Showing papers by "Ames Research Center published in 1998"

DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

Abstract: ▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

A universal time scale for vortex ring formation

Abstract: The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.

Reveal, a general reverse engineering algorithm for inference of genetic network architectures

Abstract: Given the immanent gene expression mapping covering whole genomes during development, health and disease, we seek computational methods to maximize functional inference from such large data sets. Is it possible, in principle, to completely infer a complex regulatory network architecture from input/output patterns of its variables? We investigated this possibility using binary models of genetic networks. Trajectories, or state transition tables of Boolean nets, resemble time series of gene expression. By systematically analyzing the mutual information between input states and output states, one is able to infer the sets of input elements controlling each element or gene in the network. This process is unequivocal and exact for complete state transition tables. We implemented this REVerse Engineering ALgorithm (REVEAL) in a C program, and found the problem to be tractable within the conditions tested so far. For n = 50 (elements) and k = 3 (inputs per element), the analysis of incomplete state transition tables (100 state transition pairs out of a possible 10(exp 15)) reliably produced the original rule and wiring sets. While this study is limited to synchronous Boolean networks, the algorithm is generalizable to include multi-state models, essentially allowing direct application to realistic biological data sets. The ability to adequately solve the inverse problem may enable in-depth analysis of complex dynamic systems in biology and other fields.

Data-Parallel Line Relaxation Method for the Navier -Stokes Equations

Abstract: The Gauss‐Seidel line relaxation method is modie ed for the simulation of viscous e ows on massively parallel computers. The resulting data-parallel line relaxation method is shown to have good convergence properties for a seriesoftestcases.Thenewmethodrequiressignie cantlymorememorythanthepreviouslydevelopeddata-parallel relaxation methods, but it reaches a steady-state solution in much less time for all cases tested to date. In addition, the data-parallel line relaxation method shows good convergence properties even on the high-cell-aspect-ratio grids required to simulate high-Reynolds-number e ows. The new method is implemented using message passing on the Cray T3E, and the parallel performance of the method on this machine is discussed. The data-parallel line relaxation method combines the fast convergence of the Gauss ‐Seidel line relaxation method with a high parallel efe ciency and thus shows promise for large-scale simulation of viscous e ows.

The Belief-Desire-Intention Model of Agency

Abstract: Within the ATAL community, the belief-desire-intention (BDI) model has come to be possibly the best known and best studied model of practical reasoning agents. There are several reasons for its success, but perhaps the most compelling are that the BDI model combines a respectable philosophical model of human practical reasoning, (originally developed by Michael Bratman [1]), a number of implementations (in the IRMA architecture [2] and the various PRS-like systems currently available [7]), several successful applications (including the now-famous fault diagnosis system for the space shuttle, as well as factory process control systems and business process management [8]), and finally, an elegant abstract logical semantics, which have been taken up and elaborated upon widely within the agent research community [14, 16].

Evidence for a subsurface ocean on Europa

Abstract: Ground-based spectroscopy of Jupiter's moon Europa, combined with gravity data, suggests that the satellite has an icy crust roughly 150 km thick and a rocky interior In addition, images obtained by the Voyager spacecraft revealed that Europa's surface is crossed by numerous intersecting ridges and dark bands (called lineae) and is sparsely cratered, indicating that the terrain is probably significantly younger than that of Ganymede and Callisto It has been suggested that Europa's thin outer ice shell might be separated from the moon's silicate interior by a liquid water layer, delayed or prevented from freezing by tidal heating; in this model, the lineae could be explained by repetitive tidal deformation of the outer ice shell However, observational confirmation of a subsurface ocean was largely frustrated by the low resolution (>2 km per pixel) of the Voyager images Here we present high-resolution (54 m per pixel) Galileo spacecraft images of Europa, in which we find evidence for mobile 'icebergs' The detailed morphology of the terrain strongly supports the presence of liquid water at shallow depths below the surface, either today or at some time in the past Moreover, lower-resolution observations of much larger regions suggest that the phenomena reported here are widespread

