Stability Analysis and Numerical Simulation of Differential Frost Heave

Differential frost heave is often implicated in the formation of patterned ground in regions subject to recurrent freezing and thawing. A linear stability analysis (LSA) indicates that a continuum model of frost heave is linearly unstable under typical natural freezing conditions of silty-clay soils. A two-dimensional non-linear numerical analysis corroborates the frozen time LSA results, and also indicates the importance of non-linear and time-dependent terms that ultimately lead to a preferred mode, which the LSA fails to predict. Instability of the one-dimensional solution occurs at shallow freezing depths and near-zero surface loads when positive perturbations in the ice content at the freezing front lead to a concomitant increase in thermomolecular pressure and upward ice velocity. Differential frost heave can then occur because of the increased heat flux from the perturbed surfaces. A three-dimensional model using random initial surface perturbations indicates that regular surface patterns will evolve with a length scale in the order of 2–4 meters, which corresponds quite closely with naturally-occurring non-sorted patterned ground.     

A model of an exploding,radiating star in general relativity

In a previous paper Adams, Cary and Cohen (1994) presented a model of a supernova. In that paper the equations of General Relativity describing the evolution of a spherically symmetric, radiating star were solved analytically. The evolution of the star was determined by the application of boundary conditions at the center and at the edge. Due to lmitations in the presupernova model, only the very slow inward motion of an unstable, degenerate core could be considered. The solution was also limited by the need to exclude a runaway term, one that increased exponentially with time. Without the exclusion of the runaway, the luminosity would have increased without bound and the mass would have become negative.This paper presents a completely analytic solution to the equations of General Relativity describing the evolution of a Type II supernova. Professor S.E. Woosley kindly gave us data on the physical variables of a 12M ₀ presupernova star. In our model the core collapses within 1 s, leaving a 1.3M ₀ remnant. Shortly afterward 10.6M ₀ is ejected to infinity, and 0.17M ₀ is radiated away in the form of neutrinos. The distance of the edge from the center increases proportionally to the two-thirds power of the time. The luminosity decreases proportionally to the inverse four-thirds power.Although the runaway solution was modified by the exploding rather than a static envelope, it must still be excluded by adjusting initial conditions. Its character is changed from an exponential to a very large power (55) of time. The removal of a degree of freedom by this exclusion leads to physically non-sensical results such as negative luminosity. The inclusion of a term describing motion of the mantle due to neutrino interactions provides the additional degree of freedom necessary for physically reasonable results.     

Geochemistry and origin of the Proterozoic ultrapotassic rocks of the Churchill Province,Canada

Summary Early Proterozoic ultrapotassic dikes, lava flows, and pyroclastic rocks of the Christopher Island Formation (CIF) erupted throughout an area 600 × 300 km within the Churchill Province of the Canadian Shield at 1.84 Ga. The rocks range from mafic lamprophyres (mg # 60; SiO₂ 47–54%, mean K₂O/Na₂O > 4) with phenocrysts of phlogopite + diopside + apatite ± olivine ± magnetite, to phenocryst-poor felsic rocks and sanidine porphyries (SiO₂55–69%). All samples have high incompatible element contents and display large depletions of high field strength elements relative to K, Rb, Sr, Ba, and Th. The CIF has geochemical and petrographic characteristics of both minettes and lamproites, but overall most closely resembles young Mediterranean lamproites. Felsic rocks of the CIF were produced by crystal fractionation and crustal contamination of mafic ultrapotassic magma, and include both high-silica lamproites strongly enriched in Zr, U, and Th, and weakly potassic to sodic rocks of trachytic composition. Flows and feeder dikes have relatively homogeneous _{Nd, 1840 Ma} (–6 to –11) but highly variable ES., 1840 Ma (–40 to + 100); samples classified as lamproites have higher average _Sr. Dike samples have highly variable present-day Pb isotope compositions, ranging from moderately to strongly nonradiogenic. Geochemical and isotopic data are consistent with contributions from depleted Archean lithospheric mantle, and OIB-type convecting mantle, both metasomatized by subduction-related processes during the Early Proterozoic. The lithospheric mantle probably contained Archean enriched domains as well. Proterozoic enrichment may have accompanied shallow underplating of subducted oceanic lithosphere beneath the Churchill Province during amalgamation of the Laurentian supercontinent. There are strong analogies in isotopic composition, and interpreted source region history, between the CIF and lamproites and minettes of the Wyoming Province and western Greenland, which suggest the existence of a Laurentian ultrapotassic superprovince.

