Radial Separation Research Articles

Unraveling the Strands of Saturn's F Ring

Several high-resolution Voyager 2 images of Saturn's F ring show that it is composed of at least four separate, non-intersecting strands extending ∼45° in longitude. Voyager 1 images show that the two brightest strands appear to intersect, giving rise to a “braided” morphology. From a study of all available Voyager images the detectable radial structure is cataloged and reviewed. Previous indications that there is fine material interior to the orbit of the F ring are confirmed. Evidence is presented that a model of four strands with comparable eccentricities and nearly aligned perichrones is consistent with all the Voyager observations. The observed perichrone offset of the two brightest strands suggests a minimum radial separation of ∼20 km, which implies intersection of these strands when their finite radial widths are taken into account. The longitude range of such an intersection includes that observed in the Voyager 1 “braid” images. The proximity of these two strands at some longitudes may account for the apparent differences in the ring between the Voyager encounters, as well as provide a source for the short-lived features detected in the Hubble Space Telescope images of the F ring. There is no evidence that the locations of the individual strands are determined by resonant perturbations with known satellites. It is proposed that the radial structure is formed by the localized action of small satellites orbiting within the strand region.

The N2H+–He intermolecular potential energy surface: A vibrational adiabatic correction

This paper presents a method for constructing computationally cheap adiabatically corrected ab initio potential energy surfaces (PES) for intermolecular vibrational states. The approach reasonably reproduces previously published experimental data for the N2H+–He complex in the ground and excited intramolecular vibrational states. A comparison made between a set of intermolecular PES’s with the N2H+ core frozen into the equilibrium geometry and a set where the N–H+ stretch is averaged demonstrates the importance of including this motion. This is also reflected in a considerable improvement in the agreement between the experimental and the calculated intermolecular bending and stretching frequencies and the origin red shift (νb,calc=117.9 cm−1, νs,calc=165.2 cm−1, Δνcalc=−93.0 cm−1). A comparison is also made between the Born–Oppenheimer angular radial separation (BOARS) angular average of the adiabatically corrected PES and the previously published rotational Rydberg–Klein–Rees (RRKR) PES. The results indicate that the two-dimensional νNH=1 PES has a qualitatively correct well depth and dissociation energy (De=684.7 cm−1; D0=433.6 cm−1).

Spatial variations of 0.2 to 5 MeV protons in the 1–5 AU in‐ecliptic region from Ulysses, Voyager 1 and 2, and IMP 8 gradient studies

Protons with energies ranging from 0.3 to 2 MeV are nearly always present in the environment of Earth. Solar flare events and interplanetary shock waves can be identified as producing or enhancing these fluxes. However, interplanetary particles are observed even in the absence of solar flares. Explaining the presence of these proton fluxes in the interplanetary medium and accounting for their variations is a major problem in space physics. Observations of interplanetary proton fluxes have been made continuously at 1 AU with the Interplanetary Monitoring Platform (IMP) 8 from 1973 to the present and in the 1–5 AU range by Voyagers 1 and 2 (1977–1978) and Ulysses (1990–1991). Daily averaged proton fluxes of IMP 8, Voyagers 1 and 2, and Ulysses have been carefully interpolated to matching energy passbands so that fluxes in the same passbands at two radial distances could be compared. These daily averaged fluxes were then compared as ratios and were autocorrelated and cross‐correlated as functions of time delay. The radial gradient, the energy spectra, and the distribution of these proton fluxes were also examined. The results showed that protons in the 0.3 to 5 MeV energy range using the Voyager 1/IMP 8, Voyager 2/IMP 8, and Ulysses/IMP 8 paired observations in the 1 to 5 AU in‐ecliptic region tend to “decorrelate” with increasing radial separation and become uncorrelated by about 4 or 5 AU. Higher‐energy fluxes decorrelate less rapidly, and lower‐energy proton fluxes have more dominantly positive radial gradients than those of higher energy. The radial gradient of 0.3 to 0.5 MeV proton fluxes is dominantly positive for 1–2 AU, while that of 2 to 4 MeV proton fluxes is negative. In contrast, from 2 to 4 AU the radial gradient of 0.3 to 0.5 MeV proton fluxes is weakly negative, and that of 2 to 4 MeV protons is weakly positive. This finding suggests that 0.3 to 0.5 MeV protons are more subject to interplanetary acceleration than are 2 to 4 MeV protons in the 1–2 AU range. The results also showed that radial gradients are robust and persist, evert if all heliolongitude coherence is purposely removed by shuffling the time order within 120‐day time intervals.

