Reference list for stability theory in ordinary differential equations

Reference list for stability and control theory in ordinary differential equation

Determination of Chilling Requirement of Arkansas Thornless Blackberry Cultivars

Little research has been done to determine the chilling requirement for blackberry cultivars. However, field observations from areas where fewer hours of chilling occur indicate that ‘Navaho’ requires more hours of chilling than does ‘Arapaho’. The objective of our study was to determine a method for measuring the chilling requirement using whole plants of two blackberry cultivars, Arapaho and Navaho. One-year old, bare-root plants were field-dug on 26 October 1999 and placed in a cold chamber at 3ºC. Ten single-plant replications of each cultivar were removed at 100-hour intervals up to 1000 hours. The plants were potted and placed in a greenhouse (daily minimum temperature 15ºC), and plants were arranged on benches in a completely randomized design. Budbreak was recorded on a weekly basis. Data for budbreak were analyzed as a two-factor factorial (2 cultivars and 10 chilling treatments) by SAS and means were separated by least significant difference (P = 0.05). Data indicated that the chilling requirement for Arapaho is between 400 and 500 hours. For Navaho, the data indicated the chilling requirement was between 800 and 900 hours. These data support previous observations and indicate that the method used was successful in determining the chilling requirement for blackberries

Prospects of Turbulence Studies in High-Energy Density Laser-Generated Plasma: Numerical Investigations in Two Dimensions

We investigate the possibility of generating and studying turbulence in plasma by means of high-energy density laser-driven experiments. Our focus is to create supersonic, self-magnetized turbulence with characteristics that resemble those found in the interstellar medium (ISM). We consider a target made of a spherical core surrounded by a shell made of denser material. The shell is irradiated by a sequence of laser pulses sending inward-propagating shocks that convert the inner core into plasma and create turbulence. In the context of the evolution of the ISM, the shocks play the role of supernova remnant shocks and the core represents the ionized interstellar medium. We consider the effects of both pre-existing and self-generating magnetic fields and study the evolution of the system by means of two-dimensional numerical simulations. We find that the evolution of the turbulent core is generally, subsonic with rms-Mach number $M_t\approx 0.2$. We observe an isotropic, turbulent velocity field with an inertial range power spectra of $P(k)\propto k^{-2.3}$. We account for the effects of self-magnetization and find that the resulting magnetic field has characteristic strength $\approx 3\times 10^{4}$ G. The corresponding plasma beta is $\approx 1\times 10^{4}$--$1\times 10^{5}$, indicating that the magnetic field does not play an important role in the dynamical evolution of the system. The natural extension of this work is to study the system evolution in three-dimensions, with various laser drive configurations, and targets with shells and cores of different masses. The latter modification may help to increase the turbulent intensity and possibly create transonic turbulence. One of the key challenges is to obtain transonic turbulent conditions in a quasi-steady state environment.Comment: High Energy Density Physics, in pres

Bare quark stars or naked neutron stars? The case of RX J1856.5-3754

In a cool neutron star (T less than or similar to 10(6) K) endowed with a rather highmagnetic field (B greater than or similar to 10(13) G), a phase transition may occur in the outermost layers. As a consequence, the neutron star becomes "bare,'' i.e., no gaseous atmosphere sits on the top of the crust. The surface of a cooling, bare neutron star does not necessarily emit a blackbody spectrum because the emissivity is strongly suppressed at energies below the electron plasma frequency, omega(p). Since omega(p) approximate to 1 keV under the conditions typical of the dense electron gas in the condensate, the emission from a T similar to 100 eV bare neutron star will be substantially depressed with respect to that of a perfect Planckian radiator atmost energies. Here we present a detailed analysis of the emission properties of a bare neutron star. In particular, we derive the surface emissivity for an Fe composition in a range of magnetic fields and temperatures representative of cooling isolated neutron stars, like RX J1856.5 - 3754. We find that the emitted spectrum is strongly dependent on the electron conductivity in the solid surface layers. In the cold electron gas approximation ( no electron-lattice interactions), the spectrum turns out to be a featureless depressed blackbody in the 0.1 - 2 keV band with a steeper low-energy distribution. When damping effects due to collisions between electrons and the ion lattice ( mainly due to electron-phonon interactions) are accounted for, the spectrum is more depressed at low energies and spectral features may be present, depending on the magnetic field strength. Details of the emitted spectrum are found, however, to be strongly dependent on the assumed treatment of the transition from the external vacuum to the metallic surface. The implications of our results for RX J1856.5 - 3754 and other isolated neutron stars are discussed