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Geochemie und Entstehung der Proterozoischen ultrapotassischen Gesteine der Churchill Provinz, Kanada

Zusammenfassung Altproterozoische, ultrapotassische Gänge, Lavaströme und pyroklastische Gesteine der Christopher Island Formation (CIF), eruptierten in einem Gebiet von 600 × 300 km in der Churchill Provinz des Kanadischen Schildes vor 1.84 Ga. Die Zusammensetzung dieser Gesteine variiert von mafischen Lamprophyren (mg > 60; SiO₂ = 47–54%, durchschnittliches K₂O/Na₂O > 4) mit Phänokristallent von Phlogopit + Diopsid + Apatit + Olivin + Magnetit, bis zu phänokristallarmen felsischen Gesteinen und Sanidinporphyren (SiO₂ = 55–69%). Alle Proben zeigen hohe Gehalte an inkompatiblen Elementen und zeigen beträchtliche Verarmung an high field strength Elementen relativ zu K, Rb, Sr, Ba und Th. Die CIF hat geochemische und petrographische Eigenschaften sowohl von Minetten wie von Lamproiten, aber im allgemeinen ähnelt sie am stärksten jungen mediterranen Lamproiten. Felsische Gesteine der CIF wurden durch Fraktionierung und Krustenkontamination aus mafischen ultrapotassischen Magmen gebildet. Letztere umfassen sowohl siliziumreiche Lamproite, die deutlich an Zr, U und Th angereichert sind und schwach potassische bis sodische Gesteine von trachytischer Zusammensetzung. Lavenergüsse und zufuhrgänge zeigent ein relativ homogenes _{Nd, 1840 Ma} (–6 bis –11) aber ein sehr variables _{Sr, 1840 Ma} (-40 bis + 100); Proben die als Lamproite klassifiziert wurden, zeigent höhere durchschnittliche _Sr-Werte. Proben von Gängen haben sehr variable Bleiisotopen-Zusammensetzungen, die von mäßig bis stark nichtradiogen variieren. Geochemische und Isotopendaten weisen auf Beiträge aus verarmtem archaischen lithosphärischen Mantel und aus konvektierendem OIB-Typ Mantel hin, die beide während des Alproterozoikums durch Subduktions-Vorgänge metasomatisiert wurden. Der lithosphärische Mantel enthielt wahrscheinlich auch angereicherte archaische Domänen. Proterozoische Anreicherungsvorgänge dürften seichtes Underplating subduzierter ozeanischer Lithosphäre unter der Churchill Provinz während der Amalgamation des laurentischen Superkontinentes begleitet haben. Es gibt starke Analogien in der Isotopenzusammensetzung und in der interpretierten Geschichte der Ursprungsregion, zwischen den CIF und Lamproiten und Minetten der Wyoming Provinz, und des westlichen Grönland. Diese weisen auf die Existenz einer laurentischen ultrapotassischen Superprovinz hin.

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With 7 Figures     

Phase differences between irradiance and velocity low degree solar acoustic modes revisited

Since 1984, simultaneous observations of irradiance and velocity solar acoustic modes, have been carried out by several authors in order to measure the phase difference between irradiance and velocity modes. Following the earliest observations with stratospheric balloon (Frolich and van Der Raay, 1984), a two ground-based stations (Tenerife and Baja California) were established (Jimenez et al, 1990) obtaining coherence results in the frequency range from 2.5 mHz to 4.3 mHz. These phase differences between irradiance and velocity solar acoustic modes are interpreted in terms of the non-adiabatic behaviour of the solar atmosphere. In 1988 the IPHIR (Frolich et al, 1988) instrument flown on the PHOBOS-2 mission to Mars and measured the solar irradiance during 150 consecutive days. The best velocity observations obtained in Tenerife for this period were compared with IPHIR data to compute the phase differences (Schrijver et al, 1991). The final conclusion is that good agreement is attained between space quadsi-space and ground observations which yield a phase diffenrece of about -125 degrees in the frequency range 2.5 mHz to 4.2 mHz, with a slight increase suggested by the data running up to 4.6 mHz.     