A two‐dimensional simulation of the radial and latitudinal evolution of a solar wind disturbance driven by a fast, high‐pressure coronal mass ejection

Using a hydrodynamic simulation, we have studied the two‐dimensional (symmetry in the azimuthal direction) evolution of a fast, high‐pressure coronal mass ejection (CME) ejected into a solar wind with latitudinal variations similar to those observed by Ulysses. Specifically, the latitudinal structure of the ambient solar wind in the meridional plane is approximated by two zones: At low latitudes (< 20°) the solar wind is slow and dense, while at higher latitudes the solar wind is fast and tenuous. The CME is introduced into this ambient wind as a bell‐shaped pressure pulse in time, spanning from the equator to 45° with a speed and temperature equal to that of the high‐latitude solar wind. We find that such an ejection profile produces radically different disturbance profiles at low and high latitudes. In particular, the low‐latitude portion of the ejecta material drives a highly asymmetric disturbance because of the relative difference in speed between the fast CME and slower ambient solar wind ahead. In contrast, the high‐latitude portion of the same ejecta material drives a much more radially symmetric disturbance because the relative difference in pressure between the CME and ambient background plasma dominates the dynamics. The simulations reveal a number of other interesting features. First, there is significant distortion of the CME in the interplanetary medium. By ∼ 1 AU the CME has effectively separated (in radius as well as latitude) into two pieces. The radial separation is due to the strong velocity shear between the slow and fast ambient solar wind. The latitudinal separation arises from pressure gradients associated with rarefaction regions that develop as the CME propagates outward. Second, there is significant poleward motion of the highest‐latitude portion of the CME and its associated disturbance. The main body of the CME expands poleward by ∼ 18°, while the forward and reverse waves (produced by the overexpanding portion of the CME) propagate all the way to the pole. Third, the simulations show that the high‐pressure region, which develops at low latitudes as the fast CME ploughs through the slow ambient solar wind, penetrates significantly (∼ 10°) into the high‐latitude fast solar wind. We compare the simulation results with a CME‐driven interplanetary disturbance observed at both low and high latitudes and find that the simulation reproduces many of the essential features of the observations.

Double-Stacked Dielectric Resonator for Sensitive EPR Measurements

A new approximate method for predicting the resonant frequencies and for solving the field distribution problem of a cylindrical dielectric resonator (DR) is developed. The model proposed in this paper bridges the gap between rigorous and accurate finite-element or Green function-based numerical methods on the one hand and on the other hand, simple approximate solutions in which the field distribution can be described analytically, but the resulting frequency is accurate within a few percent only. In the method described here, the approximate solution for the microwave field distribution is modified by substituting different values of the radial separation constants inside and outside of the disk-shaped DR. The model is generalized for the double-stacked DR structure and enables one to introduce corrections that take into account the presence of the shielding walls and of the cylindrical sample hole. Good agreement is found between experimental and calculated results for both the single and double-stacked structures that are designed around commercially available X-band DRs (9–10 GHz). For the resonant frequency of the lowest transverse-electric TE01δmode that is commonly used for EPR measurements, the accuracy of the method is better than 1%. Experimentally measured resonator filling factors are also in good agreement with those theoretically estimated. Both the theory and the experimental results suggest that the double-stacked DR structure with finite spacing between the ceramic cylinders is the most suitable for EPR measurements of long lossy samples.

Application of sustained off-resonance irradiation: The beat frequency measurement and radial separation of mass-selected ions

Newer applications of sustained off-resonance irradiation (SORI) in Fourier-transform ion cyclotron resonance (FT-ICR) spectrometry are described. SORI induced circular gyrations of ions with their cyclotron radii varying sinusoidally at the corresponding beat frequency. The beat is observed in the temporal variation of FT-ICR peak height as a function of the duration of the SORI burst, and it allows the direct measurement of the beat frequency. The effective cyclotron frequency is determined from the measured beat frequency and the applied burst frequency. The frequency uncertainty is greatly reduced by nearly 3 orders of magnitude compared with the uncertainty in FT-ICR peak frequency that fluctuates with the rf burst duration. In addition, the oscillating cyclotron radii of the irradiated ions allow the radial separation of mass-selected ions so that the mass-selective photodissociation can be carried out with m-bromotoluene ions.

