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At least 235 records · Page 13

Satellite Image Mosaic Engine

A computer program automatically builds large, full-resolution mosaics of multispectral images of Earth landmasses from images acquired by Landsat 7, complete with matching of colors and blending between adjacent scenes. While the code has been used extensively for Landsat, it could also be used for other data sources. A single mosaic of as many as 8,000 scenes, represented by more than 5 terabytes of data and the largest set produced in this work, demonstrated what the code could do to provide global coverage. The program first statistically analyzes input images to determine areas of coverage and data-value distributions. It then transforms the input images from their original universal transverse Mercator coordinates to other geographical coordinates, with scaling. It applies a first-order polynomial brightness correction to each band in each scene. It uses a data-mask image for selecting data and blending of input scenes. Under control by a user, the program can be made to operate on small parts of the output image space, with check-point and restart capabilities. The program runs on SGI IRIX computers. It is capable of parallel processing using shared-memory code, large memories, and tens of central processing units. It can retrieve input data and store output data at locations remote from the processors on which it is executed.

Plesea, Lucian↗

NPSS on NASA's IPG: Using CORBA and Globus to Coordinate Multidisciplinary Aeroscience Applications

Within NASA's High Performance Computing and Communication (HPCC) program, the NASA Glenn Research Center is developing an environment for the analysis/design of aircraft engines called the Numerical Propulsion System Simulation (NPSS). The vision for NPSS is to create a "numerical test cell" enabling full engine simulations overnight on cost-effective computing platforms. To this end, NPSS integrates multiple disciplines such as aerodynamics, structures, and heat transfer and supports "numerical zooming" between O-dimensional to 1-, 2-, and 3-dimensional component engine codes. In order to facilitate the timely and cost-effective capture of complex physical processes, NPSS uses object-oriented technologies such as C++ objects to encapsulate individual engine components and CORBA ORBs for object communication and deployment across heterogeneous computing platforms. Recently, the HPCC program has initiated a concept called the Information Power Grid (IPG), a virtual computing environment that integrates computers and other resources at different sites. IPG implements a range of Grid services such as resource discovery, scheduling, security, instrumentation, and data access, many of which are provided by the Globus toolkit. IPG facilities have the potential to benefit NPSS considerably. For example, NPSS should in principle be able to use Grid services to discover dynamically and then co-schedule the resources required for a particular engine simulation, rather than relying on manual placement of ORBs as at present. Grid services can also be used to initiate simulation components on parallel computers (MPPs) and to address inter-site security issues that currently hinder the coupling of components across multiple sites. These considerations led NASA Glenn and Globus project personnel to formulate a collaborative project designed to evaluate whether and how benefits such as those just listed can be achieved in practice. This project involves firstly development of the basic techniques required to achieve co-existence of commodity object technologies and Grid technologies; and secondly the evaluation of these techniques in the context of NPSS-oriented challenge problems. The work on basic techniques seeks to understand how "commodity" technologies (CORBA, DCOM, Excel, etc.) can be used in concert with specialized "Grid" technologies (for security, MPP scheduling, etc.). In principle, this coordinated use should be straightforward because of the Globus and IPG philosophy of providing low-level Grid mechanisms that can be used to implement a wide variety of application-level programming models. (Globus technologies have previously been used to implement Grid-enabled message-passing libraries, collaborative environments, and parameter study tools, among others.) Results obtained to date are encouraging: we have successfully demonstrated a CORBA to Globus resource manager gateway that allows the use of CORBA RPCs to control submission and execution of programs on workstations and MPPs; a gateway from the CORBA Trader service to the Grid information service; and a preliminary integration of CORBA and Grid security mechanisms. The two challenge problems that we consider are the following: 1) Desktop-controlled parameter study. Here, an Excel spreadsheet is used to define and control a CFD parameter study, via a CORBA interface to a high throughput broker that runs individual cases on different IPG resources. 2) Aviation safety. Here, about 100 near real time jobs running NPSS need to be submitted, run and data returned in near real time. Evaluation will address such issues as time to port, execution time, potential scalability of simulation, and reliability of resources. The full paper will present the following information: 1. A detailed analysis of the requirements that NPSS applications place on IPG. 2. A description of the techniques used to meet these requirements via the coordinated use of CORBA and Globus. 3. A description of results obtained to date in the first two challenge problems.

Lopez, Isaac↗

Programmable remapper with single flow architecture

The invention relates to image processing systems and methods and in particular to a machine which accepts a real time video image in the form of a matrix of picture elements (pixels) and remaps such image according to a selectable one of a plurality of mapping functions to create an output matrix of pixels. Such mapping functions, or transformations, may be any one of a number of different transformations depending on the objective of the user of the system. The system remaps input images from one coordinate system to another using a set of look-up tables for the data necessary for the transform. The transforms, which are operator selectable, are precomputed and loaded into massive look-up tables. Input pixels, via the look-up tables of any particular transform selected, are mapped into output pixels with the radiance information of the input pixels being appropriately weighted. An earlier embodiment of the system included two parallel processors: a collective processor which mapped multiple input pixels into a single output pixel and an interpolative processor. The interpolative processor performed an interpolation among pixels in the input image where a given input pixel may affect the value of many output pixels. Several advantages are provided over previous embodiments in that the two distinct processors are replaced by a single processor capable of performing both types of operations (collective and interpolative) with no more complexity. Previously, there has existed no image processor or 'remapper' that can operate with sufficient speed and flexibility to permit investigating different transformation patterns in real time.

Fisher, Timothy E.↗

MAX - An advanced parallel computer for space applications

MAX is a fault-tolerant multicomputer hardware and software architecture designed to meet the needs of NASA spacecraft systems. It consists of conventional computing modules (computers) connected via a dual network topology. One network is used to transfer data among the computers and between computers and I/O devices. This network's topology is arbitrary. The second network operates as a broadcast medium for operating system synchronization messages and supports the operating system's Byzantine resilience. A fully distributed operating system supports multitasking in an asynchronous event and data driven environment. A large grain dataflow paradigm is used to coordinate the multitasking and provide easy control of concurrency. It is the basis of the system's fault tolerance and allows both static and dynamical location of tasks. Redundant execution of tasks with software voting of results may be specified for critical tasks. The dataflow paradigm also supports simplified software design, test and maintenance. A unique feature is a method for reliably patching code in an executing dataflow application.

Lewis, Blair F.↗

Velocity spike at the poleward edge of the auroral zone

Data from coordinated observations of the Chatanika incoherent scatter radar and the Atmosphere Explorer C satellite are examined to study the poleward edge of the auroral zone for one pass in the morning sector. A very intense, spikelike electric field is seen at the boundary between the auroral zone and the polar cap, coincident with the convection reversal. The particle detector data are consistent with the presence of a pair of oppositely oriented potential drops parallel to the magnetic field. These potential drops are of a few hundred electron volts, and their direction is such that the precipitating electrons are accelerated on the poleward side and decelerated on the equatorward side of the electric field spike. These observations are examined in the light of recent theoretical investigations that have shown that parallel acceleration can indeed be expected to occur in the regions of large velocity shear. The Chatanika data suggest that such spikes may occur repeatedly at the poleward edge of the diffuse aurora, but that they are confined in either time or space.

