Absolute Fluctuations Research Articles

Performance of time-frequency representation techniques to measure blood flow turbulence with pulsed-wave Doppler ultrasound

The current processing performed by commercial instruments to obtain the time-frequency representation (TFR) of pulsed-wave Doppler signals may not be adequate to characterize turbulent flow motions. The assessment of the intensity of turbulence is of high clinical importance and measuring high-frequency (small-scale) flow motions, using Doppler ultrasound (US), is a difficult problem that has been studied very little. The objective was to optimize the performance of the spectrogram (SPEC), autoregressive modeling (AR), Choi–Williams distribution (CWD), Choi–Williams reduced interference distribution (CW-RID), Bessel distribution (BD), and matching pursuit method (MP) for mean velocity waveform estimation and turbulence detection. The intensity of turbulence was measured from the fluctuations of the Doppler mean velocity obtained from a simulation model under pulsatile flow. The Kolmogorov spectrum, which is used to determine the frequency of the fluctuations and, thus, the scale of the turbulent motions, was also computed for each method. The best set of parameters for each TFR method was determined by minimizing the error of the absolute frequency fluctuations and Kolmogorov spectral bandwidth measured from the simulated and computed Doppler spectra. The results showed that different parameters must be used for each method to minimize the velocity variance of the estimator, to optimize the detection of the turbulent frequency fluctuations, and to estimate the Kolmogorov spectrum. To minimize the variance and to measure the absolute turbulent frequency fluctuations, four methods provided similar results: SPEC (10-ms sine-cosine windows), AR (10-ms rectangular windows, model order = 8), CWD (wN and wM = 10-ms rectangular windows, σ = 0.01), and BD (wN = 10-ms rectangular windows, α = 16). The velocity variance in the absence of turbulence was on the order of 0.04 m/s (coefficient of variation ranging from 8.0% to 14.5%, depending on the method). With these spectral techniques, the peak of the turbulence intensity was adequately estimated (velocity bias < 0.01 m/s). To track the frequency of turbulence, the best method was BD (wN = 2-ms rectangular windows, α = 2). The bias in the estimate of the −10 dB bandwidth of the Kolmogorov spectrum was 354 ± 51 Hz in the absence of turbulence (the true bandwidth should be 0 Hz), and −193 ± 371 Hz with turbulence (the simulated −10-dB bandwidth was estimated at 1256 Hz instead of 1449 Hz). In conclusion, several TFR methods can be used to measure the magnitude of the turbulent fluctuations. To track eddies ranging from large vortex to small turbulent fluctuations (wide Kolmogorov spectrum), the Bessel distribution with appropriate set of parameters is recommended. (E-mail: cloutig@ircm.qc.ca)

Near-caustic behavior in a 270-km acoustical experiment

Data from a pulse-propagation experiment are analyzed to quantify fluctuations in the transmitted acoustic signal. In the experiment a bottom-moored, broadband source having a 460-Hz center frequency transmitted 273 km away to a bottom-moored, vertical hydrophone array spanning 180 m of the water column. Pulses were transmitted every 12 min for a total duration of nearly 100 h. Because the minimal hydrophone separation at the receiving array was less than 2 m, vertical behavior on small scales could be observed. Furthermore, the vertical position of the receiving array enabled an examination of the near-caustic portion of wavefronts, and in some cases, the caustics themselves. Unfortunately, because instrument motion measurements were unsuccessful, relative rather than absolute signal fluctuations were the principal observable in this analysis.

The fitness threshold model: Random environmental change alters adaptive landscapes

We used a probabilistic optimization model to explore the joint evolutionary effects of random phenotypic and environmental variation. Two forms of environmental noise were defined in which the optimal phenotype remained constant but all organisms experienced either the same proportionate or the same absolute fitness gains and losses. There was no evolutionary effect of proportionate fitness fluctuations. In contrast, the optimal genotype varied with absolute fitness fluctuations, despite the environmental effect being phenotype-independent. We refer to such phenotype-independent fluctuation in absolute fitness as the ‘fitness threshold model’, because shared fitness effects determine the zero-fitness points (i.e. the baseline) on an intrinsic fitness function. Thus, environmental effects that are unrelated to a focal trait can cause peak shifts in the genetic optimum for the trait. Changes in the fitness threshold not only changed peak locations, but also altered the slopes defining the peaks, and so should alter the rate of evolution towards optima. This model pertains to evolution in any system, unless there is no phenotypic or environmental variance, or the selection function and distribution of phenotypic error assume similar shapes. Our results have many basic and applied implications for topics such as the maintenance of genetic variation, the canalization of development and the management of natural populations.