Photoevaporation of Disks and Clumps by Nearby Massive Stars: Application to Disk Destruction in the Orion Nebula

Abstract: We present a model for the photoevaporation of circumstellar disks or dense clumps of gas by an external source of ultraviolet radiation. Our model includes the thermal and dynamic effects of 6-13.6 eV far-ultraviolet (FUV) photons and Lyman continuum EUV photons incident upon disks or clumps idealized as spheres of radius rd and enclosed mass M*. For sufficiently large values of rd/M*, the radiation field evaporates the surface gas and dust. Analytical and numerical approximations to the resulting flows are presented; the model depends on rd, M*, the flux of FUV and EUV photons, and the column density of neutral gas heated by FUV photons to high temperatures. Application of this model shows that the circumstellar disks (rd ~ 1014-1015 cm) in the Orion Nebula ("proplyds") are rapidly destroyed by the external UV radiation field. Close (d 1017 cm) to θ1 Ori C, the ionizing EUV photon flux controls the mass-loss rate, and the ionization front (IF) is approximately coincident with the disk surface. Gas evaporated from the cold disk moves subsonically through a relatively thin photodissociation region (PDR) dominated by FUV photons and heated to ~1000 K. As the distance from θ1 Ori C increases, the Lyman continuum flux declines, the PDR thickens, and the IF moves away from the disk surface. At d ~ 3 × 1017 cm, the thickness of the PDR becomes comparable to the disk radius. Between 3 × 1017 cm d 1018 cm, spherical divergence and the resultant pressure gradient in the 103 K PDR forms a mildly supersonic (~3-6 km s-1) but neutral Parker wind. This wind flows outward until it passes through a shock, beyond which gas moves subsonically through a stationary D-type IF. The IF is moved away from the disk surface to a standoff distance rIF 2.5rd. In this regime, the mass-loss rate is determined by the incident FUV photon flux and not the ionizing flux. However, at very large distances, d 1018 cm, the FUV photon flux drops to values that cannot maintain the disk surface temperature at ~103 K. As the PDR temperature drops, the pressure of the FUV-powered flow declines with increasing distance from θ1 Ori C, and again the EUV ionizing photons can penetrate close to the disk surface and dominate the evaporation rate. Radio, Hα, and [O III] observations of externally illuminated young stellar objects in the Trapezium region are used to determine rIF and the projected distances, d⊥, from θ1 Ori C. The observed values of rIF and d⊥ are combined with the theory to estimate the disk sizes, mass-loss rates, surface densities, and disk masses for the ensemble of extended sources in the Trapezium cluster. Observations of rIF, d⊥, and rd in HST 182-413 and a few other sources are used to calibrate parameters of the theory, especially the column of heated PDR gas. The disks have a range in sizes between 14 < log [rd/(cm)] < 15.2, mass-loss rates of -7.7 < log [/(M/yr)]<-6.2, surface densities at disk edge 0.7 < log [Σ(rd)/(g cm-2)] < 2.5 which imply disk surface densities at 1 AU from the central, embedded star of 2.8 < log [Σ0/(g cm-2)] < 3.8 and disk masses of 0.002 < Md/M☉ < 0.07. Σ and Md scale with the adopted ionization time, ti, which we take to be 105 yr. The inferred Σ(rd) for the ensemble of disks suggest that the initial surface density power law of an individual disk, Σ ∝ r-α, is bounded by 1 α 1.5.