De La Beaujardiere, O.↗

Cooperative Three-Robot System for Traversing Steep Slopes

Teamed Robots for Exploration and Science in Steep Areas (TRESSA) is a system of three autonomous mobile robots that cooperate with each other to enable scientific exploration of steep terrain (slope angles up to 90 ). Originally intended for use in exploring steep slopes on Mars that are not accessible to lone wheeled robots (Mars Exploration Rovers), TRESSA and systems like TRESSA could also be used on Earth for performing rescues on steep slopes and for exploring steep slopes that are too remote or too dangerous to be explored by humans. TRESSA is modeled on safe human climbing of steep slopes, two key features of which are teamwork and safety tethers. Two of the autonomous robots, denoted Anchorbots, remain at the top of a slope; the third robot, denoted the Cliffbot, traverses the slope. The Cliffbot drives over the cliff edge supported by tethers, which are payed out from the Anchorbots (see figure). The Anchorbots autonomously control the tension in the tethers to counter the gravitational force on the Cliffbot. The tethers are payed out and reeled in as needed, keeping the body of the Cliffbot oriented approximately parallel to the local terrain surface and preventing wheel slip by controlling the speed of descent or ascent, thereby enabling the Cliffbot to drive freely up, down, or across the slope. Due to the interactive nature of the three-robot system, the robots must be very tightly coupled. To provide for this tight coupling, the TRESSA software architecture is built on a combination of (1) the multi-robot layered behavior-coordination architecture reported in "An Architecture for Controlling Multiple Robots" (NPO-30345), NASA Tech Briefs, Vol. 28, No. 10 (October 2004), page 65, and (2) the real-time control architecture reported in "Robot Electronics Architecture" (NPO-41784), NASA Tech Briefs, Vol. 32, No. 1 (January 2008), page 28. The combination architecture makes it possible to keep the three robots synchronized and coordinated, to use data from all three robots for decision- making at each step, and to control the physical connections among the robots. In addition, TRESSA (as in prior systems that have utilized this architecture) , incorporates a capability for deterministic response to unanticipated situations from yet another architecture reported in Control Architecture for Robotic Agent Command and Sensing (NPO-43635), NASA Tech Briefs, Vol. 32, No. 10 (October 2008), page 40. Tether tension control is a major consideration in the design and operation of TRESSA. Tension is measured by force sensors connected to each tether at the Cliffbot. The direction of the tension (both azimuth and elevation) is also measured. The tension controller combines a controller to counter gravitational force and an optional velocity controller that anticipates the motion of the Cliffbot. The gravity controller estimates the slope angle from the inclination of the tethers. This angle and the weight of the Cliffbot determine the total tension needed to counteract the weight of the Cliffbot. The total needed tension is broken into components for each Anchorbot. The difference between this needed tension and the tension measured at the Cliffbot constitutes an error signal that is provided to the gravity controller. The velocity controller computes the tether speed needed to produce the desired motion of the Cliffbot. Another major consideration in the design and operation of TRESSA is detection of faults. Each robot in the TRESSA system monitors its own performance and the performance of its teammates in order to detect any system faults and prevent unsafe conditions. At startup, communication links are tested and if any robot is not communicating, the system refuses to execute any motion commands. Prior to motion, the Anchorbots attempt to set tensions in the tethers at optimal levels for counteracting the weight of the Cliffbot; if either Anchorbot fails to reach its optimal tension level within a specified time, it sends message to the other robots and the commanded motion is not executed. If any mechanical error (e.g., stalling of a motor) is detected, the affected robot sends a message triggering stoppage of the current motion. Lastly, messages are passed among the robots at each time step (10 Hz) to share sensor information during operations. If messages from any robot cease for more than an allowable time interval, the other robots detect the communication loss and initiate stoppage.

Stroupe, Ashley↗

Self-similar evolution of the nonlinear magnetic buoyancy instability

A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k parallel to B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with the simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.

Shibata, K.↗

Gear tooth topological modification

The topology of parallel axis gears, such as spur and helical gears is modified to produce quieter and more smoothly operating gear sets with more uniform load distribution. A finite element analysis of the gear in its operating mode is made to produce a plot of radial and tangential deflections of the pinion and gear tooth surfaces which will occur when the gears are loaded during operation. The resultant plot is then inverted to produce a plot, or set of coordinates, which will define the path of travel of the gear tooth grinding wheel, which path is a mirror image of the plot of the finite element analysis. The resulting gears, when subjected to operating loads, will thus be deflected tangentially and radially to their optimum operating, or theoretical true involute, positions so as to produce quieter, smoother, and more evenly loaded gear trains.

Kish, Jules G.↗

A programming environment for distributed complex computing. An overview of the Framework for Interdisciplinary Design Optimization (FIDO) project. NASA Langley TOPS exhibit H120b

The Framework for Interdisciplinary Design Optimization (FIDO) is a general programming environment for automating the distribution of complex computing tasks over a networked system of heterogeneous computers. For example, instead of manually passing a complex design problem between its diverse specialty disciplines, the FIDO system provides for automatic interactions between the discipline tasks and facilitates their communications. The FIDO system networks all the computers involved into a distributed heterogeneous computing system, so they have access to centralized data and can work on their parts of the total computation simultaneously in parallel whenever possible. Thus, each computational task can be done by the most appropriate computer. Results can be viewed as they are produced and variables changed manually for steering the process. The software is modular in order to ease migration to new problems: different codes can be substituted for each of the current code modules with little or no effect on the others. The potential for commercial use of FIDO rests in the capability it provides for automatically coordinating diverse computations on a networked system of workstations and computers. For example, FIDO could provide the coordination required for the design of vehicles or electronics or for modeling complex systems.

