Orbit and attitude determination results during launch support operations for SBS-5

Presented are orbit and attitude determination results from the launch of Satellite Business Systems (SBS)-5 satellite on September 8, 1988 by Arianespace. SBS-5 is a (HS-376) spin stabilized spacecraft. The launch vehicle injected the spacecraft into a low inclination transfer orbit. Apogee motor firing (AMF) attitude was achieved with trim maneuvers. An apogee kick motor placed the spacecraft into drift orbit. Postburn, reorientation and spindown maneuvers were performed during the next 25 hours. The spacecraft was on-station 19 days later. The orbit and attitude were determined by both an extended Kalman filter and a weighted least squares batch processor. Although the orbit inclination was low and the launch was near equinox, post-AMF analysis indicated an attitude declination error of 0.034 deg., resulting in a saving of 8.5 pounds of fuel. The AMF velocity error was 0.4 percent below nominal. The post-AMF drift rate was determined with the filter only 2.5 hours after motor firing. The filter was used to monitor and retarget the reorientation to orbit normal in real time

Non-imprisonment conditions on spacetime

The non-imprisonment conditions on spacetimes are studied. It is proved that the non-partial imprisonment property implies the distinction property. Moreover, it is proved that feeble distinction, a property which stays between weak distinction and causality, implies non-total imprisonment. As a result the non-imprisonment conditions can be included in the causal ladder of spacetimes. Finally, totally imprisoned causal curves are studied in detail, and results concerning the existence and properties of minimal invariant sets are obtained.Comment: 12 pages, 2 figures. v2: improved results on totally imprisoned curves, a figure changed, some misprints fixe

Extending Romanovski polynomials in quantum mechanics

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally-extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties of second-order differential equations of Schr\"odinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.Comment: 25 pages, no figure, small changes, 3 additional references, published versio

Modelling the dynamics of turbulent floods

Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow: resolves the vertical structure of the flow and the turbulence; includes interaction between turbulence and long waves; and gives a rational alternative to classical models for turbulent environmental flows

Modeling inflammation and oxidative stress in gastrointestinal disease development using novel organotypic culture systems.

Gastroesophageal reflux disease (GERD), Barrett's esophagus (BE), graft-versus-host disease (GVHD), and inflammatory bowel diseases such as ulcerative colitis and Crohn's disease are common human gastrointestinal diseases that share inflammation as a key driver for their development. A general outcome resulting from these chronic inflammatory conditions is increased oxidative stress. Oxidative stress is caused by the generation of reactive oxygen and nitrogen species that are part of the normal inflammatory response, but are also capable of damaging cellular DNA, protein, and organelles. Damage to DNA can include DNA strand breaks, point mutations due to DNA adducts, as well as alterations in methylation patterns leading to activation of oncogenes or inactivation of tumor suppressors. There are a number of significant long-term consequences associated with chronic oxidative stress, most notably cancer. Infiltrating immune cells and stromal components of tissue including fibroblasts contribute to dynamic changes occurring in tissue related to disease development. Immune cells can potentiate oxidative stress, and fibroblasts have the capacity to contribute to advanced growth and proliferation of the epithelium and any resultant cancers. Disease models for GERD, BE, GVHD, and ulcerative colitis based on three-dimensional human cell and tissue culture systems that recapitulate in vivo growth and differentiation in inflammatory-associated microphysiological environments would enhance our understanding of disease progression and improve our ability to test for disease-prevention strategies. The development of physiologically relevant, human cell-based culture systems is therefore a major focus of our research. These novel models will be of enormous value, allowing us to test hypotheses and advance our understanding of these disorders, and will have a translational impact allowing us to more rapidly develop therapeutic and chemopreventive agents. In summary, this work to develop advanced human cell-based models of inflammatory conditions will greatly improve our ability to study, prevent, and treat GERD, BE, GVHD, and inflammatory bowel disease. The work will also foster the development of novel therapeutic and preventive strategies that will improve patient care for these important clinical conditions

Branching of the Falkner-Skan solutions for λ < 0

The Falkner-Skan equation f'" + ff" + λ(1 - f'^2) = 0, f(0) = f'(0) = 0, is discussed for λ < 0. Two types of problems, one with f'(∞) = 1 and another with f'(∞) = -1, are considered. For λ = 0- a close relation between these two types is found. For λ < -1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f' - 1. The numerical results indicate that the solution branches with f'(∞) = 1 and those with f'(∞) = -1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for λ < -1, is presented.

Stochastic Flux-Freezing and Magnetic Dynamo

We argue that magnetic flux-conservation in turbulent plasmas at high magnetic Reynolds numbers neither holds in the conventional sense nor is entirely broken, but instead is valid in a novel statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. We discuss empirical evidence for spontaneous stochasticity, including our own new numerical results. We then use a Lagrangian path-integral approach to establish stochastic flux-freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux-conservation must remain stochastic at infinite magnetic Reynolds number. As an important application of these results we consider the kinematic, fluctuation dynamo in non-helical, incompressible turbulence at unit magnetic Prandtl number. We present results on the Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. We finally consider briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure