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Technical Report Series on Global Modeling and Data Assimilation: Filtering Techniques on a Stretched Grid General Circulation Model - Volume 16

This report documents the techniques used to filter quantities on a stretched grid general circulation model. Standard high-latitude filtering techniques (e.g., using an FFT (Fast Fourier Transformations) to decompose and filter unstable harmonics at selected latitudes) applied on a stretched grid are shown to produce significant distortions of the prognostic state when used to control instabilities near the pole. A new filtering technique is developed which accurately accounts for the non-uniform grid by computing the eigenvectors and eigenfrequencies associated with the stretching. A filter function, constructed to selectively damp those modes whose associated eigenfrequencies exceed some critical value, is used to construct a set of grid-spaced weights which are shown to effectively filter without distortion. Both offline and GCM (General Circulation Model) experiments are shown using the new filtering technique. Finally, a brief examination is also made on the impact of applying the Shapiro filter on the stretched grid.

Takacs, Lawrence L.↗

Hurricane Directional Wave Spectrum Spatial Variation in the Open Ocean

The sea surface directional wave spectrum was measured for the first time in all quadrants of a hurricane in open water using the NASA airborne scanning radar altimeter (SRA) carried aboard one of the NOAA WP-3D hurricane hunter aircraft at 1.5 km height. The SRA measures the energetic portion of the directional wave spectrum by generating a topographic map of the sea surface. At 8 Hz, the SRA sweeps a radar beam of 1 deg half-power width (two-way) across the aircraft ground track over a swath equal to 0. 8 of the aircraft height, simultaneously measuring the backscattered power at its 36 GHz (8.3 mm) operating frequency and the range to the sea surface at 64 positions. These slant ranges are multiplied by the cosine of the incidence angles to determine the vertical distances from the aircraft to the sea surface. Subtracting these distances from the aircraft height produces the sea surface elevation map. The sea surface topography is interpolated to a uniform grid, transformed by a two-dimensional FFT, and Doppler corrected. The data presented were acquired on 24 August 1998 when hurricane Bonnie was east of the Bahamas and moving slowly to the north. Wave heights up to 18 m were observed and the spatial variation of the wave field was dramatic. The dominant waves generally propagated at significant angles to the downwind direction and at times there were wave fields traveling at right angles to each other. The NOAA aircraft spent over five hours within 180 km of the hurricane Bonnie eye, and made five eye penetrations. A 2-minute animation of the directional wave spectrum spatial variation over this period will be shown.

Wright, C. W.↗

Highly Parallel Computing Architectures by using Arrays of Quantum-dot Cellular Automata (QCA): Opportunities, Challenges, and Recent Results

There has been significant improvement in the performance of VLSI devices, in terms of size, power consumption, and speed, in recent years and this trend may also continue for some near future. However, it is a well known fact that there are major obstacles, i.e., physical limitation of feature size reduction and ever increasing cost of foundry, that would prevent the long term continuation of this trend. This has motivated the exploration of some fundamentally new technologies that are not dependent on the conventional feature size approach. Such technologies are expected to enable scaling to continue to the ultimate level, i.e., molecular and atomistic size. Quantum computing, quantum dot-based computing, DNA based computing, biologically inspired computing, etc., are examples of such new technologies. In particular, quantum-dots based computing by using Quantum-dot Cellular Automata (QCA) has recently been intensely investigated as a promising new technology capable of offering significant improvement over conventional VLSI in terms of reduction of feature size (and hence increase in integration level), reduction of power consumption, and increase of switching speed. Quantum dot-based computing and memory in general and QCA specifically, are intriguing to NASA due to their high packing density (10(exp 11) - 10(exp 12) per square cm ) and low power consumption (no transfer of current) and potentially higher radiation tolerant. Under Revolutionary Computing Technology (RTC) Program at the NASA/JPL Center for Integrated Space Microelectronics (CISM), we have been investigating the potential applications of QCA for the space program. To this end, exploiting the intrinsic features of QCA, we have designed novel QCA-based circuits for co-planner (i.e., single layer) and compact implementation of a class of data permutation matrices, a class of interconnection networks, and a bit-serial processor. Building upon these circuits, we have developed novel algorithms and QCA-based architectures for highly parallel and systolic computation of signal/image processing applications, such as FFT and Wavelet and Wlash-Hadamard Transforms.

