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At least 163 records · Page 9

Quantitative Measures for Software Independent Verification and Validation

As software is maintained or reused, it undergoes an evolution which tends to increase the overall complexity of the code. To understand the effects of this, we brought in statistics experts and leading researchers in software complexity, reliability, and their interrelationships. These experts' project has resulted in our ability to statistically correlate specific code complexity attributes, in orthogonal domains, to errors found over time in the HAL/S flight software which flies in the Space Shuttle. Although only a prototype-tools experiment, the result of this research appears to be extendable to all other NASA software, given appropriate data similar to that logged for the Shuttle onboard software. Our research has demonstrated that a more complete domain coverage can be mathematically demonstrated with the approach we have applied, thereby ensuring full insight into the cause-and-effects relationship between the complexity of a software system and the fault density of that system. By applying the operational profile we can characterize the dynamic effects of software path complexity under this same approach We now have the ability to measure specific attributes which have been statistically demonstrated to correlate to increased error probability, and to know which actions to take, for each complexity domain. Shuttle software verifiers can now monitor the changes in the software complexity, assess the added or decreased risk of software faults in modified code, and determine necessary corrections. The reports, tool documentation, user's guides, and new approach that have resulted from this research effort represent advances in the state of the art of software quality and reliability assurance. Details describing how to apply this technique to other NASA code are contained in this document.

Lee, Alice↗

Mathematical Inversion of Lightning Data: Techniques and Applications

A survey of some interesting mathematical inversion studies dealing with radio, optical, and electrostatic measurements of lightning are presented. A discussion of why NASA is interested in lightning, what specific physical properties of lightning are retrieved, and what mathematical techniques are used to perform the retrievals are discussed. In particular, a relatively new multi-station VHF time-of-arrival (TOA) antenna network is now on-line in Northern Alabama and will be discussed. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The LMA supports on-going ground-validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. The LMA also provides detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and offers interesting comparisons with other meteorological/geophysical datasets. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. A new channel mapping retrieval algorithm is introduced for this purpose. To characterize the spatial distribution of retrieval errors, the algorithm has been applied to analyze literally tens of millions of computer-simulated lightning VHF point sources that have been placed at various ranges, azimuths, and altitudes relative to the LMA network. Statistical results are conveniently summarized in high-resolution, color-coded, error maps.

Koshak, William↗

Coupled CFD-PBE Predictions of Renal Stone Size Distributions in the Nephron in Microgravity

In this paper, a deterministic model is developed to assess the risk of critical renal stone formation for astronauts during space travel. A Population Balance Equation (PBE) model is used to compute the size distribution of a population of nucleating, growing and agglomerating renal calculi as they are transported through different sections of the nephron. The PBE model is coupled to a Computational Fluid Dynamics (CFD) model that solves for steady state flow of urine and transport of renal calculi along with the concentrations of ionic species, calcium and oxalate, in the nephron using an Eulerian two-phase mathematical framework. Parametric simulation are performed to study stone size enhancement and steady state volume fraction distributions in the four main sections of the nephron under weightlessness conditions. Contribution of agglomeration to the stone size distribution and effect of wall friction on the stone volume fraction distributions are carefully examined. Case studies using measured astronaut urinary calcium and oxalate concentrations in microgravity as input indicate that under nominal conditions the largest stone sizes developed in Space will be still considerably below the critical range for problematic stone development. However, results also indicate that the highest stone volume fraction occurs next to the tubule and duct walls. This suggests that there is an increased potential for wall adhesion with the possibility of evolution towards critical stone sizes.