Effects of strain on island scaling studied by Monte Carlo simulations

Strained heteroepitaxial growth is a possible means of obtaining carrier confinement in reduced-dimensional systems for applications in optoelectronic devices. The epitaxial growth of InAs on GaAs provides an excellent prototypical system due to the significant lattice mismatch of approximately 7% between the two constituents. At submonolayer coverages, highly elongated two-dimensional InAs islands were observed experimentally with a preferred width of approximately 4 nm. When the island size distributions were separated into [110] and [1̄10] components, scaling was only observed in the [1̄10] direction, and clustering was observed in the radial separation distribution. We have used lattice gas Monte Carlo simulations to explore the effects of intrinsic system anisotropies and strain on island scaling. We found that the experimentally observed scaling behavior can only be explained by taking into consideration both the system anisotropies and strain.

Free-ion yield and electron-ion recombination rate in liquefied rare gases: the case of liquid krypton

Free-ion yield in liquid krypton has been calculated at low LET as a function of the external field according to a re-encounter theory recently proposed by the author. Comparison with experimental results reveals k r/ k D≃0.22 at 120 K, where k r is the specific rate of electron-ion recombination and k D is the corresponding Debye rate. Encounter reaction efficiency for electron-ion recombination is found to lie in the range 0.08–0.11, consistent with initial radial separation of thermalized electrons between 3000 and 6000 nm.

The effects of collecting duct active NaCl reabsorption and inner medulla anatomy on renal concentrating mechanism.

First, the representation of the inner medulla incorporates an exaggerated radial separation between tubules, vessels, and collecting ducts; and, second, the hydraulic permeability in the upper portion of the inner medullary collecting ducts was erroneously set to zero. In the current work, we explore the role of collecting duct hydraulic permeability and anatomical heterogeneity via mathematical modeling. The model predicts concentrated urine for measured values of the hydraulic permeability and homogeneous lower inner medulla as long as net active NaCl reabsorption is incorporated in the upper inner medullary collecting duct epithelium. This new three-dimensional model results in two recycling paths. The upper portion of the inner medulla recycles NaCl, whereas the lower portion recycles urea.

An optimal algorithm for roundness determination on convex polygons

In tolerancing, the Out-Of-Roundness factor determines the relative circularity of planar shapes. The measurement of concern in this work is the Minimum Radial Separation, as recommended by the American National Standards Institute (ANSI). Here we show that the algorithm given in Le and Lee [6] runs in θ( n 2) time even for convex polygons. Furthermore, we present an optimal O( n) time algorithm to compute the Minimum Radial Separation of convex polygons, which represents not only a factor n improvement over the previously best known algorithm, but also a factor of log n improvement over Le and Lee's conjectured complexity for the problem.

The geometry of the minimum radial separation functional: the planar case

The minimum radial separation measure associated with a planar simple polygon is computed using an exhaustive search strategy based on the definition of the measure. The algorithm is simple and direct, based on purely geometrical arguments, and provides an alternative and useful way to examine the minimum radial separation measure. The approach of considering the radial separation functional as the basic element of analysis complements rather than replaces existing numerical techniques to find the separation centre point, and because of its fundamental character, is also highly desirable in terms of standardization. Quantitative measures of tolerance specification that arise from this treatment include an intrinsic 'average' out-of-roundness and values for standard deviation. The concavity of the separation functional at the solution minimum is a useful means to quantify tolerance, and contour plots provide constant out-of-roundness regions. A minimum area difference measure is defined, along with its area difference functional, and the geometry of the separation functionals are illustrated by example.

Convective uphill transport of NaCl from ascending thin limb of loop of Henle.

In this paper we describe a mathematical model of the renal inner medulla based on a previously proposed model [A.S. Wexler, R.E. Kalaba, and D.J. Marsh. Am. J. Physiol. 260 (Renal Fluid Electrolyte Physiol. 29): F368-F383, 1991] in which in the inner medullary ascending thin limb of Henle's loop (ATL) and collecting duct (CD) exchange with a local capillary node with the reabsorbed water and solutes flowing radially toward a central vascular bundle. Our model differs in that ascending and descending vasa recta and surrounding interstitial space are replaced by a central core. Our analysis of the coupled ATL-CD system shows that it is theoretically capable of transporting NaCl out of the ATL into the central vascular space (approximated by the central core) against a concentration gradient, which in the absence of radial diffusion can be arbitrarily large. By numerical solution of the model with the radial diffusion coefficient (D(r)) for NaCl of 0, we find that the ATL can be more than 100 mosmol/l hypotonic with respect to the core. We also find that with restricted diffusion the osmolality of the CD at the papilla is significantly greater than that of the loop of Henle. As D(r) approaches the diffusion coefficient of NaCl in free solution, the osmolality of the loop increases and that of the CD decreases. Thus, overall, contrary to intuitive expectations, the radial separation and uphill transport of NaCl do not give any significant increase in loop concentration, which depends primarily on the quantity of urea reabsorbed from the CD.