Height variations and secular changes in sea level

The problem of understanding, assessing and quantifying the causes of sea-level changes has received increased attention during the past several years, in particular in connection with predictions regarding a rise in the global mean sea level due to global warming. The impact aspect of sea-level rise is of particular concern for many coastal areas in densely populated regions of the world. The present availability of space geodetic techniques providing high-accuracy measurements of station positions and of their time variations makes it possible to separate vertical crustal movements and absolute sea-level fluctuations. Gravimetric methods play an important role in the assessment of sea-level variations by providing completely independent measurements of vertical crustal movements. Satellite altimetry now enables the measurement of the spatial variability of sea level. Geological observations can infer former sea levels which are important to understand the present trends. This paper addresses the study of height variations and secular changes in sea level by discussing the most interesting questions and issues, by presenting the current understanding of the phenomena involved, and finally by illustrating the measuring and modeling techniques to be adopted for a comprehensive approach to the problem.

Bed-by-bed fold growth by kink-band migration: Sant llorenç de Morunys, eastern Pyrenees

Growth strata deposited over and against the flank of the Sant Llorenç de Morunys fold during its final stages of deformation have been mapped at high resolution as the basis for unraveling the kinematics of fold growth. We use restoration techniques based on normal balancing assumptions to decipher the detailed kinematic history of folding. The progressive restorations, as well as balanced forward modeling, show that the last few hundred meters of fold growth were dominated by kink-band migration of a sort that is typical of much faultrelated folding. The kink-band migration has produced complex anticlinal hinge-zone geometry, including segmented fold hinges linked by disconformities and unconformities, which has direct and detailed explanation in terms of fluctuations in deposition rate relative to curved-hinge kink-band migration rate. Large fluctuations in the convolution of non-steady sedimentation and deformation are demonstrated, although the absolute fluctuations in deformation and sedimentation are unknown. At a length scale of 100 m, kink-band migration with little or no deposition is interspersed with sedimentation with little or no deformation. At the length scale of 500 m, deposition ranges from 200% to 50% of uplift.

Absolute concentration measurements inside a jet plume using video digitization

An experimental system based on digitized video image analysis is used to measure the local value of the concentration inside a plume. Experiments are carried out in a wind-tunnel for a smoke-seeded turbulent jet plume illuminated with a laser beam. Each test is filmed, subsequently video images are digitized and analysed in order to determine the smoke absolute concentration corresponding to each pixel gray level. This non-intrusive measurement technique is first calibrated and different laws connecting gray level to concentration are established. As a first application, concentration measurements are made inside a turbulent jet plume and compared with measurements conducted using a classic gas analysis method. We finally present and discuss the possibilities offered for the measurements of absolute concentration fluctuations.

Density fluctuations in different types of solar wind flow at 1 AU and comparison with results from Doppler scintillation measurements near the Sun

Density fluctuations with periods in the range 10 min to 1 hour are investigated using ISEE 3 plasma measurements of solar wind flows at 1 AU. Coronal hole, interstream, plasma sheet, coronal mass ejection, and interaction region flow types are considered. The ISEE 3 results are consistent with the interpretation of large‐scale variations in density fluctuations observed by Doppler scintillation measurements inside 0.2 AU. The highest absolute and fractional density fluctuations are found ahead of and within the plasma from coronal mass ejections, with the maximum values occurring between the associated interplanetary shocks and the driver gas. For the quasi‐stationary solar wind, density and fractional density fluctuations are highest and most variable in the plasma sheet in which the heliospheric current sheet is embedded, and lowest and least variable in the high‐speed coronal hole flow. A superposed epoch analysis of heliospheric current sheet crossings shows that the regions of enhanced density fluctuations previously identified in Doppler scintillation measurements near the Sun persist to 1 AU and are broader there. The results of this study confirm the advantages of using density fluctuations rather than density as a tracer of solar wind flows of differing origins at the Sun and as a detector of propagating interplanetary disturbances.