Fijany, Amir↗

Fast Particle Methods for Multiscale Phenomena Simulations

We are developing particle methods oriented at improving computational modeling capabilities of multiscale physical phenomena in : (i) high Reynolds number unsteady vortical flows, (ii) particle laden and interfacial flows, (iii)molecular dynamics studies of nanoscale droplets and studies of the structure, functions, and evolution of the earliest living cell. The unifying computational approach involves particle methods implemented in parallel computer architectures. The inherent adaptivity, robustness and efficiency of particle methods makes them a multidisciplinary computational tool capable of bridging the gap of micro-scale and continuum flow simulations. Using efficient tree data structures, multipole expansion algorithms, and improved particle-grid interpolation, particle methods allow for simulations using millions of computational elements, making possible the resolution of a wide range of length and time scales of these important physical phenomena.The current challenges in these simulations are in : [i] the proper formulation of particle methods in the molecular and continuous level for the discretization of the governing equations [ii] the resolution of the wide range of time and length scales governing the phenomena under investigation. [iii] the minimization of numerical artifacts that may interfere with the physics of the systems under consideration. [iv] the parallelization of processes such as tree traversal and grid-particle interpolations We are conducting simulations using vortex methods, molecular dynamics and smooth particle hydrodynamics, exploiting their unifying concepts such as : the solution of the N-body problem in parallel computers, highly accurate particle-particle and grid-particle interpolations, parallel FFT's and the formulation of processes such as diffusion in the context of particle methods. This approach enables us to transcend among seemingly unrelated areas of research.

Koumoutsakos, P.↗

Hurricane Directional Wave Spectrum Spatial Variation in the Open Ocean and at Landfall

The sea surface directional wave spectrum was measured for the first time in all quadrants of a hurricane in open water using the NASA airborne scanning radar altimeter (SRA) carried aboard one of the NOAA WP-3D hurricane hunter aircraft at 1.5 km height. The SRA measures the energetic portion of the directional wave spectrum by generating a topographic map of the sea surface. At 8 Hz, the SRA sweeps a radar beam of 1' half-power width (two-way) across the aircraft ground track over a swath equal to 0.8 of the aircraft height, simultaneously measuring the backscattered power at its 36 GHz (8.3 mm) operating frequency and the range to the sea surface at 64 positions. These slant ranges are multiplied by the cosine of the off-nadir angles to determine the vertical distances from the aircraft to the sea surface. Subtracting these distances from the aircraft height produces the sea surface elevation map. The sea surface topography is interpolated to a uniform grid, transformed by a two dimensional FFT, and Doppler corrected. The open-ocean data were acquired on 24 August 1998 when hurricane Bonnie was east of the Bahamas and moving toward 330 deg at about 5 m/s. Individual waves up to 18 m height were observed and the spatial variation of the wave field was dramatic. The dominant waves generally propagated at significant angles to the downwind direction. At some positions there were three different wave fields of comparable energy crossing each other. The NOAA aircraft spent over five hours within 180 km of the eye, and made five eye penetrations. On 26 August 1998, the NOAA aircraft flew at 2.2 km height when hurricane Bonnie was making landfall near Wilmington, NC, documenting the directional wave spectrum in the region between Charleston, SC and Cape Hatteras, NC. The aircraft flight lines included segments near and along the shoreline as well as far offshore. Animations of the directional wave spectrum spatial variation along the aircraft tracks on the two flights will be presented using a 100: 1 time compression.

Walsh, Edward J.↗

Measuring Directional Wave Spectra and Wind Speed with a Scanning Radar Altimeter

The geometry for the NASA Scanning Radar Altimeter (SRA) is shown. It transmits a 8-ns duration pulse at Ka-band (8.3 mm) and measures time of flight as it scans a 1 degree (two-way) beam from left to right across the aircraft ground track. The most recent configuration determines the surface elevation at 64 points spaced at uniform angular intervals of about 0.7 across a swath whose width is about 0.8 times the aircraft altitude. The system generates these raster lines of the surface topography beneath the aircraft at about a 10 Hz rate. In postflight processing the SRA wave topographic data are transformed with a two-dimensional Fast Fourier Transformation (FFT) and Doppler corrected to produce directional wave spectra. The SRA is not absolutely calibrated in power, but by measuring the relative fall-off of backscatter with increasing incidence angle, the SRA can also determine the mean square slope (mss) of the sea surface, a surrogate for wind speed. For the slope-dependent specular point model of radar sea surface scattering, an expression approximated by a geometric optics form, for the relative variation with incidence angle of the normalized backscatter radar cross section would be sigma (sup 0) (sub rel) = sec (exp 4) theta exp (-tan squared theta/mss) where theta is the off-nadir incidence angle.