Chemical abundance behavior of type I planetary nebulae

In this work 13 Planetary Nebulae have been classified as Type I according to Peimbert's criteria (Peimbert, 1978). These objects have been added to a previous sample (Maciel and Faúndez-Abans, 1985) and diagrams of O/H versus N/H, S/H, Ne/H and Ar/H, as well as N/H versus S/H, Ne/H and Ar/H have been drawn. All of them exhibit a tendency for linear correlation; moreover, the behavior of O and N versus Ar and S are very similar, with approximately the same slope. When the excitation class parameter was included in the diagrams, no clear tendency can be discerned, for any class.     

Periodic orbits of an electric charge in a magnetic dipole field

Periodic orbits in the Stormer problem are studied using the symmetry lines of the Poincaré map introduced by De Vogelaere. Many known facts are explained by mean of these lines. The dynamics of four special symmetry lines when the Stormer parameter ₁ changes is presented, and we obtain a clear global view of the structure of the simple periodic orbits and their bifurcations, including the asymmetrical ones. New asymmetrical multiple periodic orbits are obtained.     

The spectra and light curves of two gamma-ray bursts

During the last half of 1977 the UCSD/MIT Hard X-Ray and Low Energy Gamma-Ray Experiment of HEAO-1 observed two of the three gamma-ray bursts detected by at least three satellites. The first of these bursts (20 October, 1977) had a fluence of (3.1±0.5)×10^–5 erg cm^–2 integrated over the energy range 0.135–2.05 MeV and over its duration of 38.7 s, placing it among the largest bursts observed. The second (10 November, 1977) had a fluence of (2.1±0.8)×10^–5 erg cm^–2 integrated over the energy range 0.125–3 MeV and over its duration of 2.8 s. The light curves of both bursts exhibit time fluctuations down to the limiting time resolution of the detectors (0.1 s). The spectrum of the 20 October, 1977 burst can be fitted with a power law (index –1.93±0.16), which is harder than other reported gamma-ray burst spectral fits. This burst was detected up to 2.05 MeV, and approximately half of its energy was emitted at photon energies above 0.5 MeV. The spectrum of the 10 November, 1977 burst is softer (index –2.4±0.7) and is similar to the spectrum of the 27 April, 1972 burst.Paper presented at the Symposium on Cosmic Gamma-Ray Bursts held at Toulouse, France, 26–29 November, 1979.     

Study of geothermal water intrusion due to groundwater exploitation in the Puebla Valley aquifer system, Mexico

Significant intrusion of geothermal water into fresh groundwater takes place in the Puebla Valley aquifer system, Mexico. The decline in the potentiometric surface due to the overexploitation of the groundwater induces this intrusion. This hydrological system comprises three aquifers located in Plio-Quaternary volcanic sediments and Mesozoic calcareous rocks. The hydraulic balance of the aquifer shows that the annual output exceeds the natural inputs by 12 million m³. Between 1973 and 2002, a drop in the potentiometric surface, with an 80 m cone of depression, was identified in a 5-km-wide area located southwest of the city of Puebla. Chemical analyses performed on water samples since 1990 have shown an increase in total dissolved solids (TDS) of more than 500 mg/L, coinciding with the region showing a cone of depression in the potentiometric surface. A three-dimensional flow and transport model, based on the hydrogeological and geophysical studies, was computed by using the MODFLOW and MT3D software. This model reproduces the evolution of the aquifer system during the last 30 years and predicts for 2010 an additional drawdown in the potentiometric surface of 15 m, and an increase in the geothermal water intrusion.