Environmental regulation of sexual maturation and reproduction in tilapia

Abstract The critical predictive and/or proximate environmental cues identified in the literature that affect the onset of first sexual maturation and reproduction of tilapiine cichlids of the genera Tilapia, Sarotherodon, and Oreochromis are light intensity, food quality and availability, environmental stability, and level of social interaction. Absolute values and fluctuations of these environmental parameters interact with endogenous rhythms, the genome, and life history events to produce observed variations in the onset of sexual maturation and reproduction. A greater understanding of the relationship between environment and reproduction is required to improve the ability of aquaculturists to control tilapia breeding.

The dispersion in the near-infrared surface brightness fluctuations in the Virgo cluster

view Abstract Citations (57) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Dispersion in the Near-Infrared Surface Brightness Fluctuations in the Virgo Cluster Pahre, Michael A. ; Mould, Jeremy R. Abstract We observed NGC 3379 and nine Virgo elliptical galaxies at 2.16 microns using a NICMOS3 256 X 256 detector array. We have measured the surface brightness fluctuations in the K-band for all but one Virgo galaxy (an E/S0), thus extending the previous measurements in K by a factor of 3. We find for NGC 3379 that the apparent fluctuations magnitude m^bar^_K_ = 24.48 +/- 0.11, and we find no evidence at the 0.20 mag level for radial gradients in the apparent fluctuations magnitude. In the Virgo Cluster, we find that NGC 4365 has a similar fluctuation magnitude to the other galaxies in the sample, which is in contrast to previous I-band fluctuations observations which put it in the background W cloud; we note that this discrepancy could also be the result of a different stellar population. We also find an anomalous bright apparent fluctuations magnitude for the dwarf, low-surface brightness elliptical NGC 4489, which might be attributable to its lower signal-to-noise ratio (but is significant at the 3 σ level) or to an unusual stellar population. The average fluctuations magnitude for the Virgo galaxies (excluding NGC 4489) is m^bar^_K_ = 25.16 +/- 0.18, with a 1 σ_rms_ dispersion of 0.25 mag. When we assume the distance moduli to these galaxies from I-band surface brightness fluctuations measurements, we find that for the sample of Virgo galaxies (excluding NGC 4365 and 4489), plus NGC 3379 M31, and M32 (the latter two from Luppino & Tonry 1993), the absolute fluctuations magnitude M_bar__K_ = 5.74 +/- 0.18. We find an observed 1 arms dispersion in the measurements of M^bar^_K_ of 0.20 magnitude, which is nearly that of our typical uncertainty of 0.18 mag in each measurement of M^bar^_K_. The theoretical predictions of Worthey (1993) for M^bar^_K_ as a function of both (V - I) color and Mg_2_ index are shown to be consistent with the observations, differing only by +0.31 and -0.09 mag, respectively, from our mean measurement of M^bar^_K_ = - 5.74 +/- 0.18. This difference is well within the quoted uncertainties of the models (0.4 to 0.5 mag) and our measurements. The simple stellar population models of Buzzoni (1993) are shown to be too faint in M^bar^_K_ by ~ 0.5 mag, which we suggest to be due to their exclusion of an empirically based M-giant population. We suggest that the origin of the dispersion in the measurement of M^bar^_K_ may be due to variations in metallicity; larger samples of early-type galaxies should be able to determine if there is such a relationship between metallicity and M^bar^_K_. We present models of M^bar^_K_ based upon the addition to the stellar population of an anomalous asymptotic giant branch population contributing 10% of the light at 2 microns and show that this produces an absolute fluctuations magnitude 0.7 to 1.5 mag brighter. Such a population may be consistent with the observations of M^bar^_K_ in M32 by Luppino & Tonry (1993), but could only be present in NGC 4365 and 4489 of our sample, the two galaxies which are measured to have brighter m^bar^_K_ relative to m^bar^_I_. Finally, we suggest that with the typically better seeing at the K band (compared with the optical), and with the brightness of the fluctuations at this wavelength, measurements of distances to greater redshifts are possible than with optical measurements of surface brightness fluctuations, although the problem of calibrating the relationship between M^bar^_K_ and (V - I) color or Mg_2_ index needs to be solved in order to reduce the uncertainties of such distance measurements. Publication: The Astrophysical Journal Pub Date: October 1994 DOI: 10.1086/174667 Bibcode: 1994ApJ...433..567P Keywords: Astronomical Models; Brightness Distribution; Distance; Elliptical Galaxies; Infrared Astronomy; Variations; Virgo Galactic Cluster; Asymptotic Giant Branch Stars; Cameras; Color; M Stars; Magnesium; Mercury Cadmium Tellurides; Metallicity; Power Spectra; Red Shift; Reflecting Telescopes; Astrophysics; GALAXIES: CLUSTERS: INDIVIDUAL NAME: VIRGO; GALAXIES: CLUSTERS OF; GALAXIES: INDIVIDUAL NGC NUMBER: NGC 3379; GALAXIES: PHOTOMETRY; INFRARED: GALAXIES full text sources ADS | data products SIMBAD (15) NED (13)