Walsh, E. J.↗

Advanced Engine Health Management Applications of the SSME Real-Time Vibration Monitoring System

The Real Time Vibration Monitoring System (RTVMS) is a 32-channel high speed vibration data acquisition and processing system developed at Marshall Space Flight Center (MSFC). It Delivers sample rates as high as 51,200 samples/second per channel and performs Fast Fourier Transform (FFT) processing via on-board digital signal processing (DSP) chips in a real-time format. Advanced engine health assessment is achieved by utilizing the vibration spectra to provide accurate sensor validation and enhanced engine vibration redlines. Discrete spectral signatures (such as synchronous) that are indicators of imminent failure can be assessed and utilized to mitigate catastrophic engine failures- a first in rocket engine health assessment. This paper is presented in viewgraph form.

Fiorucci, Tony R.↗

Hurricane Directional Wave Spectrum Spatial Variation in the Open Ocean and at Landfall

The sea surface directional wave spectrum was measured for the first time in all quadrants of a hurricane in open water using the NASA airborne scanning radar altimeter (SRA) carried aboard one of the NOAA WP-3D hurricane hunter aircraft at 1.5 km height. The SRA measures the energetic portion of the directional wave spectrum by generating a topographic map of the sea surface. At 8 Hz, the SRA sweeps a radar beam of 1 E half-power width (two-way) across the aircraft ground track over a swath equal to 0.8 of the aircraft height, simultaneously measuring the backscattered power at its 36 GHz (8.3 mm) operating frequency and the range to the sea surface at 64 positions. These slant ranges are multiplied by the cosine of the incidence angles to determine the vertical distances from the aircraft to the sea surface. Subtracting these distances from the aircraft height produces the sea surface elevation map. The sea surface topography is interpolated to a uniform grid, transformed by a two-dimensional FFT, and Doppler corrected. The open-ocean data were acquired on 24 August 1998 when hurricane Bonnie was east of the Bahamas and moving slowly to the north. Individual waves with heights up to 18 m were observed and the spatial variation of the wave field was dramatic. The dominant waves generally propagated at significant angles to the downwind direction. At some positions there were three different wave fields of comparable energy crossing each other. The NOAA aircraft spent over five hours within 180 km of the hurricane Bonnie eye, and made five eye penetrations. A 3-minute animation of the directional wave spectrum spatial variation over this period will be shown as well as summary plots of the wave field spatial variation. On 26 August 1998, the NOAA aircraft flew at 2.2 km height when hurricane Bonnie was making landfall near Wilmington, NC, documenting the directional wave spectrum in the region between Charleston, SC and Cape Hatteras, NC. The aircraft ground track included both segments along the shoreline and Pamlico Sound as well as far offshore. An animation of the directional wave spectrum spatial variation at landfall will be presented and contrasted with the spatial variation when Bonnie was in the open ocean on 24 August 1998.

Walsh, E. J.↗

Abrupt Changes at the Permian/Triassic Boundary: Tempo of Events from High-Resolution Cyclostratigraphy