Robust and efficient Cartesian mesh generation for component-based geometry

Abstract: This work documents a new method for rapid and robust Cartesian mesh generation for component-based geometry. The new algorithm adopts a novel strategy that first intersects the components to extract the wetted surface before proceeding with volume mesh generation in a second phase. The intersection scheme is based on a robust geometry engine that uses adaptive precision arithmetic and automatically and consistently handles geometric degenerades with an algorithmic tie-breaking routine. The intersection procedure has worst-case computational complexity of O(N log N) and is demonstrated on test cases with up to 121 overlapping and intersecting components, including a variety of geometric degeneracies. The volume mesh generation takes the intersected surface triangulation as input and generates the mesh through cell division of an initially uniform coarse grid. In refining hexagonal cells to resolve the geometry, the new approach preserves the ability to directionally divide cells that are well aligned with local geometry. The mesh generation scheme has linear asymptotic complexity with memory requirements that total approximately 14-17 words/cell. The mesh generation speed is approximately 10 6 cells/minute on a typical engineering workstation

Studies in Astronomical Time Series Analysis. V. Bayesian Blocks, a New Method to Analyze Structure in Photon Counting Data*

Abstract: I describe a new time-domain algorithm for detecting localized structures (bursts), revealing pulse shapes, and generally characterizing intensity variations. The input is raw counting data, in any of three forms: time-tagged photon events (TTE), binned counts, or time-to-spill (TTS) data. The output is the most probable segmentation of the observation into time intervals during which the photon arrival rate is perceptibly constant, i.e., has no statistically significant variations. The idea is not that the source is deemed to have this discontinuous, piecewise constant form, rather that such an approximate and generic model is often useful. Since the analysis is based on Bayesian statistics, I call the resulting structures Bayesian blocks. Unlike most, this method does not stipulate time bins—instead the data determine a piecewise constant representation. Therefore the analysis procedure itself does not impose a lower limit to the timescale on which variability can be detected. Locations, amplitudes, and rise and decay times of pulses within a time series can be estimated independent of any pulse-shape model—but only if they do not overlap too much, as deconvolution is not incorporated. The Bayesian blocks method is demonstrated by analyzing pulse structure in BATSE γ-ray data.

Geological evidence for solid-state convection in Europa's ice shell

Abstract: The ice-rich surface of the jovian satellite Europa is sparsely cratered, suggesting that this moon might be geologically active today1. Moreover, models of the satellite's interior indicate that tidal interactions with Jupiter might produce enough heat to maintain a subsurface liquid water layer2,3,4,5. But the mechanisms of interior heat loss and resurfacing are currently unclear, as is the question of whether Europa has (or had at one time) a liquid water ocean6,7. Here we report on the morphology and geological interpretation of distinct surface features—pits, domes and spots—discovered in high-resolution images of Europa obtained by the Galileo spacecraft. The features are interpreted as the surface manifestation of diapirs, relatively warm localized ice masses that have risen buoyantly through the subsurface. We find that the formation of the features can be explained by thermally induced solid-state convection within an ice shell, possibly overlying a liquid water layer. Our results are consistent with the possibility that Europa has a liquid water ocean beneath a surface layer of ice, but further tests and observations are needed to demonstrate this conclusively.

Carbon in the Universe

Abstract: Carbon is a major player in the evolutionary scheme of the universe because of its abundance and its ability to form complex species It is also a key element in the evolution of prebiotic molecules The different forms of cosmic carbon are reviewed ranging from carbon atoms and carbon-bearing molecules to complex, solid-state, carbonaceous structures The current state of knowledge is assessed on the observational and laboratory fronts Fundamental astrophysical implications are examined as well as the impact of these studies on the hitherto poorly understood physical and chemical properties of carbon materials in space

A sequence database for the identification of ectomycorrhizal basidiomycetes by phylogenetic analysis

Abstract: We have assembled a sequence database for 80 genera of Basidiomycota from the Hymenomycete lineage (sensu Swann & Taylor 1993) for a small region of the mitochondrial large subunit rRNA gene. Our taxonomic sample is highly biased toward known ectomycorrhizal (EM) taxa, but also includes some related saprobic species. This gene fragment can be amplified directly from mycorrhizae, sequenced, and used to determine the family or subfamily of many unknown mycorrhizal basidiomycetes. The method is robust to minor sequencing errors, minor misalignments, and method of phylogenetic analysis. Evolutionary inferences are limited by the small size and conservative nature of the gene fragment. Nevertheless two interesting patterns emerge: (i) the switch between ectomycorrhizae and saprobic lifestyles appears to have happened convergently several and perhaps many times; and (ii) at least five independent lineages of ectomycorrhizal fungi are characterized by very short branch lengths. We estimate that two of these groups radiated in the mid-Tertiary, and we speculate that these radiations may have been caused by the expanding geographical range of their host trees during this period. The aligned database, which will continue to be updated, can be obtained from the following site on the WorldWide Web: http://mendel.berkeley.edu/boletus.html.