Townsend, James C.↗

Digital Channel Simulator Developed and Tested

The Digital Channel Simulator (DCS) is a real-time test set developed in-house by the NASA Glenn Research Center at Lewis Field that simulates the characteristics of the modulator, demodulator, and transmission medium in a typical communications system to enable controlled laboratory testing of codec pairs. The DCS can support data rates up to 100 megasymbols per second (Msymbols/sec) with symbol sizes up to 10 bits and is compatible with both TTL (transistor transistor logic) and ECL (emitter coupled logic) interfaces. Because of its use of digital integrated circuits (IC's), the DCS offers the user accurate and repeatable testing while maintaining a simple reconfiguration of the modulation scheme and noise characteristics. The PC-based graphical user interface (GUI) assures user friendly operation for configuring, controlling, and monitoring the DCS and system during tests. In a typical communications system, the modulator places a symbol in constellation space and puts it on a carrier to be sent to the demodulator. Because of noise on the channel, the I and Q position in constellation space cannot be recovered exactly, and the received coordinates shift. To mimic this process in the laboratory, the DCS uses a mapper to place the symbol in constellation space. It simulates the shift in coordinates by digitally adding "noise" to the I and Q values. The mapper and noise source are implemented in lookup tables. Modulation schemes and noise characteristics are set by the values loaded in these tables. The mapper also has a pass-through mode to facilitate modulator testing, allowing noise to be added to 8-bit I and Q values of modulated data without a second mapping. To achieve high symbol rates, eight processing circuits are placed in parallel between an ECL demultiplexer and multiplexer. A graphical user interface was developed to calculate, load, and verify the values for the lookup tables. This interface can also be used to debug and verify proper operation of the channel simulator or to control an experiment. Operation of the DCS has been verified through three tests: a low-speed comprehensive system test, a high-speed (20 Msymbols/sec) test of the TTL interface, and a high-speed (100 Msymbols/sec) test of the ECL interface. The DCS is now ready for use by NASA and external customers.

Bizon, Thomas P.↗

Stereo imaging based particle velocimeter

Three dimensional coordinates of an object are determined from it's two dimensional images for a class of points on the object. Two dimensional images are first filtered by a Laplacian of Gaussian (LOG) filter in order to detect a set of feature points on the object. The feature points on the left and the right images are then matched using a Hopfield type optimization network. The performance index of the Hopfield network contains both local and global properties of the images. Parallel computing in stereo matching can be achieved by the proposed methodology.

Batur, Celal↗

The TPS Advanced Development Project for CEV

The CEV TPS Advanced Development Project (ADP) is a NASA in-house activity for providing two heatshield preliminary designs (a Lunar direct return as well as a LEO only return) for the CEV, including the TPS, the carrier structure, the interfaces and the attachments. The project s primary objective is the development of a single heatshield preliminary design that meets both Lunar direct return and LEO return requirements. The effort to develop the Lunar direct return capable heatshield is considered a high risk item for the NASA CEV development effort due to the low TRL (approx. 4) of the candidate TPS materials. By initiating the TPS ADP early in the development cycle, the intent is to use materials analysis and testing in combination with manufacturing demonstrations to reduce the programmatic risk of using advanced TPS technologies in the critical path for CEV. Due to the technical and schedule risks associated a Lunar return heatshield, the ADP will pursue a parallel path design approach, whereby a back-up TPS/heatshield design that only meets LEO return requirements is also developed. The TPS materials and carrier structure design concept selections will be based on testing, analysis, design and evaluation of scalability and manufacturing performed under the ADP. At the TPS PDR, the preferred programmatic strategy is to transfer the continued (detailed) design, development, testing and evaluation (DDT&E) of both the Lunar direct and LEO return designs to a government/prime contractor coordinated sub-system design team. The CEV prime contractor would have responsibility for the continued heatshield sub-system development. Continued government participation would include analysis, testing and evaluation as well as decision authority at TPS Final System Decision (FSD) (choosing between the primary and back-up heatshields) occurring between TPS PDR and TPS Critical Design Review (CDR). After TPS FSD the prime CEV contractor will complete the detailed design, certification testing, procurement, and integration of the CEV TPS.