The Permian/Triassic (P/Tr) boundary (251.4 +/- 3 Myr) is marked by the most severe mass extinction in the geologic record. Recently, precise absolute dating has bracketed the marine extinctions and associated carbon-isotope anomaly within less than 1 Myr. We improve this resolution through high-resolution stratigraphy across the P/Tr boundary in the 331-m Gartnerkofel-1 core and nearby Reppwand outcrop section (Carnic Alps, Austria) utilizing FFT and wavelet timeseries analyses of cyclic components in down-hole core logs of density and natural gamma-ray intensity, and carbon-isotopic ratios of bulk samples. The wavelet analysis indicates continuity of deposition across the P/Tr boundary interval, and the timeseries analyses show evidence for persistent cycles in the ratio of approximately 40: 10: 4.7: 2.3 meters, correlated with Milankovitch-band orbital cycles of approximately 412: 100: 40: 20 kyr (eccentricity 1 and 2, obliquity, and precession), and giving a consistent average sedimentation rate of approximately 10 cm/1,000 yr. Milankovitch periods in delta C-13 and density in these shallow-water carbonates were most likely the result of climatically induced oscillations of sea level and climate, coupled with changes in ocean circulation and productivity, that affected sedimentation. Fluctuations in gamma radiation reflect varying input of clay minerals and the presence of shaly interbeds. Throughout the P/Tr boundary interval in the core, the 100,000-year eccentricity cycle seems to be dominant. Weaker obliquity and precession cycles are in line with the location of the Austrian section in the latest Permian, close to the Equator in the western bight of the Tethys, where obliquity and precessional effects on seasonal contrast might be subdued. Using the improved resolution provided by cycle analysis in the GK-1 core, we find that the dramatic change in the faunal record that marks the P/Tr boundary takes place over less than 6m, or less than 60,000 years. In the nearby Reppwand outcrop section, the same faunal changes occurs over only 0.8 m or about 8,000 years, close to the limit of time-resolution induced by bioturbation and reworking in these sediments. The sharp negative global carbon-isotope shift took place within less than or equal to 40,000 yr, and the isotope excursions persisted for approximately 480,000 yr into the Early Triassic. The results indicate that the severe marine faunal event that marks the P/Tr boundary was very sudden, perhaps less than the resolution window in the GK-1 core, and suggest a catastrophic cause. The wavelet-analysis approach to high-resolution cyclostratigraphy can be applied to other P/Tr boundary sections, and when combined with precise absolute dating and magnetostratigraphic methods promises a significant increase in resolution in determining the correlation and tempo of the end-Permian extinctions and related events worldwide.

Rampino, M. R.↗

STS-47 Astronaut Crew Training Clip

The crew of STS-47, Commander Robert L. Gibson, Pilot Curtis L. Brown, Payload Commander Mark C. Lee, Mission Specialists N. Jan Davis, Jay Apt, and Mae C. Jemison, and Payload Specialist Mamoru Mohri, is seen during various parts of their training, including SAREX training in the Full Fuselage Trainer (FFT), firefighting training. A familiarization flight in the KC-135, a food tasting, photo training in the Crew Compartment Trainer, and bailout training in the Weightless Environment Training Facility (WETF) are also shown.

Source record↗

Measurement of Microscopic Growth Rates in Float-Zone Silicon Crystals

Time dependent convective flows during crystal growth of doped semiconductors lead to fluctuations of the composition, so called dopant striations. In general, it is difficult to decide which is the main mechanism for the generation of these striations, it might be either the fluctuation of the concentration field in the melt and the extent of the solute boundary layer ahead of the solid-liquid interface or a variation of the growth velocity. Direct access to the concentration field is rather complicated to achieve, especially considering the high process temperature and the chemical activity of liquid silicon. The contribution of growth rate fluctuations to the formation of compositional fluctuations can be determined by measuring microscopic growth rates. The classical method of current pulses requires electrical feed-throughs and good electrical contacts, both are critical issues for the growth of high purity silicon crystals. Using a radiation based heating system, the heating power can be modulated very fast and effectively. We added to the normal heater power a sinusoidal off-set in the frequency range of 1 to 10 Hz, generating a narrow spaced weak rippling in the grown crystals which are superposed to the dopant striations caused by natural and by thermocapillary convection. The pulling speed was varied between 1 and 4mm/min. The microscope images of etched crystals slices have been analyzed by peak-search algorithms (measuring the spacing between each artificially induced marker) and by FFT. Performing growth experiments under a time-dependent flow regime, fluctuations of the microscopic growth velocity of Delta(v)/v(sub average) up to 50% have been measured. Damping the time-dependent convection by the use of an axial, static magnetic field of 500mT, the microscopic growth rate became constant within the resolution limit of this method. The results will be discussed using analytical methods for the calculation of microscopic growth velocity and by comparing them with measurements of temperature fluctuations in the melt during growth experiments itself.