A Planetary Companion to a Nearby M4 Dwarf, Gliese 876*

Abstract: Doppler measurements of the M4 dwarf star Gliese 876 taken at both Lick and Keck Observatories reveal periodic, Keplerian velocity variations with a period of 61 days. The orbital fit implies that the companion has a mass of M=2.1 MJUP${r JUP}$ -->$t SUBgt {r JUP}t/SUBgt $ -->/sin${r sin}$ -->${r sin}$ -->i, an orbital eccentricity of e=0.27 ± 0.03, and a semimajor axis of a=0.21 AU. The planet is the first found around an M dwarf and was drawn from a survey of 24 such stars at Lick Observatory. It is the closest extrasolar planet yet found, providing opportunities for follow-up detection. The presence of a giant planet on a noncircular orbit, 0.2 AU from a 0.32 M☉ star, presents a challenge to planet formation theory. This planet detection around an M dwarf suggests that giant planets are numerous in the Galaxy.

Photochemistry in biomass burning plumes and implications for tropospheric ozone over the tropical South Atlantic

Abstract: Photochemistry occuring in biomass burning plumes over the tropical south Atlantic is analyzed using data collected during the Transport and Atmospheric Chemistry Near the Equator-Atlantic aircraft expedition conducted during the tropical dry season in September 1992 and a photochemical point model. Enhancement ratios (ΔY/ΔX, where Δ indicates the enhancement of a compound in the plume above the local background mixing ratio, Y are individual hydrocarbons, CO, O3, N2O, HNO3, peroxyacetyl nitrate (PAN), CH2O, acetone, H2O2, CH3OOH, HCOOH, CH3COOH or aerosols and X is CO or CO2) are reported as a function of plume age inferred from the progression of Δnon-methane hydrocarbons/ΔCO enhancement ratios. Emission, formation, and loss of species in plumes can be diagnosed from progression of enhancement ratios from fresh to old plumes. O3 is produced in plumes over at least a 1 week period with mean ΔO3/ΔCO = 0.7 in old plumes. However, enhancement ratios in plumes can be influenced by changing background mixing ratios and by photochemical loss of CO. We estimate a downward correction of ∼20% in enhancement ratios in old plumes relative to ΔCO to correct for CO loss. In a case study of a large persistent biomass burning plume at 4-km we found elevated concentrations of PAN in the fresh plume. The degradation of PAN helped maintain NOx mixing ratios in the plume where, over the course of a week, PAN was converted to HNO3. Ozone production in the plume was limited by the availability of NOx, and because of the short lifetime of O3 at 4-km, net ozone production in the plume was negligible. Within the region, the majority of O3 production takes place in air above median CO concentration, indicating that most O3 production occurs in plumes. Scaling up from the mean observed ΔO3/ΔCO in old plumes, we estimate a minimum regional O3 production of 17×1010molecules O3 cm−2 s−1. This O3 production rate is sufficient to fully explain the observed enhancement in tropospheric O3 over the tropical South Atlantic during the dry season.