Reuther, James↗

The Effectiveness of a Route Crossing Tool in a Simulated New York Airspace

Congested airspace is the cause of many delays in the terminal area and these delays can have a ripple effect on the rest of a nation's airspace. The New York terminal area is an example of where this happens in the U. S. An important goal, therefore, is to increase the efficiency of operations in congested terminal airspace where possible. Modeling studies of arrival and departure flows have shown that sharing of arrival and departure airspace increases efficiency in terminal operations. One source of inefficiency in terminal operations is that departure aircraft are frequently held level under arrival flows when it would be more efficient to climb the departure aircraft earlier. A Route Crossing Tool was developed to help controllers climb Newark (EWR) departures to the south earlier by temporarily sharing airspace with arrivals coming into LaGuardia (LGA) from the south. Instead of flying under the arrivals, a departure to the south could climb earlier by flying through the arrival airspace if there was a suitable gap between arrivals. A Human-in-the-Loop (HITL) simulation was conducted in this environment which compared three tool conditions: Baseline (no tool), a Single Route Crossing tool in which one route through the arrival flow was evaluated for crossing, and a Multi-Route Crossing tool in which five parallel routes were evaluated. In all conditions, the departures could be held level under the arrival flow. The results showed that controllers climbed a higher proportion of departures in the Multi-Route tool condition than in the other two conditions, with a higher proportion of departures climbed in smaller gaps and in front of trailing arrivals. The controllers indicated that the Multi-Route and Single Route tools helped them estimate distances more accurately and rated safety, workload, and coordination in the simulation as acceptable.

terminal airspace↗

Some New Problems on Shells and Thin Structures

Cylindrical shells of arbitrary section, reinforced by longitudinal and transverse members (stringers and ribs) are considered by us, for a sufficiently close spacing of the ribs, as in our previously published papers (references 1 end 2), as thin-walled orthotropic spatial systems at the cross-sections of which only axial (normal and shearing) forces can arise. The longitudinal bending and twisting moments, due to their weak effect on the stress state of the shell, are taken equal to zero. Along the longitudinal sections of the shell there may arise transverse forces in addition to the normal ~d shearing forces. Under the so-called static assumptions there is taken for the computation model of the shell a thin-walled spatial system consisting along its length (along a generator) of an infinite number of elementary strips capable of bending. Each of these strips is likened to a curved rod operating in each of its sections not only in tension (compression)but also in transverse bending and shear. The interaction between two adjoining transverse strips in the shell expresses itself in the transmission from one strip to the other of only the normal and shearing stresses. The static structure of the computation model here described is shown in figure 1, where the connections through which the normal and shearing stresses transmitted from one transverse strip to smother are indicated schematically by the rods located in the middle surface of the shell. In addition to the static hypothesis we introduce also geometric hypotheses. According to the latter the elongational deformations of the shell along lines parallel to the generator of its middle surface and the shear deformations in the middle surface, as ma+gitudes having . little effect on the state of the fundamental internal forces of the shell, are taken equal to zero. The deformations of the shell in our computational model are such that in the first place the lines of this surface perpendicular to the generator are inextensible at each point end in the second place the angles between the lines of principal curvature (the coordinate lines) which are straight before the deformation remain straight after the deformation.