Microgravity↗

Coupled CFD-PBE Predictions of Renal Stone Size Distributions in the Nephron in Microgravity

In this paper, a deterministic model is developed to assess the risk of critical renal stone formation for astronauts during space travel. A Population Balance Equation (PBE) model is used to compute the size distribution of a population of nucleating, growing and agglomerating renal calculi as they are transported through different sections of the nephron. The PBE model is coupled to a Computational Fluid Dynamics (CFD) model that solves for steady state flow of urine and transport of renal calculi along with the concentrations of ionic species, calcium and oxalate, in the nephron using an Eulerian two-phase mathematical framework. Parametric simulation are performed to study stone size enhancement and steady state volume fraction distributions in the four main sections of the nephron under weightlessness conditions. Contribution of agglomeration to the stone size distribution and effect of wall friction on the stone volume fraction distributions are carefully examined. Case studies using measured astronaut urinary calcium and oxalate concentrations in microgravity as input indicate that under nominal conditions the largest stone sizes developed in Space will be still considerably below the critical range for problematic stone development. However, results also indicate that the highest stone volume fraction occurs next to the tubule and duct walls. This suggests that there is an increased potential for wall adhesion with the possibility of evolution towards critical stone sizes.

Crystal Growth↗

Verification and Improvement of Flamelet Approach for Non-Premixed Flames

Studies in the mathematical modeling of the high-speed turbulent combustion has received renewal attention in the recent years. The review of fundamentals, approaches and extensive bibliography was presented by Bray, Libbi and Williams. In order to obtain accurate predictions for turbulent combustible flows, the effects of turbulent fluctuations on the chemical source terms should be taken into account. The averaging of chemical source terms requires to utilize probability density function (PDF) model. There are two main approaches which are dominant in high-speed combustion modeling now. In the first approach, PDF form is assumed based on intuitia of modelliers (see, for example, Spiegler et.al.; Girimaji; Baurle et.al.). The second way is much more elaborate and it is based on the solution of evolution equation for PDF. This approach was proposed by S.Pope for incompressible flames. Recently, it was modified for modeling of compressible flames in studies of Farschi; Hsu; Hsu, Raji, Norris; Eifer, Kollman. But its realization in CFD is extremely expensive in computations due to large multidimensionality of PDF evolution equation (Baurle, Hsu, Hassan).

Zaitsev, S.↗

Cosmic Complexity

What explains the extraordinary complexity of the observed universe, on all scales from quarks to the accelerating universe? My favorite explanation (which I certainty did not invent) ls that the fundamental laws of physics produce natural instability, energy flows, and chaos. Some call the result the Life Force, some note that the Earth is a living system itself (Gaia, a "tough bitch" according to Margulis), and some conclude that the observed complexity requires a supernatural explanation (of which we have many). But my dad was a statistician (of dairy cows) and he told me about cells and genes and evolution and chance when I was very small. So a scientist must look for me explanation of how nature's laws and statistics brought us into conscious existence. And how is that seemll"!gly Improbable events are actually happening a!1 the time? Well, the physicists have countless examples of natural instability, in which energy is released to power change from simplicity to complexity. One of the most common to see is that cooling water vapor below the freezing point produces snowflakes, no two alike, and all complex and beautiful. We see it often so we are not amazed. But physlc!sts have observed so many kinds of these changes from one structure to another (we call them phase transitions) that the Nobel Prize in 1992 could be awarded for understanding the mathematics of their common features. Now for a few examples of how the laws of nature produce the instabilities that lead to our own existence. First, the Big Bang (what an insufficient name!) apparently came from an instability, in which the "false vacuum" eventually decayed into the ordinary vacuum we have today, plus the most fundamental particles we know, the quarks and leptons. So the universe as a whole started with an instability. Then, a great expansion and cooling happened, and the loose quarks, finding themselves unstable too, bound themselves together into today's less elementary particles like protons and neutrons, liberating a little energy and creating complexity. Then, the expanding universe cooled some more, and neutrons and protons, no longer kept apart by immense temperatures, found themselves unstable and formed helium nuclei. Then, a little more cooling, and atomic nuclei and electrons were no longer kept apart, and the universe became transparent. Then a little more cooling, and the next instability began: gravitation pulled matter together across cosmic distances to form stars and galaxies. This instability is described as a "negative heat capadty" in which extracting energy from a gravitating system makes it hotter -- clearly the 2nd law of thermodynamics does not apply here! (This is the physicist's part of the answer to e e cummings' question: what is the wonder that's keeping the stars apart?) Then, the next instability is that hydrogen and helium nuclei can fuse together to release energy and make stars burn for billions of years. And then at the end of the fuel source, stars become unstable and explode and liberate the chemical elements back into space. And because of that, on planets like Earth, sustained energy flows support the development of additional instabilities and all kinds of complex patterns. Gravitational instability pulls the densest materials into the core of the Earth, leaving a thin skin of water and air, and makes the interior churn incessantly as heat flows outwards. And the heat from the sun, received mostly near the equator and flowing towards the poles, supports the complex atmospheric and oceanic circulations. And because or that, the physical Earth is full of natural chemical laboratories, concentrating elements here, mixing them there, raising and lowering temperatures, ceaselessly experimenting with uncountable events where new instabilities can arise. At least one of them was the new experiment called life. Now that we know that there are at least as many planets as there are stars, it is hard to imagine that nature's ceasess experimentation would not be able to produce life elsewhere -- but we don't know for sure. And life went on to cause new Instabilities, constantly evolving, with living things in an extraordinary range of environments, changing the global environment, with boom-and-bust cycles. with predators for every kInd of prey, with criminals for every possible crime, with governments to prevent them, and instabilities of the governments themselves. One of the instabilities Is that humans demand new weapons and new products of all sort, leading to serious investments in science and technology. So the natural/human world of competition and combat is structured to lead to advanced weaponry and cell phones. So here we are In 2012, with people writing essays and wondering whether their descendents will be artificial life forms travelling back into space. And, pondering what are the origins of those forces of nature that give rise to everything. Verllnde has argued that gravitation, the one force that has so far resisted our efforts at a Quantum description, is not even a fundamental force, but is itself it a statistical force, like osmosis. What an amazing turn of events! But after all I've just said, I should not be surprised a bit.