Dynamic density: an air traffic management metric

Abstract: The definition of a metric of air traffic controller workload based on air traffic characteristics is essential to the development of both air traffic management automation and air traffic procedures. Dynamic density is a proposed concept for a metric that includes both traffic density (a count of aircraft in a volume of airspace) and traffic complexity (a measure of the complexity of the air traffic in a volume of airspace). It was hypothesized that a metric that includes terms that capture air traffic complexity will be a better measure of air traffic controller workload than current measures based only on traffic density. A weighted linear dynamic density function was developed and validated operationally. The proposed dynamic density function includes a traffic density term and eight traffic complexity terms. A unit-weighted dynamic density function was able to account for an average of 22% of the variance in observed controller activity not accounted for by traffic density alone. A comparative analysis of unit weights, subjective weights, and regression weights for the terms in the dynamic density equation was conducted. The best predictor of controller activity was the dynamic density equation with regression-weighted complexity terms.

Brahms: simulating practice for work systems design

Abstract: A continuing problem in business today is the design of human–computer systems that respect how work actually gets done. The overarching context of work consists ofactivities, which people conceive as ways of organizing their daily life and especially their interactions with each other. Activities include reading mail, going to workshops, meeting with colleagues over lunch, answering phone calls, and so on. Brahms is a multiagent simulation tool for modeling the activities of groups in different locations and the physical environment consisting of objects and documents, including especially computer systems. A Brahms model of work practice revealscircumstantial, interactional influenceson how work actually gets done, especially how people involve each other in their work. In particular, a model of practice reveals how people accomplish a collaboration through multiple and alternative means of communication, such as meetings, computer tools, and written documents. Choices of what and how to communicate are dependent uponsocial beliefs and behaviors—what people know about each other’s activities, intentions, and capabilities and their understanding of the norms of the group. As a result, Brahms models can help human–computer system designers to understandhow tasks and information actually flowbetween people and machines, what work is required to synchronize individual contributions, and how tools hinder or help this process. In particular, workflow diagrams generated by Brahms arethe emergent product of local interactions between agents and representational artifacts, not pre-ordained, end-to-end paths built in by a modeler. We developed Brahms as a tool to support the design of work by illuminating how formal flow descriptions relate to the social systems of work; we accomplish this by incorporating multiple views—relating people, information, systems, and geography—in one tool. Applications of Brahms could also include system requirements analysis, instruction, implementing software agents, and a workbench for relating cognitive and social theories of human behavior.

Multimodality instrument for tissue characterization

Abstract: A system with multimodality instrument for tissue identification includes a computer-controlled motor driven heuristic probe with a multisensory tip. For neurosurgical applications, the instrument is mounted on a stereotactic frame for the probe to penetrate the brain in a precisely controlled fashion. The resistance of the brain tissue being penetrated is continually monitored by a miniaturized strain gauge attached to the probe tip. Other modality sensors may be mounted near the probe tip to provide real-time tissue characterizations and the ability to detect the proximity of blood vessels, thus eliminating errors normally associated with registration of pre-operative scans, tissue swelling, elastic tissue deformation, human judgement, etc., and rendering surgical procedures safer, more accurate, and efficient. A neural network program adaptively learns the information on resistance and other characteristic features of normal brain tissue during the surgery and provides near real-time modeling. A fuzzy logic interface to the neural network program incorporates expert medical knowledge in the learning process. Identification of abnormal brain tissue is determined by the detection of change and comparison with previously learned models of abnormal brain tissues. The operation of the instrument is controlled through a user friendly graphical interface. Patient data is presented in a 3D stereographics display. Acoustic feedback of selected information may optionally be provided. Upon detection of the close proximity to blood vessels or abnormal brain tissue, the computer-controlled motor immediately stops probe penetration. The use of this system will make surgical procedures safer, more accurate, and more efficient. Other applications of this system include the detection, prognosis and treatment of breast cancer, prostate cancer, spinal diseases, and use in general exploratory surgery.

