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

Status of Muon Collider Research and Development and Future Plans

The status of the research on muon colliders is discussed and plans are outlined for future theoretical and experimental studies. Besides continued work on the parameters of a 3-4 and 0.5 TeV center-of-mass (CoM) energy collider, many studies are now concentrating on a machine near 0.1 TeV (CoM) that could be a factory for the s-channel production of Higgs particles. We discuss the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-Z target and proceeding through the phase rotation and decay ($\pi \to \mu \nu_{\mu}$) channel, muon cooling, acceleration, storage in a collider ring and the collider detector. We also present theoretical and experimental R & D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This report is an update of the progress on the R & D since the Feasibility Study of Muon Colliders presented at the Snowmass'96 Workshop [R. B. Palmer, A. Sessler and A. Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics (Stanford Linear Accelerator Center, Menlo Park, CA, 1997)].Comment: 95 pages, 75 figures. Submitted to Physical Review Special Topics, Accelerators and Beam

Bioreactors as engineering support to treat cardiac muscle and vascular disease

Cardiovascular disease is the leading cause of morbidity and mortality in the Western World. The inability of fully differentiated, load-bearing cardiovascular tissues to in vivo regenerate and the limitations of the current treatment therapies greatly motivate the efforts of cardiovascular tissue engineering to become an effective clinical strategy for injured heart and vessels. For the effective production of organized and functional cardiovascular engineered constructs in vitro, a suitable dynamic environment is essential, and can be achieved and maintained within bioreactors. Bioreactors are technological devices that, while monitoring and controlling the culture environment and stimulating the construct, attempt to mimic the physiological milieu. In this study, a review of the current state of the art of bioreactor solutions for cardiovascular tissue engineering is presented, with emphasis on bioreactors and biophysical stimuli adopted for investigating the mechanisms influencing cardiovascular tissue development, and for eventually generating suitable cardiovascular tissue replacements

Carbon cycling in the North American coastal ocean: a synthesis

A quantification of carbon fluxes in the coastal ocean and across its boundaries with the atmosphere, land, and the open ocean is important for assessing the current state and projecting future trends in ocean carbon uptake and coastal ocean acidification, but this is currently a missing component of global carbon budgeting. This synthesis reviews recent progress in characterizing these carbon fluxes for the North American coastal ocean. Several observing networks and high-resolution regional models are now available. Recent efforts have focused primarily on quantifying the net air–sea exchange of carbon dioxide (CO2). Some studies have estimated other key fluxes, such as the exchange of organic and inorganic carbon between shelves and the open ocean. Available estimates of air–sea CO2 flux, informed by more than a decade of observations, indicate that the North American Exclusive Economic Zone (EEZ) acts as a sink of 160±80&thinsp;Tg&thinsp;C&thinsp;yr−1, although this flux is not well constrained. The Arctic and sub-Arctic, mid-latitude Atlantic, and mid-latitude Pacific portions of the EEZ account for 104, 62, and −3.7&thinsp;Tg&thinsp;C&thinsp;yr−1, respectively, while making up 51&thinsp;%, 25&thinsp;%, and 24&thinsp;% of the total area, respectively. Combining the net uptake of 160±80&thinsp;Tg&thinsp;C&thinsp;yr−1 with an estimated carbon input from land of 106±30&thinsp;Tg&thinsp;C&thinsp;yr−1 minus an estimated burial of 65±55&thinsp;Tg&thinsp;C&thinsp;yr−1 and an estimated accumulation of dissolved carbon in EEZ waters of 50±25&thinsp;Tg&thinsp;C&thinsp;yr−1 implies a carbon export of 151±105&thinsp;Tg&thinsp;C&thinsp;yr−1 to the open ocean. The increasing concentration of inorganic carbon in coastal and open-ocean waters leads to ocean acidification. As a result, conditions favoring the dissolution of calcium carbonate occur regularly in subsurface coastal waters in the Arctic, which are naturally prone to low pH, and the North Pacific, where upwelling of deep, carbon-rich waters has intensified. Expanded monitoring and extension of existing model capabilities are required to provide more reliable coastal carbon budgets, projections of future states of the coastal ocean, and quantification of anthropogenic carbon contributions.</p

Bayesian Spectrum Analysis for Laser Vibrometry Processing

Laser vibration sensing provides a sensitive non-contact means of measuring vibrations of objects. These measurements are used in industrial quality control and wear monitoring as well as the analysis of the vibrational characteristics of objects. In laser vibrometry, the surface motion is monitored by heterodyne laser Doppler velocimetry, and the received heterodyne signal is sampled to produce a time-series which is processed to obtain a vibrational spectrum of the object under test. Laser vibrometry data has been processed with a traditional FM discriminator approach and by spectrogram and time-frequency distribution processing techniques. The latter techniques have demonstrated improved performance over the FM discriminator method, but do not take full advantage of the prior knowledge one has about the signal of interest. We consider here a statistical signal processing approach to laser vibrometry data. In this approach the quantities of interest are the frequencies of vibration, while the phase and quadrature amplitudes are considered nuisance parameters. Because of the optimal use of prior knowledge about the laser vibrometry signal, the frequencies can be determined with much greater precision and greater noise immunity than using Fourier- or time-frequency-based approaches. Furthermore, the statistical approach is known to have superior performance when the data extends over a small number of vibrational periods. We illustrate the method with data from a beroptic laser Doppler velocimeter. Our results show that while the choice of processing method for determining the instantaneous velocity is relatively unimportant, the Bayesian method exhibits superior performance in determining the vibrational frequency

Short‐run wavelet‐based covariance regimes for applied portfolio management

Decisions on asset allocations are often determined by covariance estimates from historical market data. In this paper, we introduce a wavelet-based portfolio algorithm, distinguishing between newly embedded news and long-run information that has already been fully absorbed by the market. Exploiting the wavelet decomposition into short- and long-run covariance regimes, we introduce an approach to focus on particular covariance components. Using generated data, we demonstrate that short-run covariance regimes comprise the relevant information for periodical portfolio management. In an empirical application to US stocks and other international markets for weekly, monthly, quarterly, and yearly holding periods (and rebalancing), we present evidence that the application of wavelet-based covariance estimates from short-run information outperforms portfolio allocations that are based on covariance estimates from historical data