Mather, John C.↗

Parasitic Interference in Nulling Interferometry

Nulling interferometry aims to detect faint objects close to bright stars. Its principle is to produce a destructive interference along the line of sight so that the stellar flux is rejected, while the flux of the off-axis source can be transmitted. In practice, various instrumental perturbations can degrade the nulling performance. Any imperfection in phase, amplitude or polarization produces a spurious flux that leaks to the interferometer output and corrupts the transmitted off-axis flux. One of these instrumental perturbations is the crosstalk phenomenon, which occurs because of multiple parasitic reflections inside transmitting optics, and/or diffraction effects related to beam propagation along finite size optics. It can include a crosstalk of a beam with itself, and a mutual crosstalk between different beams. This can create a parasitic interference pattern, which degrades the intrinsic transmission map - or intensity response - of the interferometer. In this context, we describe how this instrumental effect impairs the performance of a Bracewell interferometer. A simple formalism is developed to derive the corresponding modified intensity response of the interferometer, as a function of the two parameters of interest: the crosstalk level (or contamination rate) and the phase shift between the primary and secondary - parasitic - beams. We then apply our mathematical approach to a few scientific cases, both analytically and using the GENIESIM simulation software, adapted to handle coherent crosstalk. Our results show that a coherent crosstalk level of about 1 per cent implies a 20 per cent drop of the signal-to-noise ratio at most. Careful attention should thus be paid to reduce the crosstalk level inside an interferometric instrument and ensure an instrumental stability that provides the necessary sensitivity through calibration procedures.

circumstellar matter↗

Implementation of a Tabulated Failure Model Into a Generalized Composite Material Model Suitable for Use in Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased use in the aerospace and automotive communities. The aerospace community has identified several key capabilities which are currently lacking in the available material models in commercial transient dynamic finite element codes. To attempt to improve the predictive capability of composite impact simulations, a next generation material model is being developed for incorporation within the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters such as modulus and strength. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is used to allow for the uncoupling of the deformation and damage analyses. For the failure model, a tabulated approach is utilized in which a stress or strain based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure. Failure surfaces can be defined with any arbitrary shape, unlike traditional failure models where the mathematical functions used to define the failure surface impose a specific shape on the failure surface. In the current paper, the complete development of the failure model is described and the generation of a tabulated failure surface for a representative composite material is discussed.