Global analysis of empirical relations between annual climate and seasonality of NDVI

Abstract: This paper describes the use of satellite data to calibrate a new climate-vegetation greenness relationship for global change studies. We examined statistical relationships between annual climate indexes (temperature, precipitation, and surface radiation) and seasonal attributes If the AVHRR Normalized Difference Vegetation Index (NDVI) time series for the mid-1980's in order to refine our understanding of intra-annual patterns and global abiotic controls on natural vegetation dynamics. Multiple linear regression results using global 1o gridded data sets suggest that three climate indexes: degree days (growing/chilling), annual precipitation total, and an annual moisture index together can account to 70-80 percent of the geographic variation in the NDVI seasonal extremes (maximum and minimum values) for the calibration year 1984. Inclusion of the same annual climate index values from the previous year explains no substantial additional portion of the global scale variation in NDVI seasonal extremes. The monthly timing of NDVI extremes is closely associated with seasonal patterns in maximum and minimum temperature and rainfall, with lag times of 1 to 2 months. We separated well-drained areas from lo grid cells mapped as greater than 25 percent inundated coverage for estimation of both the magnitude and timing of seasonal NDVI maximum values. Predicted monthly NDVI, derived from our climate-based regression equations and Fourier smoothing algorithms, shows good agreement with observed NDVI for several different years at a series of ecosystem test locations from around the globe. Regions in which NDVI seasonal extremes are not accurately predicted are mainly high latitude zones, mixed and disturbed vegetation types, and other remote locations where climate station data are sparse.

Infrared Spectroscopy of Matrix Isolated Polycyclic Aromatic Hydrocarbons. 2. PAHs Containing Five or More Rings

Abstract: Matrix isolation techniques have been used to measure the mid-infrared spectra of the polycyclic aromatic hydrocarbons (PAHs) naphthalene, anthracene, phenanthrene, 1,2-benzanthracene, chrysene, pyrene, tetracene, and triphenylene. The band positions and relative strengths are compared to previous laboratory studies, where available, and with available theoretical calculations.1 Comparisons with theory indicate that density functional theory (DFT) does an excellent job of describing the majority of the infrared active fundamentals of the PAHs considered here. Band positions typically match to within 5 cm-1, with the worst mismatches usually no more than 15 cm-1. Matches in band strengths are not as precise but, with the exception of the CH stretching bands, are generally good to better than 35% for most strong and moderate bands and to factors of 2 to 3 for weaker bands. Theory predicts CH stretching band strengths that are about a factor of 2 times too strong. The laboratory spectra contain large numbers...

Detection of Abundant CO2 Ice in the Quiescent Dark Cloud Medium toward Elias 16

Abstract: We report the first detection of solid carbon dioxide (CO2) in quiescent regions of a dark cloud in the solar neighborhood, a result that has important implications for models of ice formation and evolution in the interstellar medium. The K-type field star Elias 16 was previously known to display solid-state absorption features of H2O and CO ices arising in the Taurus Dark Cloud. Our detection of the CO2 feature at 4.27 μm in this line of sight implies a column density N(CO2)=4.6+ 1.3−0.6×1017 cm-2, equivalent to ~18% and 70% of the H2O and CO column densities, respectively. Comparison with laboratory data indicates that (unlike CO) the CO2 resides primarily in a polar (H2O-rich) component of the ices. CO2 is formed easily in the laboratory by the photolysis of ice mixtures containing CO, but the detection toward Elias 16 indicates that CO2 formation can occur in dark clouds in the absence of a local embedded source of radiation. Possible alternative mechanisms for CO2 production include grain surface reactions and energetic processing driven by the interstellar radiation field or cosmic rays.

A universal time scale for vortex ring formation

Abstract: The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.

Modeling the Diversity of Outer Planetary Systems

Abstract: In order to better understand the range of dynamically long-lived giant planet systems, we present the results of a set of bottom-up numerical simulations designed to generate plausible giant planet systems from a large number of planetary embryos. Our simulations produced systems that are stable for at least a billion years and that exhibit a wide range of characteristics. Some of these systems are reminiscent of the outer solar system. The number of planets ranged from one to seven. Many systems contained only Uranus-mass objects. We constructed systems that were more compact than the outer solar system and systems that were much sparser, with planets on very eccentric orbits. Perhaps most surprisingly, some of the systems that we constructed were stable for at least a billion years despite undergoing macroscopic orbital changes on much shorter timescales.