Reference list for stability theory in ordinary differential equations

Reference list for stability and control theory in ordinary differential equation

Infrared Observations During the Secondary Eclipse of HD 209458 b II. Strong Limits on the Infrared Spectrum Near 2.2 Microns

We report observations of the transiting extrasolar planet, HD 209458 b, designed to detect the secondary eclipse. We employ the method of `occultation spectroscopy', which searches in combined light (star and planet) for the disappearance and reappearance of weak infrared spectral features due to the planet as it passes behind the star and reappears. Our observations cover two predicted secondary eclipse events, and we obtained 1036 individual spectra of the HD 209458 system using the SpeX instrument at the NASA IRTF in September 2001. Our spectra extend from 1.9 to 4.2 microns with a spectral resolution of 1500. We have searched for a continuum peak near 2.2 microns (caused by CO and water absorption bands), as predicted by some models of the planetary atmosphere to be approximately 6E-4 of the stellar flux, but no such peak is detected at a level of about 3E-4 of the stellar flux. Our results represent the strongest limits on the infrared spectrum of the planet to date and carry significant implications for understanding the planetary atmosphere. In particular, some models that assume the stellar irradiation is re-radiated entirely on the sub-stellar hemisphere predict a flux peak inconsistent with our observations. Several physical mechanisms can improve agreement with our observations, including the re-distribution of heat by global circulation, a nearly isothermal atmosphere, and/or the presence of a high cloud.Comment: Accepted to the Astrophysical Journal 17 pages, 6 figure

The application of airborne imaging radars (L and X-band) to earth resources problems

For abstract, see N75-24064

Turbulence in Three-Dimensional Simulations of Magnetopause Reconnection

We present detailed analysis of the turbulence observed in three-dimensional particle-in-cell simulations of magnetic reconnection at the magnetopause. The parameters are representative of an electron diffusion region encounter of the Magnetospheric Multiscale (MMS) mission. The turbulence is found to develop around both the magnetic X line and separatrices, is electromagnetic in nature, is characterized by a wave vector $k$ given by $k\rho_e\sim(m_eT_e/m_iT_i)^{0.25}$ with $\rho_e$ the electron Larmor radius, and appears to have the ion pressure gradient as its source of free energy. Taken together, these results suggest the instability is a variant of the lower hybrid drift instability. The turbulence produces electric field fluctuations in the out-of-plane direction (the direction of the reconnection electric field) with an amplitude of around $\pm 10$~mV/m, which is much greater than the reconnection electric field of around $0.1$~mV/m. Such large values of the out-of-plane electric field have been identified in the MMS data. The turbulence in the simulations controls the scale lengths of the density profile and current layers in asymmetric reconnection, driving them closer to $\sqrt{\rho_e\rho_i}$ than the $\rho_e$ or $d_e$ scalings seen in 2-D reconnection simulations, and produces significant anomalous resistivity and viscosity in the electron diffusion region.Comment: 11 pages, 10 figure

Study of fuel cells using storable rocket propellants quarterly report no. 2, 18 may - 17 aug. 1965

Catalysts for Aerozine-50 reforming and nitrogen tetroxide decomposition for development of rocket fuel cells operating on storable propellan

Super-Alfv\'enic propagation of reconnection signatures and Poynting flux during substorms

The propagation of reconnection signatures and their associated energy are examined using kinetic particle-in-cell simulations and Cluster satellite observations. It is found that the quadrupolar out-of-plane magnetic field near the separatrices is associated with a kinetic Alfv\'en wave. For magnetotail parameters, the parallel propagation of this wave is super-Alfv\'enic (V_parallel ~ 1500 - 5500 km/s) and generates substantial Poynting flux (S ~ 10^-5 - 10^-4 W/m^2) consistent with Cluster observations of magnetic reconnection. This Poynting flux substantially exceeds that due to frozen-in ion bulk outflows and is sufficient to generate white light aurora in the Earth's ionosphere.Comment: Submitted to PRL on 11/1/2010. Resubmitted on 4/5/201

The Effects of Turbulence on Three-Dimensional Magnetic Reconnection at the Magnetopause

Two- and three-dimensional particle-in-cell simulations of a recent encounter of the Magnetospheric Multiscale Mission (MMS) with an electron diffusion region at the magnetopause are presented. While the two-dimensional simulation is laminar, turbulence develops at both the x-line and along the magnetic separatrices in the three-dimensional simulation. The turbulence is strong enough to make the magnetic field around the reconnection island chaotic and produces both anomalous resistivity and anomalous viscosity. Each contribute significantly to breaking the frozen-in condition in the electron diffusion region. A surprise is that the crescent-shaped features in velocity space seen both in MMS observations and in two-dimensional simulations survive, even in the turbulent environment of the three-dimensional system. This suggests that MMS's measurements of crescent distributions do not exclude the possibility that turbulence plays an important role in magnetopause reconnection.Comment: Revised version accepted by GR

A Statistical Model of Magnetic Islands in a Large Current Layer

We develop a statistical model describing the dynamics of magnetic islands in very large current layers that develop in space plasma. Two parameters characterize the island distribution: the flux contained in the island and the area it encloses. We derive an integro-differential evolution equation for this distribution function, based on rules that govern the small-scale generation of secondary islands, the rates of island growth, and island merging. Our numerical solutions of this equation produce island distributions relevant to the magnetosphere and corona. We also derive and analytically solve a differential equation for large islands that explicitly shows the role merging plays in island growth.Comment: 4 pages, 3 figure

Empires and Percolation: Stochastic Merging of Adjacent Regions

We introduce a stochastic model in which adjacent planar regions $A, B$ merge stochastically at some rate $\lambda(A,B)$, and observe analogies with the well-studied topics of mean-field coagulation and of bond percolation. Do infinite regions appear in finite time? We give a simple condition on $\lambda$ for this {\em hegemony} property to hold, and another simple condition for it to not hold, but there is a large gap between these conditions, which includes the case $\lambda(A,B) \equiv 1$. For this case, a non-rigorous analytic argument and simulations suggest hegemony.Comment: 13 page