Mathematical models for petroleum-forming processes: carbon isotope fractionation

A mathematical model has been developed in which carbon isotope fractionation during thermal cracking of n-paraffins can be simulated. The model has been calibrated based on data from laboratory cracking experiments carried out on n-octadecane. Relative rate constants for cleavage of C¹²-C¹², C¹²-C¹³ and C¹³-C¹³ bonds agree with the experimental values obtained by other workers.Application of this model to the process of petroleum formation gives good agreement with some existing experimental data, but suggests that a review of our understanding of isotope fractionation during thermal cracking may be necessary. The relative importance of the degree to which the organic material has been cracked and of the type of the organic material in influencing δC¹³ values is discussed.The present model predicts that cracking of n-paraffin distributions having initial odd or even carbon number predominances can induce isotopic inhomogeneity among the homologs of the resulting distribution. The model exhibits some deficiencies in explaining or predicting the δC¹³ values of ethane and propane in relation to methane in gases and of oils and associated methane. Explanations for these discrepancies may lie in the simplicity of our mathematical model, in our assumption of initial isotopic homogeneity within molecules and in our use of only n-paraffins as the source molecules for the cracking reactions.     

On the bifurcations of a certain family of periodic orbits

In their numerical study of a particular family of periodic orbits in a certain potential, Contopoulos and Zikides (1980; Contopoulos, 1981) have calculated numerically successive values of the energyh at which the family becomes unstable. They showed that the ratio of successive values ofh-h _esc, whereh _esc is the energy of escape, is approximately 9.22. Here we show that the limiting ratio ash→h _esc is exp (π/√2) in this problem, and that the limiting ratio for bifurcations of this type varies from one problem to another.     

The structure of Neptune's upper atmosphere: The stellar occultation of 24 May 1981

Observations of the 24 May 1981 occultation of an uncatalogued star by Neptune made at the Cerro Tololo Inter-American Observatory have been analyzed to yield temperature profiles of Neptune's upper atmosphere for number densities near 5 × 10¹³ cm^?3. The mean temperatures at immersion (latitude ?56°) and emersion (latitude ?16°) obtained by numerical inversion were 140 ± 10°K and 154 ± 10°K, respectively. The immersion and emersion profiles are remarkably similar in overall shape, suggestive of global atmospheric layering. From the astrometry of the event, precise relative positions of Neptune and the occulted were obtained.     

Io's 4-μm band and the role of adsorbed SO2

The role of adsorbed SO₂ on Io's surface particles in producing the observed spectral absorption band near 4 μm in Io's reflectance spectrum is explored. Calculations show that a modest 50% monolayer coating of adsorbed SO₂ molecules on submicron grains of sulfur of alkali sulfide, assumed to make up Io's uppermost optical surface (“radialith”), will result in a ν₁ + ν₃ absorption band near 4 μm with depth ～30% below the adjacent continuum, consistent with the observed strength of the Io band. The precise wavelength position of the ν₁ + ν₃ band of SO₂ in different phase states such as frost, ice, adsorbate, and gas are summarized from the experimental literature and compared with the available telescopic measurements of the Io band position. The results suggest that the 4-μm band in Io's full disk spectrum can best be explained by the presence on Io's surface of widespread SO₂ in the form of adsorbate rather than ice or frost.     

Streambank dewatering for increased stability

Streambank erosion is often the dominant source of sediment leaving modified watersheds. Mass failure of high, steep banks is one of the most serious forms of streambank erosion. The risk of a given bank experiencing mass failure is a function of bank height, angle, and soil strength, which is governed by soil moisture. Two methods for bank dewatering were tested in adjacent sections of streambank bordering a deeply incised channel in northern Mississippi: a low‐cost pump system and subsurface horizontal drains. Pore water pressures (both positive and negative pressures, or matric suction) were continuously monitored for 2 years at the pumped site, at an adjacent untreated control section, and for 1 year at the site stabilized with horizontal drains. Resulting data were used to calculate a time series of the factor of safety using a computer model. Over the course of two wet seasons, average bank retreats for the control and pumped plots were 0·43 and 0·21 m, respectively. More limited monitoring revealed that the site with passive drains retreated about 0·23 m. At the pumped site pore water pressure was 3–4 kPa lower than at the control site during the most critical periods. Accordingly, computed factors of safety were above the failure threshold at the pumped site, but fell below unity at the control site on 11 occasions over the period of observation. Similarly, the drained site displayed generally lower pore water pressure and higher safety factors except for two events when drains were evidently overwhelmed with the volume of local surface and subsurface flows. These results suggest, but do not prove, that bank dewatering promoted lower rates of bank retreat and higher levels of stability since the three sites had slight differences in soils, geometry and boundary conditions. Initial cost of the dewatering treatments were significantly less than orthodox bank stabilization measures, but operation and maintenance requirements may be greater. Published in 2009 by John Wiley & Sons, Ltd.     