X-Ray Wakes in Abell 160

`Wakes' of X-ray emission have now been detected trailing behind a few (at least seven) elliptical galaxies in clusters. To quantify how widespread this phenomenon is, and what its nature might be, we have obtained a deep (70 ksec) X-ray image of the poor cluster Abell 160 using the ROSAT HRI. Combining the X-ray data with optical positions of confirmed cluster members, and applying a statistic designed to search for wake-like excesses, we confirm that this phenomenon is observed in galaxies in this cluster. The probability that the detections arise from chance is less than 0.0038. Further, the wakes are not randomly distributed in direction, but are preferentially oriented pointing away from the cluster centre. This arrangement can be explained by a simple model in which wakes arise from the stripping of their host galaxies' interstellar media due to ram pressure against the intracluster medium through which they travel.Comment: 7 pages, 7 figures, accepted for publication in MNRA

Three-dimensional simulations of the orientation and structure of reconnection X-lines

This work employs Hall magnetohydrodynamic (MHD) simulations to study the X-lines formed during the reconnection of magnetic fields with differing strengths and orientations embedded in plasmas of differing densities. Although random initial perturbations trigger the growth of X-lines with many orientations, at late time a few robust X-lines sharing an orientation reasonably consistent with the direction that maximizes the outflow speed, as predicted by Swisdak and Drake [Geophys. Res. Lett., 34, L11106, (2007)], dominate the system. The existence of reconnection in the geometry examined here contradicts the suggestion of Sonnerup [J. Geophys. Res., 79, 1546 (1974)] that reconnection occurs in a plane normal to the equilibrium current. At late time the growth of the X-lines stagnates, leaving them shorter than the simulation domain.Comment: Accepted by Physics of Plasma

Inverse Geometry for Stereolithographic Manufacturing

As parts produced by stereolithography form and cure, they warp and shrink to produce Pitrts that are not quite the san~ ~ as those originally specified. This research attempts to solve the inverse geomptry problem, that is, what shape should be specified initially so that the she pe produced is the desired one. Assuming that 'the process is repeatable, we ~neasure the difference between the ideal and actua). part dimensions. A finite-element based model is built which mirrors the distortion from the ideal geometry. A "pre-deformed" geometry is then built so that it deforms to the ideal geometry under the conditions imposed on the finite element model. This pre-warped geometry is the geometry we seek.Mechanical Engineerin

H2O abundances in the atmospheres of three hot Jupiters

The core accretion theory for giant planet formation predicts enrichment of elemental abundances in planetary envelopes caused by runaway accretion of planetesimals, which is consistent with measured super-solar abundances of C, N, P, S, Xe, and Ar in Jupiter's atmosphere. However, the abundance of O which is expected to be the most dominant constituent of planetesimals is unknown for solar system giant planets, owing to the condensation of water in their ultra-cold atmospheres, thereby posing a key unknown in solar system formation. On the other hand, hundreds of extrasolar hot Jupiters are known with very high temperatures (>~1000 K) making them excellent targets to measure H2O abundances and, hence, oxygen in their atmospheres. We constrain the atmospheric H2O abundances in three hot Jupiters (HD 189733b, HD 209458b, and WASP-12b), spanning a wide temperature range (1200-2500 K), using their near-infrared transmission spectra obtained using the HST WFC3 instrument. We report conclusive measurements of H2O in HD 189733b and HD 209458b, while that in WASP-12b is not well constrained by present data. The data allow nearly solar as well as significantly sub-solar abundances in HD 189733b and WASP-12b. However, for HD 209458b, we report the most precise H2O measurement in an exoplanet to date that suggests a ~20-135 sub-solar H2O abundance. We discuss the implications of our results on the formation conditions of hot Jupiters and on the likelihood of clouds in their atmospheres. Our results highlight the critical importance of high-precision spectra of hot Jupiters for deriving their H2O abundances.Comment: ApJ Letters, in pres