Effect of vasa recta flow on concentrating ability of models of renal inner medulla.

In this study we extend the analysis of the preceding two studies [J. L. Stephenson, J. F. Jen, H. Wang, and R. P. Tewarson. Am. J. Physiol. 268 (Renal Fluid Electrolyte Physiol. 37): F698-F709, 1995; and J. F. Jen, H. Wang, R. P. Tewarson, and J. L. Stephenson. Am. J. Physiol. 268 (Renal Fluid Electrolyte Physiol. 37): F000-F000, 1995] to a model that includes vasa recta. Distribution of nephron and vasa recta lengths is represented by shunting from descending to ascending flow. It is found that the effect of radial separation of structures on concentrating ability is closely linked to vasa recta flow. With minimal or no vasa recta flow the extent of radial mixing has little effect on concentrating ability. As vasa recta flow increases, concentrating ability is decreased by radial mixing. Convective uphill transport of NaCl is again observed, but concentrating ability appears to depend primarily on urea delivery to the inner medulla from the collecting duct rather than on the mechanism of salt transport out of thin ascending limb. Central core models give an upper bound on concentrating ability but do not attain the maximum urine osmolality of the rat with experimental values of tubular permeabilities.

Towards quantum mechanical characterization of the dissociation dynamics of ketene

A combination of numerical techniques designed for efficient computations with very large basis sets which enables the spectral analysis of transitional-mode eigenstates in the dissociation of ketene is described. At the heart of our methods is a pseudo-spectral algorithm for the action of the transitional mode Hamiltonian (describing the rocking/bending motion of the dissociating fragments) on a state vector. This allows the multiplication of the state vector by the Hamiltonian matrix without explicitly storing the matrix, thus enabling very large basis sets to be managed. With the radial separation between the fragments frozen, transitional-mode eigenstates at energies close to threshold, where the adiabatic channels are moderately well separated, are readily computed with the Lanczos iterative technique. At higher energies the spectrum rapidly becomes extremely dense and convergence of the Lanczos algorithm is very slow. However, combinations of eigenfunctions with a bandwidth of a few wavenumbers or better can be obtained by shifted inverse iteration. Illustrative results from computations using the Klippenstein–Marcus model interaction potential for ketene are presented.

A turbulent fluid model for the evolution of zonal jets in a pre-planetary nebular disk

Abstract It is known that a turbulent, two-dimensional fluid at high Reynolds number under a suitable restoring force can evolve toward larger scales, that is, to waves and zonal jets. A two-dimensional disk of turbulent fluid gravitationally bound to a central mass is considered as a model for a pre-planetary disk. It is found that for general conditions, azimuthal zonal jets can form in the disk. Planetesimals are assumed to accrete between these jets. Their radial separation distances, s(r), should be roughly s(r)∼ π{[e/(1 - e 2)]}1/2 r, where e is orbital eccentricity, and r is semimajor radius. In the corotating reference frame, jets alternate in direction, forming counterstreaming pairs. For eccentricities comparable to Solar System planetary orbital eccentricities, jet pair separations roughly double with each successive jet pair. The predicted spacings are in better agreement with observation than predicitions by the Titius-Bode(TB) Rule. This model predicts that TB-like spacing should be common i...

Density profile control in a fusion reactor using pellet injection

The relationships between plasma parameters that are dependent on the density profile (fusion rate, core and edge densities and temperatures, density and temperature profile peaking), fuel particle pumping in the divertor (expressed as particle throughput) and pellet injection parameters (size, velocity and injection frequency) are examined for tokamak reactor plasmas. These relationships are illustrated with the results of transport simulations of steady state conditions for a nominal set of reactor parameters representative of the International Thermonuclear Experimental Reactor (ITER) using pellet parameters characteristic of both present and advanced injectors. The radial separation between the pellet source and the pumping in the divertor region, even with very modest pellet velocities, allows for the possibility of density profile control in the plasma edge. When matching both fusion power and edge density constraints, fuel particle throughput decreases with increasing pellet penetration. The sensitivity of the results to the details of the transport model and to the limit on the edge density is also examined

