Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

The complex variables boundary element method (CVBEM) is used to study interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The equation is solved using the CVBEM technique with circular and straight boundary elements and polynomial approximations (with square root asymptotics for crack tip elements) for the unknown functions. The algorithm is verified through comparison with known semi‐analytical and numerical solutions that involve interaction between a circular opening and specific systems of cracks or other openings. New numerical results concerning the interaction of the circular opening with the cracks and circular inclusions are presented. The method is applied to an important problem in the petroleum industry: modelling propagation of hydraulic fractures in the vicinity of a borehole. Copyright © 2000 John Wiley & Sons, Ltd.     

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.     

RESPONSES OF A GLOBAL CGCM TO CO2 INCREASE

The responses of the climate system to increase of atmospheric carbon dioxide(CO₂)arestudied by using a new version of the Bureau of Meteorological Research Centre(BMRC)globalcoupled general circulation model(CGCM).Two simulations are run:one with atmospheric CO₂concentration held constant at 330 ppm,the other with a tripling of atmospheric CO₂(990 ppm).Results from the 41-year control coupled integration are applied to analyze the mean state,seasonal cycle and interannual variability in the model.Comparisons between the greenhouseexperiment and the control experiment then provide estimations of the influence of increased CO₂on climate changes and climate variability.Especially discussed is the question on whether theclimate changes concerned with CO₂ inerease will impact interannual variability in tropical Pacific,such as ENSO.     

Relationship between the effective diffusion coefficient of soil radon and groundwater recharge in semi-arid areas

Herein, the relationship between soil radon behavior and groundwater recharge in the town of Hosha, a semi-arid area of Jordan is explored. The annual rainfall average in this area is between 60–100 mm year⁻¹. Soil radon concentration levels, using CR-39 detectors, have been measured at several depths. Nine sampling sites on a hill slope, in the summer and winter 2006 were chosen. Other soil parameters such as moisture, soil type and porosity were also measured. Correlation between the latter and the calculated effective diffusion coefficients, based on a linear approximation, was done in order to explore water movement. A weak correlation between the soil radon concentration and water recharge in this particular semi-arid area is observed. The results show that water recharge takes place vertically, i.e., water moves downward and in one of the nine sampling sites this movement seems to be more rapid compared to the other sites.     

Sources of the Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent

Based on generalization of available geochronological data, Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent are divided into three groups: 142–125, 124–115, and <110 Ma. The age of these associations decreases with approaching the Pacific margin of Asia. In the same direction, they show a change in sources of their parental melts: continental crust (142–125 Ma) → continental crust + PREMA (DM) (124–115 Ma) → continental crust + PREMA (DM) + EMII (<110 Ma). Isotope-geochemical (Sr-Nd) study indicates that intrusive and volcanic rocks of the Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent were originated in geodynamic settings that provided access of enriched mantle sources to magma formation. The most probable of these settings are as follows: (1) plate sliding accompanying by the formation of slab window beneath continental margin; (2) passage of the Asian margin over the East Asian mantle hot field in the Late Mesozoic; (3) asthenospheric upwelling due to delamination of the lower crust during closure of the Mongolian-Okhotsk ocean caused by collision between the Amurian microcontinent, Dzhugdzhur-Stanovoy, and Selenga-Stanovoy superterranes in the Central Asian fold belt.     

Agpaitic magmatism at Norra Kärr? RbSr isotopic evidence

RbSr isotopic analyses of 10'whole-rock samples from the controversial peralkaline Norra Kärr complex of southern Sweden suggest an age (1580±62 m.y.) considerably older than had previously been anticipated, and indicate an initial ⁸⁷Sr/⁸⁶Sr ratio of 0.7072±0.0035 (errors at 2σ). The isotopic data are consistent with a primary magmatic origin for the Norra Kärr agpaites, but data from 8 mineral separates show that they have experienced at least one period of metamorphic disturbance since the original intrusion; the last episode of isotopic readjustment must have occurred after 1250 m.y. before present, and is attributed to the Sveconorwegian (Grenville) metamorphism.     

Simultaneous solution for water,heat and salt balances in a Mediterranean coastal lagoon (Mar Menor,Spain)

A modelling approach is proposed to evaluate the environmental dynamics of coastal lagoons. The water, heat and salt balances are addressed simultaneously, providing a better estimation of evaporation and water exchanges. Compared to traditional approaches, the model presented accounts for the effects of water salinity, heat storage and net energy advected in the water body. The model was applied daily to the Mar Menor coastal lagoon (SE Spain) from 2003 through 2006. Water exchanges with the Mediterranean Sea were estimated based on the monthly trend of the lagoon salinity and were correlated with monthly averages of wind speed. The mean daily water exchange with the sea was 1.77 hm³ d⁻¹. This exchange accounted for only 1% of the heat losses in the lagoon heat balance, and it is the most important flow in the water balance. The mean annual evaporation flux amounted to 101.3 W m⁻² (3.55 mm d⁻¹), while the sensible heat flux amounted to 19.7 W m⁻², leading to an annual Bowen ratio on the order of 0.19. To validate the model, daily water temperatures were predicted based on the daily heat balance of the water body and were compared with remote sensing data from water surface standard products.