Compensation for Spherical Geometric and Absorption Effects on Lower Thermospheric Emission Intensities Derived from High Earth Orbit Images

Remote sensing of the atmosphere from high earth orbit is very attractive due to the large field of view obtained and a true global perspective. This viewpoint is complicated by earth curvature effects so that slant path enhancement and absorption effects, small from low earth orbit, become dominant even at small nadir view angles. The effect is further complicated by the large range of local times and solar zenith angles in a single image leading to a modulation of the image intensity by a significant portion of the diurnal height variation of the absorbing layer. The latter effect is significant in particular for mesospheric, stratospheric and auroral emissions due to their depth in the atmosphere. As a particular case, the emissions from atomic oxygen (130.4 and 135.6 nm) and molecular nitrogen (two LBH bands, LBHS from 140 to 160 nm and LBHL from 160 to 180 nm) as viewed from the Ultraviolet Imager (UVI) are examined. The LBH emissions are of particular interest since LBHS has significant 02 absorption while LBHL does not, In the case of auroral emissions this differential absorption, well examined in the nadir, gives information about the height of the emission and therefore the energy of the precipitating particles. Using simulations of the viewing geometry and images from the UVI we examine these effects and obtain correction factors to adjust to the nadir case with a significant improvement of the derived characteristic energy. There is a surprisingly large effect on the images from the 02 diurnal layer height changes. An empirical compensation to the nadir case is explored based on the local nadir and local zenith angles for each portion of the image. These compensations are demonstrated as applied to the above emissions in both auroral and dayglow images and compared to models. The extension of these findings to other instruments, emissions and spectral regions is examined

Numerical study of pattern formation following a convective instability in non-Boussinesq fluids

We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The formation of hexagonal patterns, rolls and spirals is studied, as well as the transitions and competition among them. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two dimensional model is consistent with the prediction of marginal stability theory for one dimensional fronts.Comment: 9 pages, report FSU-SCRI-92-6

Predicting watershed erosion production and over-land sediment transport using a GIS, in: Carrying the Torch for Erosion Control: An Olympic Task

ABSTRACT Soil erosion from forested lands can seriously degrade stream water quality. Sediment production and over-land sediment transport models have been developed which predict ecosystem management impacts on soil erosion and movement across watersheds. The predictions of soil erosion are for whole watersheds, not for points within the watershed. Soil erosion and transport models are usually run independently. From a spatial perspective, the models are difficult to define and the output is difficult to interpret. Our research utilizes a user friendly, modular based, Geographic Information System (GIS) for predicting soil erosion and over-land sediment transport under a variety of management practices including road building, timber harvesting, burning, and creation of wildlife food plots, given a range of storm intensities broken into four seasons (i.e., spring, summer, fall, winter). Through the use of a GIS, model predictions of sediment can be spatially distributed across the watershed and displayed as map outputs of eroded soil deposition. The major objective of this paper is to demonstrate how a GIS and a modular modeling approach can be used by land managers to develop alternative management scenarios for cumulative effects assessment in forested watersheds. As improved soil erosion and transport models are developed, new models can be easily exchanged with current models using a GIS as an integrating database tool. &apos

Degeneracy Algorithm for Random Magnets

It has been known for a long time that the ground state problem of random magnets, e.g. random field Ising model (RFIM), can be mapped onto the max-flow/min-cut problem of transportation networks. I build on this approach, relying on the concept of residual graph, and design an algorithm that I prove to be exact for finding all the minimum cuts, i.e. the ground state degeneracy of these systems. I demonstrate that this algorithm is also relevant for the study of the ground state properties of the dilute Ising antiferromagnet in a constant field (DAFF) and interfaces in random bond magnets.Comment: 17 pages(Revtex), 8 Postscript figures(5color) to appear in Phys. Rev. E 58, December 1st (1998

On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d \geq 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen-Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that a series of published numerical studies are problematic: shrinking the mesh size in these simulations does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics (Dec 2011

Hilbert Lattice Equations

There are five known classes of lattice equations that hold in every infinite dimensional Hilbert space underlying quantum systems: generalised orthoarguesian, Mayet's E_A, Godowski, Mayet-Godowski, and Mayet's E equations. We obtain a result which opens a possibility that the first two classes coincide. We devise new algorithms to generate Mayet-Godowski equations that allow us to prove that the fourth class properly includes the third. An open problem related to the last class is answered. Finally, we show some new results on the Godowski lattices characterising the third class of equations.Comment: 24 pages, 3 figure