Perturbation analysis of the helical flow of non-Newtonian fluids with application to a recirculating coaxial cylinder rheometer

This paper analyzes the flow of non-Newtonian fluids between infinitely long coaxial cylinders, when the inner cylinder rotates with given angular velocity Ω, and a given axial flow rate, Q, is superimposed on this rotational motion. Such helical flow is of significance in the modelling of the action of a recirculating coaxial cylinder rheometer, where the axial flow is superimposed on the standard cup-and-bob rheometer to allow accurate rheological measurements involving fluids that are settling in nature. Such fluids are encountered in many mineral, food, and chemical processes of industrial significance. The analysis presented here applies the perturbation approach to analyze the above flows in two situations of physical interest: 1. the case of low axial flow rates; and 2. the case where the radial separation of the cylinders is small. In each case, the appropriate perturbation parameter is identified, and appropriate expressions for the velocity field are obtained for non-Newtonian fluids of interest. More significantly, this analysis allows the construction of approximate forms of the Reiner-Rivlin relation for this flow, which relates the angular velocity Ω to the observed torque, M, at the inner cylinder, through the rheological parameters defining the fluid. Subsequent measurement of Ω and M allows these parameters to be determined for a given fluid model. Where possible, the findings of the perturbation analysis are compared directly with experimental measurements involving a model of such a recirculating rheometer.

Unimolecular decomposition in a spherically symmetric potential

Unimolecular decompositions are considered where the interaction between the separating fragments can be described by a function solely of their radial separation. It is shown how previous treatments, confined to idealized models, can be generalized. Kinetic energy distributions and rate constants may be calculated accordingly when the angular momentum is low. Applications to evaporation from van der Waals molecules are noted. A limit to the interaction parameters is then found where these properties become ‘‘thermodynamic,’’ despite the absence of angular momentum. This result is used to obtain a general form for the effects of angular momentum on a rate constant. It reduces to traditional ideas in the hard-sphere limit.

High-performance liquid chromatographic method for the simultaneous determination of pentisomide and its major metabolite N-desisopropylpentisomide in plasma, urine and tissues using solid-phase extraction.

A rapid, sensitive and selective high-performance liquid chromatographic method for the simultaneous determination of pentisomide and its major metabolite desisopropylpentisomide in plasma, urine and tissues has been developed. The method for plasma samples, urine samples and tissue samples, after homogenizing with 50% ethanol, involves extraction of samples via activated Bond-Elut C8 disposable columns with methanol at pH 10 after addition of internal standard, and initially on column washing of samples at pH 10 with water and acetonitrile. The obtained methanolic extract is evaporated to dryness under nitrogen at 25 degrees C; the sample residue is then reconstituted in mobile phase and an aliquot of this solution is injected into the liquid chromatograph. Separation is performed using a Nova-Pak C18 4 microns particle size column operating in combination with radial compression separation unit and a methanol-water-di-sec.-butylamine-phosphoric acid (40:60:0.5:0.2, v/v) pH 3.5 mobile phase with ultraviolet detection at 258 nm. Endogenous substances or a variety of drugs concomitantly used in pentisomide therapy, with the exception of disopyramide, do not interfere with the assay. The mean recovery of pentisomide and desisopropylpentisomide from plasma and urine and from tissues is more than 91 and 86%, respectively. The limit of detection of the assay is 10 ng/ml for both drugs. The intra- and inter-day coefficient of variation for replicate analyses of spiked plasma samples is less than 7 and 8%, respectively. Mean steady-state plasma levels of pentisomide and desisopropylpentisomide in patients on chronic oral therapy are reported.

ASTROMETRIC PERFORMANCE CHARACTERISTICS OF THE HUBBLE SPACE TELESCOPE FINE GUIDANCE SENSORS

ABSTRACT Each of the three Fine Guidance Sensors for the Hubble Space Telescope constitutes a sixth science instrument to be used for astrometry. We detail the tests and results used in choosing one of the three sensors to be the prime astrometer. The Astrometry Science team has chosen Fine Guidance Sensor (FGS) 3. FGS 3 produces position measurements on a star with V=17 with a per-axis precision of 0.003 arcsec. The interferometer response function should permit double-star astrometry at least down to V=16 for the central region of FGS 3. In a ten-hour test of the stability of POS-mode astrometric measurements made in FGS 3, we found no scale or orientation variations greater than two parts in 105. During this same time period, we found no statistically significant systematic guide star radial separation changes. Spacecraft jitter is found to be the prime determinant of astrometry success or failure.