Dold, P.↗

Thermodynamic Behavior of Nano-sized Gold Clusters on the (001) Surface

We have studied thermal expansion of the surface layers of the hexagonally reconstructed Au (001) surface using a classical Molecular Dynamics (MD) simulation technique with an Embedded Atomic Method (EAM) type many-body potential. We find that the top-most hexagonal layer contracts as temperature increases, whereas the second layer expands or contracts depending on the system size. The magnitude of expansion coefficient of the top layer is much larger than that of the other layers. The calculated thermal expansion coefficients of the top-most layer are about -4.93 x 10(exp -5)Angstroms/Kelvin for the (262 x 227)Angstrom cluster and -3.05 x 10(exp -5)Angstroms/Kelvin for (101 x 87)Angstrom cluster. The Fast Fourier Transform (FFT) image of the atomic density shows that there exists a rotated domain of the top-most hexagonal cluster with rotation angle close to 1 degree at temperature T less than 1000Kelvin. As the temperature increases this domain undergoes a surface orientational phase transition. These predictions are in good agreement with previous phenomenological theories and experimental studies.

Paik, Sun M.↗

Applications Performance Under MPL and MPI on NAS IBM SP2

On July 5, 1994, an IBM Scalable POWER parallel System (IBM SP2) with 64 nodes, was installed at the Numerical Aerodynamic Simulation (NAS) Facility Each node of NAS IBM SP2 is a "wide node" consisting of a RISC 6000/590 workstation module with a clock of 66.5 MHz which can perform four floating point operations per clock with a peak performance of 266 Mflop/s. By the end of 1994, 64 nodes of IBM SP2 will be upgraded to 160 nodes with a peak performance of 42.5 Gflop/s. An overview of the IBM SP2 hardware is presented. The basic understanding of architectural details of RS 6000/590 will help application scientists the porting, optimizing, and tuning of codes from other machines such as the CRAY C90 and the Paragon to the NAS SP2. Optimization techniques such as quad-word loading, effective utilization of two floating point units, and data cache optimization of RS 6000/590 is illustrated, with examples giving performance gains at each optimization step. The conversion of codes using Intel's message passing library NX to codes using native Message Passing Library (MPL) and the Message Passing Interface (NMI) library available on the IBM SP2 is illustrated. In particular, we will present the performance of Fast Fourier Transform (FFT) kernel from NAS Parallel Benchmarks (NPB) under MPL and MPI. We have also optimized some of Fortran BLAS 2 and BLAS 3 routines, e.g., the optimized Fortran DAXPY runs at 175 Mflop/s and optimized Fortran DGEMM runs at 230 Mflop/s per node. The performance of the NPB (Class B) on the IBM SP2 is compared with the CRAY C90, Intel Paragon, TMC CM-5E, and the CRAY T3D.

Saini, Subhash↗

Communication Studies of DMP and SMP Machines

Understanding the interplay between machines and problems is key to obtaining high performance on parallel machines. This paper investigates the interplay between programming paradigms and communication capabilities of parallel machines. In particular, we explicate the communication capabilities of the IBM SP-2 distributed-memory multiprocessor and the SGI PowerCHALLENGEarray symmetric multiprocessor. Two benchmark problems of bitonic sorting and Fast Fourier Transform are selected for experiments. Communication-efficient algorithms are developed to exploit the overlapping capabilities of the machines. Programs are written in Message-Passing Interface for portability and identical codes are used for both machines. Various data sizes and message sizes are used to test the machines' communication capabilities. Experimental results indicate that the communication performance of the multiprocessors are consistent with the size of messages. The SP-2 is sensitive to message size but yields a much higher communication overlapping because of the communication co-processor. The PowerCHALLENGEarray is not highly sensitive to message size and yields a low communication overlapping. Bitonic sorting yields lower performance compared to FFT due to a smaller computation-to-communication ratio.

Sohn, Andrew↗

STS-112 Crew Training Clip

Footage shows the crew of STS-112 (Jeffrey Ashby, Commander; Pamela Melroy, Pilot; David Wolf, Piers Sellers, Sandra Magnus, and Fyodor Yurchikhin, Mission Specialists) during several parts of their training. The video is arranged into short segments. In 'Topside Activities at the NBL', Wolf and Sellers are fitted with EVA suits for pool training. 'Pre-Launch Bailout Training in CCT II' shows all six crew members exiting from the hatch on a model of a shuttle orbiter cockpit. 'EVA Training in the VR Lab' shows a crew member training with a virtual reality simulator, interspersed with footage of Magnus, and Wolf with Melroy, at monitors. There is a 'Crew Photo Session', and 'Pam Melroy and Sandy Magnus at the SES Dome' also features a virtual reality simulator. The final two segments of the video involve hands-on training. 'Post Landing Egress at the FFT' shows the crew suiting up into their flight suits, and being raised on a harness, to practice rapelling from the cockpit hatch. 'EVA Prep and Post at the ISS Airlock' shows the crew assembling an empty EVA suit onboard a model of a module. The crew tests oxygen masks, and Sellers is shown on an exercise bicycle with an oxygen mask, with his heart rate monitored (not shown).

