Cyclotron amplification of geomagnetic micropulsations Pc1 in the magnetosphere

A numerical analysis of cyclotron instabilities is carried out by computing the dispersion relation for a three component cold plasma-beam system. Rates of growth and damping for various values of the stream density are calculated from the dispersion relation. The rates of growth and damping increase monotonically as the number density of the proton stream increases. It is found that the frequencies at the rates of maximum growth and the damping decrease slightly to lower frequencies and a sharp peak at these frequencies becomes blunt. The minimum e-folding times of an ion cyclotron wave for (a) σ_s = 10⁻⁴, σ_i = 10⁻² and (b) σ_s = 10⁻¹, σ_i = 10⁻² are about 3·84 and 0·16 sec respectively in the vicinity of the equatorial plane at 6 Re, where σ_s and σ_i are the ratios of the beam density N_s and the helium ion (H₆⁺) density N_i to the total positive ions in the plasma-beam system.     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

Crystallization processes in an artificial magma: variations in crystal shape,growth rate and composition with melt cooling history

A large (4.8 m³, 1.3x10⁷ g) artificial mafic melt with a bulk composition similar to that of a basalt (but with a high CaO content of 17 wt%) was generated during a demonstration of in situ vitrification and was allowed to cool naturally. During the melting process, convection was vigorous, resulting in a chemically and thermally homogeneous melt body. Once heating was complete, the cooling rate was rapid with the temperature dropping from 1500°C to 500°C in 6 days within the interior of the 3 m diameter, 1.5 m thick body. A 20 h period of constant temperature (1140°C) observed during colling was the result of latent heat released by widespread crystallization. The final crystalline assemblage consists of diopsidic to hedenbergitic pyroxene and anorthitic feldspar, with a subordinate amount of potassic feldspar, plus a small amount of evolved glass. The compositions and proportions of phases agree well with those predicted by the MELTS thermodynamic model. Thermal and textural evidence suggest that convection within the melt ceased coincident with formation of the first crystals. Textural investigation of core samples reveals large (up to 1 cm in length) acicular diopsidic pyroxenes in a matrix of smaller feldspar and zoned pyroxene crystals (500 m in length). Crystal shape and pyroxene composition vary as a function of position within the solidified body, as a function of cooling rate. Both crystal size and degree of crystallinity are highest in the central, most slowly-cooled parts of the rock. Crystal shape is characterized by tabular, equilibrium-growth forms in the slowly-cooled areas, grading to highly skeletal, dendritic forms at the rapidly-cooled edges of the body. The pyroxene crystals are dominantly homogeneous diopside, but crystals are characterized by thin Fe-rich hedenbergitic rims. These rims were deposited when Mg in the melt was depleted by diopside growth, and melt temperature had cooled sufficiently to allow Fe-rich pyroxene growth. Crystal growth rates can be calculated based on thermal behavior of the melt, reinforced by thermodynamic modelling, and are determined to be between 10^-7 and 10^-8 cm/s in the central part of the melt. These estimates agree well with growth rates in natural systems with similar cooling rates. Pyroxene crystals that formed at a higher cooling rates are characterized by higher Al and lower Mg contents relative to tabular equilibrium crystalline forms, presumably as a result of disequilibrium melt compositions at the crystal-melt interface.New Mexico Bureau of Mines and Mineral Resources, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA     

Distribution and morphology of sinkholes triggered by flooding following Tropical Storm Alberto at Albany, Georgia, USA

Flooding of the Flint River in July 1994 triggered the collapse of at least 312 sinkholes in the karstic Dougherty Plain at Albany, Georgia. We examined the distribution and morphology of these new sinkholes to evaluate the mode of formation, to characterize early stages of the evolution of sinkhole form, and to estimate the lowering of the surface associated with the development of new sinkholes.Eighty-eight percent of sinkholes occur inside the limits of flooding, especially in areas of sandy overburden, and they often follow joint-controlled linear trends. Sinkhole dimensions are log-normally distributed with median values of circumference = 5.7 m, length = 1.8 m, width = 1.6 m, and depth = 0.7 m; asymmetry (L:W) = 1.2. Cross-sectional forms range from narrow cylinders to large bowls, with many sinkholes having undercut sides.Flooding triggered the formation of sinkholes by saturating and liquefying overburden, which caused soil arches to collapse and flow into cavities in bedrock. The prevalence of sinkholes near the periphery of flooding suggests that drainage and loss of buoyant support as flood waters subsided may also have contributed to failure. A volume ratio index is used to quantify the three dimensional geometric form of sinkholes. Initially, small cylindrical shafts open over a bedrock joint, followed by progressive slumping that leads to widening and increases in volume to a final bowl form. Estimates of the aggregate volume of overburden transported underground in flooded areas range from 7,990 to 11,130 m3. Averaged over flooded areas, this accounts for 0.26 to 0.37 mm/km² lowering of the surface. Based on a 500 year recurrence interval for the flood event, values for lowering of the surface range from 0.52 to 0.74 mm per 1,000 years. These values are an order of magnitude less than estimates of carbonate dissolution and suggest that transport of overburden underground is limited by triggering events.     

A furrow runs through it: An example of sustainable traditional irrigation in Western Cape Province,South Africa

Water and water related matters are important issues in water scarce countries like the Republic of South Africa. This is especially true for the agricultural sector that relies heavily on the availability of water for irrigation to ensure a secure food supply. In South Africa, present day irrigation projects rely on government subsidies and are usually large undertakings beyond the reach of individuals or small communities. The sustainability of such large irrigation projects is still a matter of debate. A 100 years ago a different set of rules applied. Irrigation could only be achieved by hand-dug furrows that supplied water in relatively small quantities to small farming communities. This paper investigated such a small community, the Leeukloof farming community in the Western Cape Province of the Republic of South Africa. For the past 93 years this community has maintained a furrow that supplies water not only to farms bordering the Perdeberg River, which supplies the furrow with water, but also to farms not bordering the river. The authors try to reconstruct the changes in agricultural practices brought about by the furrow, methods of water extraction during each phase, as well as the development and role of the furrow system. The perception by the community of the necessity of this method of water extraction from the river system is also investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace’s theorem revisited

Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg₂SiO₄). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate representation of thermodynamic properties and sound wave velocities of Mg₂SiO₄ in its complete pressure–temperature stability range. We also show that the accuracy of our results is not significantly affected by the use of a different equation of state.     

Computational parameter estimation for a maize crop

During a whole growing season, the evolution of the displacement height, d, and roughness length, z ₀, of a maize crop has been estimated by a measurement programme. The results have been used to check different types of existing models to calculate these parameters from canopy characteristics only; a simple geometric model and two matching models have been investigated. A geometric model is based on geometric features of the surface only. After a simple modification, the geometric model gives good results for the displacement height as well as for the roughness length.A matching model, based on gradient-diffusion theory, yields good results for the displacement height. The roughness parameter, however, is overestimated by 17%. By a simple modification, the model results could be improved considerably.A matching model, based on a second-order closure procedure, yields excellent results for the displacement height and good results for the roughness length. But it appears that, when applying this model, the plant density index and plant area density distribution as a function of height must be well known.     

The normal-force coefficient of a thin closed fence

In a full-scale field study, the drag coefficient of a thin closed fence was estimated. A measurement plate was constructed more or less in the center of the barrier in order to estimate the normal-force on the fence. The normal-force coefficient was studied under near-neutral stratification for various Reynolds numbers and different angles of attack.