polymer matrix composites↗

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗

Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind

The PI (Cranmer) and Co-I (A. van Ballegooijen) made substantial progress toward the goal of producing a unified model of the basic physical processes responsible for solar wind acceleration. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a 1D model of plasma heating and acceleration. The accomplishments in Year 2 are divided into these two categories: 1a. Focused Study of Kinetic Magnetohydrodynamic (MHD) Turbulence. lb. Focused Study of Non - WKB Alfven Wave Rejection. and 2. The Unified Model Code. We have continued the development of the computational model of a time-study open flux tube in the extended corona. The proton-electron Monte Carlo model is being tested, and collisionless wave-particle interactions are being included. In order to better understand how to easily incorporate various kinds of wave-particle processes into the code, the PI performed a detailed study of the so-called "Ito Calculus", i.e., the mathematical theory of how to update the positions of particles in a probabilistic manner when their motions are governed by diffusion in velocity space.

Cranmer, Steven R.↗

Molecular flow venting of a volume with an outgassing or desorbing source

A venting equation commonly used to describe the transient evolution of pressure within a volume containing an outgassing or offgassing source and a restrictive vent conductance under conditions of molecular flow has been solved analytically. Solutions are found for sources of finite thickness characterized by classical diffusion-limited behavior (proportional to inverse square root of time), as well as responses for thick material sources often observed in testing that are characterized by a more general form of power-law decay, up to inverse time behavior associated with surface desorption. Solutions involve evaluating integrals where both numerators and denominators of the integrands diverge with time, making wide-ranging transient solutions difficult to directly compute numerically. Usually, one can avoid evaluating these integrals by assuming quasistatic conditions at long time scales. A novel approach is used in this work to analytically produce solutions by generating bespoke mathematical functions, some of which solve integrals that have apparently had no previous analytical solution.

Michael Woronowicz↗

Molecular flow venting of a volume with an outgassing or desorbing source

"A venting equation commonly used to describe the transient evolution of pressure within a volume containing an outgassing or offgassing source and a restrictive vent conductance under conditions of molecular flow has been solved analytically. Solutions are found for sources of finite thickness characterized by classical diffusion-limited behavior (proportional to inverse square root of time), as well as responses for thick material sources often observed in testing that are characterized by a more general form of power-law decay, up to inverse time behavior associated with surface desorption. Solutions involve evaluating integrals where both numerators and denominators of the integrands diverge with time, making wide-ranging transient solutions difficult to directly compute numerically. Usually, one can avoid evaluating these integrals by assuming quasistatic conditions at long time scales. A novel approach is used in this work to analytically produce solutions by generating bespoke mathematical functions, some of which solve integrals that have apparently had no previous analytical solution."

Michael Woronowicz↗

Quasi-static winds from neutron stars

A series of numerical models is constructed for radiatively driven, quasi-static winds from the surfaces of hot neutron stars. A mathematical technique is devised that in many cases facilitates the integration of the fluid equations in the vicinity of the sonic point, and an improved treatment of radiative transfer is developed that is appropriate to the exotic physical conditions encountered in the models. Boundary conditions which are more realistic than previous ones are used in these models. In agreement with earlier studies, it is found that radiatively driven winds are likely to be directly relevant to the existence of precursors in fast X-ray transients and to apparent radius variations during the course of some type I bursts, and that the presence of such a wind should prevent the bolometric luminosity of a neutron star from exceeding the Eddington limit by more than a small fractional amount. Formulas describing the wind models are presented which are usable as boundary conditions for calculations of the evolution of the deeper, hydrostatic layers of a neutron-star envelope.

Joss, Paul C.↗

Investigation of evolution-related aspects of bacterial rhodopsins

We have investigated evolution-related aspects of bacterial rhodopsins, the unique retinal-based energy transducing systems of halophilic archae. The approach was to describe both structural and functional aspects: the structure by sequencing genes to explore which regions are conserved, and the function by comparing proton and chloride transport in the closely related systems, bacteriorhodopsin and halorhodopsin, respectively. In the latter, we have made a good start toward the ultimate goal of separating the attributes of the general principles of retinal-based ionic pumps from those of the specific ion specificities, by determining the thermodynamics of the internal steps of the protein-mediated active transport process, as well as some of the intraprotein ion-transfer steps. Our present emphasis is on continuing to acquire the tools for studying what distinguishes proton transport from chloride transport. We consider it important, therefore, that we have been able to provide firm mathematical grounds for the kinetics analyses which underlies these studies. Our molecular biological studies have received a great boost from the expression vector for the bop gene based on a halobacterial plasmid, that we recently developed.