Advanced Glaucoma Intervention Study: 2. Visual Field Test Scoring and Reliability

Background: The Advanced Glaucoma Intervention Study (AGIS) is a multicenter, randomized clinical trial designed (1) to determine the better of two surgical management strategies for glaucoma when medical treatment alone no longer adequately controls the disease and (2) to clarify the clinical course and prognosis of open-angle glaucoma after surgical interventions have begun. The investigators of this study have developed quantitative methods to assess the test reliability and measure the severity of glaucomatous visual field defects with the 24-2 threshold program of the Humphrey Visual Field Analyzer. This report details these methods and presents information about long-term fluctuation during a time interval short enough to render change due to disease unlikely. Methods: In AGIS, reliability assessment of automated visual field tests is based on the number of questions asked; percent of fixation losses, false-positive responses, and false-negative responses; and amount of short-term fluctuation. The AGIS visual field defect score is based on the number and depth of clusters of adjacent depressed test sites in the upper and lower hemifields and in the nasal area of the total deviation printout of the threshold program single-field test STATPAC-2 analysis. The score ranges from 0 (no defect) to 20 (all test sites deeply depressed). The fluctuation in score between two tests obtained during an interval preceding AGIS surgical interventions, ranging from 1 day to 6 weeks on 756 eyes of 562 patients, is analyzed. Results: The scores of the first visual field tests, which determined eligibility for the study, range from 1 to 17. Large positive or negative intertest fluctuations (absolute changes of 4 or more) occurred in the second tests for 16% of eyes; more scores improved (11%) than worsened (5%). The frequency of large fluctuations tended to increase as the time interval between tests increased. Absolute intertest fluctuations were independent of age. Conclusion: For visual field tests obtained with the automated perimeter, AGIS investigators have developed objective, quantitative methods of scoring test reliability and severity of glaucomatous field loss. For 16% of eyes, long-term fluctuations were large enough (≥4 points) to suggest improvement or worsening of the glaucomatous defect even though the interval in which the fluctuations occurred was short enough (median time, approximately 1 week) to render changes in disease status unlikely. Background: The Advanced Glaucoma Intervention Study (AGIS) is a multicenter, randomized clinical trial designed (1) to determine the better of two surgical management strategies for glaucoma when medical treatment alone no longer adequately controls the disease and (2) to clarify the clinical course and prognosis of open-angle glaucoma after surgical interventions have begun. The investigators of this study have developed quantitative methods to assess the test reliability and measure the severity of glaucomatous visual field defects with the 24-2 threshold program of the Humphrey Visual Field Analyzer. This report details these methods and presents information about long-term fluctuation during a time interval short enough to render change due to disease unlikely. Methods: In AGIS, reliability assessment of automated visual field tests is based on the number of questions asked; percent of fixation losses, false-positive responses, and false-negative responses; and amount of short-term fluctuation. The AGIS visual field defect score is based on the number and depth of clusters of adjacent depressed test sites in the upper and lower hemifields and in the nasal area of the total deviation printout of the threshold program single-field test STATPAC-2 analysis. The score ranges from 0 (no defect) to 20 (all test sites deeply depressed). The fluctuation in score between two tests obtained during an interval preceding AGIS surgical interventions, ranging from 1 day to 6 weeks on 756 eyes of 562 patients, is analyzed. Results: The scores of the first visual field tests, which determined eligibility for the study, range from 1 to 17. Large positive or negative intertest fluctuations (absolute changes of 4 or more) occurred in the second tests for 16% of eyes; more scores improved (11%) than worsened (5%). The frequency of large fluctuations tended to increase as the time interval between tests increased. Absolute intertest fluctuations were independent of age. Conclusion: For visual field tests obtained with the automated perimeter, AGIS investigators have developed objective, quantitative methods of scoring test reliability and severity of glaucomatous field loss. For 16% of eyes, long-term fluctuations were large enough (≥4 points) to suggest improvement or worsening of the glaucomatous defect even though the interval in which the fluctuations occurred was short enough (median time, approximately 1 week) to render changes in disease status unlikely.

Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G''(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G''(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G'' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G'' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.

Monte Carlo studies of spin-stiffness fluctuations in the two-dimensional classical Heisenberg model

A recent one-loop calculation has shown that, in the d-dimensional classical Heisenberg model at low temperatures, the absolute thermal fluctuations of the spin-stiffness constant are scale independent for d4. We report the confirmation of this unexpected theoretical prediction by extensive Monte Carlo simulations in d=2. In addition, we find that the strength of the logarithmic correction for the relative fluctuations depends on the details of the boundary conditions.

Scale-independent fluctuations of spin stiffness in the Heisenberg model and its relationship to universal conductance fluctuations.

It is shown that, at low temperatures, the absolute thermal fluctuations of the spin-stiffness constant in the classical Heisenberg model are independent of the scale L for d4, if L is larger than the lattice spacing but smaller than the correlation length, while the relative fluctuation is proportional to ${\mathit{L}}^{4\mathrm{\ensuremath{-}}2\mathit{d}}$, where d is the dimensionality, and is thus scale independent in d=2 (with logarithmic corrections). The phenomenon is strikingly similar to the universal conductance fluctuations known for the problem of an electron in a random potential.

Atomic hydrogen behaviour in Heliotron E

In order to understand atomic hydrogen behaviour and particle confinement properties in Heliotron E plasmas, techniques of laser induced fluorescence (LIF) have been extensively used, combined with measurements of absolute Balmer alpha emissions and density fluctuations. The results revealed that for an average electron density n¯ e > 1.5 × 10 19 m −3, Hα fluorescence allowed the measurements of atomic hydrogen densities and yielded the recycled Franck-Condon neutrals (~ 3 eV) to penetrate into core plasmas, whereas for n¯ e < 1.0 × 10 19 m −3, such measurements were perturbed by dissociative-excitation of H 2 molecules into the n = 2 state. Also, the global confinement times showed a clear correlation with electron density fluctuations.

Aspects of transport properties of quasi-one-dimensional electron systems

We study the low temperature transport properties of a guasi-one-dimensional electron system for both Drude and variable-range-hopping conduction. In the first case, the density of states and conductivity are theoretically calculated in realistic structures as a function of the chemical potential. These calculations show a well defined oscillatory structure, provided the level broadening and temperature are very low. In the latter case, we find evidence of the transition from a one-dimensional variable-range-hopping law of ln R ∼ T − 1 2 to a two-dimensional behavior of ln R ∼ T − 1 3 as the width of the sample increases. Consistent with experimental data, calculated absolute fluctuations in the resistance are substantially suppressed with the increase in width, relative resistance fluctuations are, however, insensitive to changes in the width.

Transition from one- to two-dimensional fluctuating variable-range-hopping conduction in microstructures.

We study numerically variable-range-hopping conduction in long narrow channels of finite widths as a function of temperature, chemical potential, and the width of the channel. We find clear evidence of the transition from a one-dimensional Mott variable-range-hopping law of $\mathrm{ln}R\ensuremath{\sim}{T}^{\ensuremath{-}\frac{1}{2}}$ to a two-dimensional behavior of $\mathrm{ln}R\ensuremath{\sim}{T}^{\ensuremath{-}\frac{1}{3}}$ in the average resistance $R$ as the width of the channel increases. Consistent with experimental data, calculated absolute fluctuations in the channel resistance are substantially suppressed with the increase in width. Relative resistance fluctuations seem to be much more insensitive to the dimensionality of the system. Our results are in excellent agreement with the available experimental data and show conclusively that variable range hopping is the dominant low-temperature transport mechanism in these narrow channel systems.