Vlasov, V. S.↗

Implementing Connected Component Labeling as a User Defined Operator for SciDB

We have implemented a flexible User Defined Operator (UDO) for labeling connected components of a binary mask expressed as an array in SciDB, a parallel distributed database management system based on the array data model. This UDO is able to process very large multidimensional arrays by exploiting SciDB's memory management mechanism that efficiently manipulates arrays whose memory requirements far exceed available physical memory. The UDO takes as primary inputs a binary mask array and a binary stencil array that specifies the connectivity of a given cell to its neighbors. The UDO returns an array of the same shape as the input mask array with each foreground cell containing the label of the component it belongs to. By default, dimensions are treated as non-periodic, but the UDO also accepts optional input parameters to specify periodicity in any of the array dimensions. The UDO requires four stages to completely label connected components. In the first stage, labels are computed for each subarray or chunk of the mask array in parallel across SciDB instances using the weighted quick union (WQU) with half-path compression algorithm. In the second stage, labels around chunk boundaries from the first stage are stored in a temporary SciDB array that is then replicated across all SciDB instances. Equivalences are resolved by again applying the WQU algorithm to these boundary labels. In the third stage, relabeling is done for each chunk using the resolved equivalences. In the fourth stage, the resolved labels, which so far are "flattened" coordinates of the original binary mask array, are renamed with sequential integers for legibility. The UDO is demonstrated on a 3-D mask of O(1011) elements, with O(108) foreground cells and O(106) connected components. The operator completes in 19 minutes using 84 SciDB instances.

UDO↗

A Unique Power System For The ISS Fluids And Combustion Facility

Unique power control technology has been incorporated into an electrical power control unit (EPCU) for the Fluids and Combustion Facility (FCF). The objective is to maximize science throughput by providing a flexible power system that is easily reconfigured by the science payload. Electrical power is at a premium on the International Space Station (ISS). The EPCU utilizes advanced power management techniques to maximize the power available to the FCF experiments. The EPCU architecture enables dynamic allocation of power from two ISS power channels for experiments. Because of the unique flexible remote power controller (FRPC) design, power channels can be paralleled while maintaining balanced load sharing between the channels. With an integrated and redundant architecture, the EPCU can tolerate multiple faults and still maintain FCF operation. It is important to take full advantage of the EPCU functionality. The EPCU acts as a buffer between the experimenter and the ISS power system with all its complex requirements. However, FCF science payload developers will still need to follow guidelines when designing the FCF payload power system. This is necessary to ensure power system stability, fault coordination, electromagnetic compatibility, and maximum use of available power for gathering scientific data.

Fox, David A.↗

A spectral multi-domain technique with application to generalized curvilinear coordinates

Spectral collocation methods have proven to be efficient discretization schemes for many aerodynamic and fluid mechanic problems. The high order accuracy and resolution shown by these methods allows one to obtain engineering accuracy solutions on coarse meshes, or alternatively, to obtain solutions with very small error. One drawback to these techniques was the requirement that a complicated physical domain must map into a simple computational domain for discretization. This mapping must be smooth if the high order accuracy and expontential convergence rates associated with spectral methods are to be preserved. Additionally even smooth stretching transformations can decrease the accuracy of a spectral method, if the stretching is severe. A further difficulty with spectral methods was in their implementation on parallel processing computers, where efficient spectral algorithms were lacking. The above restrictions are overcome by splitting the domain into regions, each of which preserve the advantages of spectral collocation, and allow the ratio of the mesh spacing between regions to be several orders of magnitude higher than allowable in a single domain. Such stretchings would be required to resolve the thin viscous region in an external aerodynamic problem. Adjoining regions are interfaced by enforcing a global flux balance which preserves high-order continuity of the solution, regardless of the type of the equations being solved.

Macaraeg, M. G.↗

Temporal variations in the dawn and dusk midlatitude trough and plasmapause position

The temporal development of the latitudinal position of a 600-km midlatitude electron density trough at dawn and dusk during the period 25-27 May 1967, which encompassed a large magnetic storm, was measured by the RF capacitive probe on the polar orbiting Ariel 3 satellite. The substorm-related changes in the L coordinate of the trough minimum and the point of most rapid change of density gradient on the low latitude side of the trough are similar. Oscillations of the trough position at dusk are in phase with substorm activity whereas movement of the trough at dawn is only apparent with the onset of the large storm. Detailed model calculations of the plasmasphere dynamics assuming a spatially invariant equatorial convection E-field which varies in step with the K sub p index produces a plasmapause motion which parallels the observed trough behaviour.

Grebowsky, J. M.↗