Source record↗

Experimental and Theoretical Investigations of the Solidification of Eutectic Al-Si Alloy

The eutectic alloys have a wide spectrum of applications due to their good castability and physical and mechanical properties. The interphase spacing resulting during solidification is an important microstructural feature that significantly influences the mechanical behavior of the material. Thus, knowledge of the evolution of the interphase spacing during solidification is necessary in order to properly design the solidification process and optimize the material properties. While the growth of regular eutectics is rather well understood, the irregular eutectics such as Al-Si or Fe-graphite exhibit undercoolings and lamellar spacings much larger than those theoretically predicted. Despite of a considerable amount of experimental and theoretical work a clear understanding of the true mechanism underlying the spacing selection in irregular eutectics is yet to be achieved. A new experimental study of the solidification of the eutectic Al-Si alloy will be reported in this paper. The measured interface undercoolings and lamellar spacing will be compared to those found in the literature in order to get more general information regarding the growth mechanism of irregular eutectics. A modification of the present theory of the eutectic growth is also proposed. The results of the modified mathematical model, accounting for a non-isothermal solid/liquid interface, will be compared to the experimental measurements.

Sen, S.↗

A physical model for earthquakes. I - Fluctuations and interactions. II - Application to southern California

The idea that earthquakes represent a fluctuation about the long-term motion of plates is expressed mathematically through the fluctuation hypothesis, under which all physical quantities which pertain to the occurance of earthquakes are required to depend on the difference between the present state of slip on the fault and its long-term average. It is shown that under certain circumstances the model fault dynamics undergo a sudden transition from a spatially ordered, temporally disordered state to a spatially disordered, temporally ordered state, and that the latter stages are stable for long intervals of time. For long enough faults, the dynamics are evidently chaotic. The methods developed are then used to construct a detailed model for earthquake dynamics in southern California. The result is a set of slip-time histories for all the major faults, which are similar to data obtained by geological trenching studies. Although there is an element of periodicity to the events, the patterns shift, change and evolve with time. Time scales for pattern evolution seem to be of the order of a thousand years for average recurring intervals of about a hundred years.

Rundle, John B.↗

A Lightning Channel Retrieval Algorithm for the North Alabama Lightning Mapping Array (LMA)

A new multi-station VHF time-of-arrival (TOA) antenna network is, at the time of this writing, coming on-line in Northern Alabama. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The network will support on-going ground validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. It will also provide for many interesting and detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and will offer many interesting comparisons with other meteorological/geophysical wets associated with lightning and thunderstorms. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. In this study, a new revised channel mapping retrieval algorithm is introduced. The algorithm is an extension of earlier work provided in Koshak and Solakiewicz (1996) in the analysis of the NASA Kennedy Space Center (KSC) Lightning Detection and Ranging (LDAR) system. As in the 1996 study, direct algebraic solutions are obtained by inverting a simple linear system of equations, thereby making computer searches through a multi-dimensional parameter domain of a Chi-Squared function unnecessary. However, the new algorithm is developed completely in spherical Earth-centered coordinates (longitude, latitude, altitude), rather than in the (x, y, z) cartesian coordinates employed in the 1996 study. Hence, no mathematical transformations from (x, y, z) into spherical coordinates are required (such transformations involve more numerical error propagation, more computer program coding, and slightly more CPU computing time). The new algorithm also has a more realistic definition of source altitude that accounts for Earth oblateness (this can become important for sources that are hundreds of kilometers away from the network). In addition, the new algorithm is being applied to analyze computer simulated LMA datasets in order to obtain detailed location/time retrieval error maps for sources in and around the LMA network. These maps will provide a more comprehensive analysis of retrieval errors for LMA than the 1996 study did of LDAR retrieval errors. Finally, we note that the new algorithm can be applied to LDAR, and essentially any other multi-station TWA network that depends on direct line-of-site antenna excitation.

Koshak, William↗