Conceptual framework for assessing the response of delta channel networks to Holocene sea level rise

Recent research has identified two fundamental unit processes that build delta distributary channels. The first is mouth-bar deposition at the shoreline and subsequent channel bifurcation, which is driven by progradation of the shoreline; the second is avulsion to a new channel, a result of aggradation of the delta topset. The former creates relatively small, branching networks such as Wax Lake Delta; the latter generates relatively few, long distributaries such as the Mississippi and Atchafalaya channels on the Mississippi Delta. The relative rate of progradation to aggradation, and hence the creation of accommodation space, emerges as a controlling parameter on channel network form. Field and experimental research has identified sea level as the dominant control on Holocene delta growth worldwide, and has empirically linked channel network changes to changes in the rate of sea level rise. Here I outline a simple modeling framework for distributary network evolution, and use this to explore large-scale changes in Holocene channel pattern that have been observed in deltas such as the Rhine-Meuse and Mississippi. Rapid early- to mid-Holocene sea level rise forced many deltas into an aggradational mode, where I hypothesize that avulsion and the generation of large-scale branches should dominate. Slowing of sea level rise in the last ～6000 yr allowed partitioning of sediment into progradation, facilitating the growth of smaller-scale distributary trees at the shorelines of some deltas, and a reduction in the number of large-scale branches. Significant antecedent topography modulates delta response; the filling of large incised valleys, for example, caused many deltas to bypass the aggradational phase. Human effects on deltas can be cast in terms of geologic controls affecting accommodation: constriction of channels forces rapid local progradation and mouth-bar bifurcation, while accelerated sea level rise increases aggradation and induces more frequent channel avulsion.     

A revised listing of the number of sunspot groups made by Pastorff, 1819 to 1833

J. W. Pastorff of Drossen, Germany, made about 1477 observations of sunspots between 1819 and 1833. These observations were erroneously interpreted by A. C. Ranyard in 1874 and then used by Rudolf Wolf in his calculations of the Wolf Sunspot Numbers. The result is a noisier daily time series and overestimation of the monthly and yearly means for these years. Pastorff was actually a very good observer. In this paper, Pastorff's original observations are reexamined and more nearly correct values for the number of sunspot groups are tabulated. We show some examples of the problems created by Ranyard's interpretation and the consequences for the history of solar activity that a correct interpretation of Pastorff's observations will have. Pastorff's observations provide valuable information on the first strong cycle after the Dalton Minimum (1795–1823).     

Electron Temperatures and Flow Speeds of the Low Solar Corona: MACS Results from the Total Solar Eclipse of 29 March 2006 in Libya

An experiment was conducted in conjunction with the total solar eclipse on 29 March 2006 in Libya to measure both the electron temperature and its flow speed simultaneously at multiple locations in the low solar corona by measuring the visible K-coronal spectrum. Coronal model spectra incorporating the effects of electron temperature and its flow speed were matched with the measured K-coronal spectra to interpret the observations. Results show electron temperatures of (1.10±0.05) MK, (0.70±0.08) MK, and (0.98±0.12) MK, at 1.1 R _⊙ from Sun center in the solar north, east and west, respectively, and (0.93±0.12) MK, at 1.2 R _⊙ from Sun center in the solar west. The corresponding outflow speeds obtained from the spectral fit are (103±92) km s⁻¹, (0+10) km s⁻¹, (0+10) km s⁻¹, and (0+10) km s⁻¹. Since the observations were taken only at 1.1 R _⊙ and 1.2 R _⊙ from Sun center, these speeds, consistent with zero outflow, are in agreement with expectations and provide additional confirmation that the spectral fitting method is working. The electron temperature at 1.1 R _⊙ from Sun center is larger at the north (polar region) than the east and west (equatorial region).