3MB). Submitted to SIAM J. Sci. Comput

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

Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map

The breakup of shearless invariant tori with winding number $\omega=[0,1,11,1,1,...]$ (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this winding number can assume the shape of meanders (folded-over invariant tori which are not graphs over the x-axis in $(x,y)$ phase space), whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this winding number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated.Comment: submitted to Chao