Source record↗

STS-111 Crew Training Clip

The STS-111 Crew is in training for space flight. The crew consists of Commander Ken Cockrell, Pilot Paul Lockhart, Mission Specialists Franklin Chang-Diaz and Philippe Perrin. The crew training begins with Post Insertion Operations with the Full Fuselage Trainer (FFT). Franklin Chang-Diaz, Philippe Perrin and Paul Lockhart are shown in training for airlock and Neutral Buoyancy Lab (NBL) activities. Bailout in Crew Compartment Training (CCT) with Expedition Five is also shown. The crew also gets experience with photography, television, and habitation equipment.

Source record↗

The Burst and Transient Source Experiment(BATSE)Earth Occultation Catalog of Low-Energy Gamma-Ray Sources. Short title: BATSE Earth Occultation Catalog v2.0

The Burst and Transient Source Experiment (BATSE), aboard the Compton Gamma Ray Observatory (CGRO), provided a record of the low-energy gamma-ray sky (approx. 20-1000 keV) between 1991 April and 2000 May (9.1y). BATSE monitored the high energy sky using the Earth occultation technique (EOT) for point sources whose emission extended for times on the order of the CGRO orbital period (approx. 92m) or greater. Using the EOT to extract flux - 2 - information, a catalog of sources using data from the BATSE large area detectors has been prepared. The first part of the catalog consists of results from the all-sky monitoring of 58 sources, mostly Galactic, with intrinsic variability on timescales of hours to years. For these sources, we have included tables of flux and spectral data, and outburst times for transients. Light curves (or flux histories) covering the entire nine mission are being placed on the world wide web. We then performed a deep-sampling of these 58 objects, plus a selection of 121 more objects, combining data from the entire 9.ly BATSE dataset. Source types considered were primarily accreting binaries, but a small number of representative active galaxies, X-ray-emitting stars, and supernova remnants were also included. The sample represents a compilation of sources monitored and/or discovered with BATSE and other high energy instruments between 1991 and 2000, known sources taken from the HEAO 1 A-4 (Levine et al. 1984) and Macomb and Gehrels (1999) catalogs. The deep sample results include definite detections of 82 objects and possible detections of 36 additional objects. The definite detections spanned three classes of sources: accreting black hole and neutron star binaries, active galaxies and supernova remnants. The average fluxes measured for the fourth class, the X-ray emitting stars, were below the confidence limit for definite detection. Flux data for the deep sample are presented in four energy bands: 20-40, 40-70, 70-160, and 160-430 keV. The limiting average flux level (9.1 y) for the sample varies from 3.5 to 20 mCrab (5delta) between 20 and 430 keV, depending on systematic error, which in turn is primarily dependent on the sky location. To strengthen the credibility of detection of weaker sources (approx.5-25 mCrab), we generated Earth occultation images, searched for periodic behavior using FFT and epoch folding methods, and critically evaluated the energy-dependent emission in the four flux bands. The deep sample results are intended for guidance in performing future all-sky surveys or pointed observations in the hard X-ray and low-energy gamma-ray band, as well as more detailed studies with the BATSE EOT.

Harmon, B. A.↗

Long-Term X-Ray Variability of Circinus X-1

We present an analysis of long term X-ray monitoring observations of Circinus X-1 (Cir X-1) made with four different instruments: Vela 5B, Ariel V ASM, Ginga ASM, and RXTE ASM, over the course of more than 30 years. We use Lomb-Scargle periodograms to search for the approx. 16.5 day orbital period of Cir X-1 in each of these data sets and from this derive a new orbital ephemeris based solely on X-ray measurements, which we compare to the previous ephemerides obtained from radio observations. We also use the Phase Dispersion Minimization (PDM) technique, as well as FFT analysis, to verify the periods obtained from periodograms. We obtain dynamic periodograms (both Lomb-Scargle and PDM) of Cir X-1 during the RXTE era, showing the period evolution of Cir X-1, and also displaying some unexplained discrete jumps in the location of the peak power.

CIRCINUS X-1↗