Rocket-borne and groundbased observations of coincident field-aligned currents, electron beams, and plasma density enhancements in the afternoon auroral oval

Results are reported from a rocket experiment conducted at Søndre Strømfjord, Greenland, on 22 August 1976, at 16.00 M.L.T. A series of plasma, particles, and fields and wave experiments were carried on board the payload, and the venture was supported by data from the AE- C satellite and by groundbased ionosondes and magnetometers at the launch site and at Godhavn. Two regions of field-aligned electron precipitation, electron density and temperature enhancements, and field-aligned upflowing current sheets were intercepted by the rocket. The density enhancements were also observed by groundbased ionosondes. Significant discrepancies were found between the currents carried by the streaming electrons in the 0.15–10 keV range and the upflowing currents seen by the on board magnetometer, suggesting that the upflowing current could not be the primary driver of the electron acceleration mechanism. The E-region was unstable to the combined Gradient-Drift and Farley-Buneman instability, and plasma turbulence was observed in situ, but the absolute density fluctuations were too small to return detectable HF-radar power to the ground.

Simultaneous rocket probe, scintillation, and incoherent scatter radar observations of irregularities in the auroral zone ionosphere

Two rocket payloads carrying plasma density probes with high spatial resolution have been flown in the auroral zone during active conditions. Simultaneous Wideband satellite scintillation and Chatanika incoherent scatter radar observations were made in order to study the properties of high‐latitude irregularities and their effects on radio wave transmission. Unlike barium cloud striations and bottomside equatorial spread F, the observed power law dependence of the irregularities does not seem to be due to steepening of kilometer‐scale structures, rather, a turbulent process seems to occur. In addition the power law indexes determined both from the probe and from the scintillation measurements indicates an in situ one‐dimensional spectrum less steep than the k−2 value often reported. Both the probe and the scintillation data indicate absolute electron density fluctuations (Δn2e)½ of several times 109 m−3 during the expansion phase of an auroral substorm, with a layer thickness of several hundred kilometers. The observed S4 levels at VHF were in the range of 0.1–0.4. This level of scintillation, as well as the absolute density fluctuation levels and the power spectral density at the kilometer scale, are shown to be comparable with bottomside equatorial spread F. It is suggested that differences between the power spectral index in the present data set and the other ionospheric experiments mentioned above may be due to a highly conductive E layer and its effects upon the nonlinear evolution of irregularities. During another flight with lower magnetic activity but several bright auroral areas in the trajectory, much lower levels of absolute and relative density fluctuations were observed with a corresponding lower value for S4. Two very sharp changes in electron density were observed (e‐folding scales of 1.45 and 0.7 km) near the field line projected position of the auroral arcs. The associated density spectra were peaked at short wavelengths. The detection of very structured plasma within minutes of the poleward expansion phase of a substorm suggests that the F layer irregularities were formed in the precipitation event. On the other hand, evidence is also presented for production or enhancement of irregularities in the presence of horizontal density gradients which suggests that plasma instabilities also play a role in the production of auroral zone irregularities.

Porosity fluctuations in a monodisperse granular packed bed

1. Equations were obtained for the absolute and relative fluctuations of the porosity in a monodisperse packed bed. 2. Estimates of these fluctuations were made for various volumes of the packed bed and granules of variable shape.

12. Satellite orbits and atmospheric densities at altitudes up to 750 kilometers obtained from the vanguard orbit determination program

The satellites 1958 β2 (Vanguard I) and 1958 γ (Explorer III) represent extremes from the orbit-determination standpoint. The absolute fluctuations in the mean motion were smallest for the former, and largest for the latter, among the satellites for which precision Minitrack radio observations were available. Accordingly, the orbit of the former has been determined with the greater precision. Even in the case of 1958 γ, however, the rootmean- square value of the residuals is less than twenty minutes of arc. The radial distances between adjacent arcs at the times for transferring from one arc to the next are of the same order as the residuals within the individual arcs. The results obtained with this satellite are of interest since they indicate what can be done in the way of determining the orbits of satellites having very low perigees and very high fineness ratios. Errors of less than four minutes of arc have been obtained for some of the orbital arcs of 1958 β2[1].