Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids

Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study — for static and dynamical situations — the equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes are compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material with a Drucker-Prager yield criterion. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. We first collapse our dynamical approach to its statical limit to derive regions in spin-shape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the Drucker-Prager failure law is available [Sharma, I., Jenkins, J.T., Burns, J.A., 2005a. Bull. Am. Astron. Soc. 37, 643; Sharma, I., Jenkins, J.T., Burns, J.A., 2005b. Equilibrium shapes of ellipsoidal soil asteroids. In: García-Rojo, R., Hermann, H.J., McNamara, S. (Eds.), Proceedings of the 5th International Conference on Micromechanics of Granular Media, vol. 1. A.A. Balkema, UK; Holsapple, K.A., 2007. Icarus 187, 500-509]. Here, we obtain the equilibrium landscapes for general triaxial ellipsoids, as well as provide the requisite governing formulae. In addition, we demonstrate that it may be possible to better interpret the results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361] within the context of a Drucker-Prager material. The graphical result for prolate ellipsoids in the static limit is the same as those of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] because, when worked out, his final equations will match ours. This is because, though the formalisms to reach these expressions differ, in statics, at the lowest level of approximation, volume-averaging and the approach of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] coincide. We note that the approach applied here was obtained independently [Sharma, I., Jenkins, J.T., Burns, J.A., 2003. Bull. Am. Astron. Soc. 35, 1034; Sharma, I., 2004. Rotational Dynamics of Deformable Ellipsoids with Applications to Asteroids. Ph.D. thesis, Cornell University] and it provides a general, though approximate, framework that is amenable to systematic improvements and is flexible enough to incorporate the dynamical effects of a changing shape, different rheologies and complex rotational histories. To demonstrate our technique, we investigate the non-equilibrium dynamics of rigid-plastic, spinning, prolate asteroids to examine the simultaneous histories of shape and spin rate for rubble piles. We have succeeded in recovering most results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361], who obtained equilibrium shapes by studying numerically the passage into equilibrium of aggregates containing discrete, interacting, frictionless, spherical particles. Our mainly analytical approach aids in understanding and quantifying previous numerical simulations.     

High-Resolution Quasi-3D Electric Resistivity Tomography for Deciphering Groundwater Potential Zones in Lateritic Terrain

Natural Resources Research - Groundwater is under constant threat of exploitation with increasing demands. Therefore, there is a need for more advanced methods for exploring potential groundwater...     

Luminescence chronology of incision and channel pattern changes in the River Ganga, India

The River Ganga in the central Gangetic plain shows the incision of 20 m of Late Quaternary sediments that form a vast upland terrace (T₂). The incised Ganga River Valley shows two terraces, namely the river valley (terrace-T₁) and the present-day flood plain (terrace-T₀). Terrace-T₁ shows the presence of meander scars, oxbow lakes, scroll plains, which suggests that a meandering river system prevailed in the past. The present-day river channel flows on terrace-T₀ and is braided, sensu stricto. It is thus inferred that the River Ganga experienced at least two phases of tectonic adjustments: (1) incision and (2) channel metamorphosis from meandering to braided.Optical dating of samples from three different terraces has bracketed the phase of incision to be <6 and 4 ka. Different ages of the top of terrace-T₂ show that this surface experienced differential erosion due to tectonic upwarping in the region, which also caused the river incision. River metamorphosis occurred some time during 4 and 0.5 ka.     

Finite element analysis of reinforced embankment foundation

A finite element analysis of a reinforced embankment-foundation system has been conducted using a coupled formulation and elastoplasticity theory. Such important factors as type of reinforcement, the type of clay, depth of foundation and drainage condition affecting the system have been systematically investigated using appropriate constitutive models to depict various components of the system and material parameters of two typical soft clay deposits found in India. The displacements, reinforcement force and maximum heights of the embankments are among the aspects presented and discussed. It is shown that the effectiveness of the reinforcement is dependent on its stiffness and the shear strength of the clay deposit. The foundation depth has significant effect on the nature and magnitude of displacement, the reinforcement force and the height of embankment. Drainage conditions are shown to markedly influence the effectiveness of reinforcement. Copyright © 1999 John Wiley & Sons, Ltd.     

Environment and Deep-Sea Mining: A Perspective

Abstract

As the quest for deep-sea mineral resources is gaining momentum, environment and ocean mining have become important aspects of study. Because many of these deposits occur in international waters, the concern for environmental conservation in view of the effects of deep-sea mining is resulting in these effects being studied in different oceans, and efforts to develop regulations governing this exploitation are also underway at national and international levels. The impact assessment of deep-sea mining needs to encompass a variety of subjects, including environmental, socioeconomic, technological, and legal aspects. At the same time, effects of in situ environmental conditions on mining activities also need to be considered for effecient performance by the mining system. Differences in the degree of impact have been noticed during the mining simulation experiments by different investigating agencies. Therefore, interparameter comparisons, standardization of methods, and improvement in mining design are important considerations for proper utilization of resources, conservation of environment, and cost efficiency of the mining operations.     

Total solar eclipse of July 22, 2009: Its impact on the total electron content and ionospheric electron density in the Indian zone

The longest total solar eclipse during the 21st century occurred in South and East Asia on July 22, 2009. Ionospheric response to this rare total solar eclipse which was observed right from the time of sunrise in the Indian zone, has been studied in terms of the total electron content (TEC) obtained from three global positioning system (GPS) receivers located at Udaipur, Hyderabad and Bengaluru, and electron density obtained using space based GPS-Radio Occultation technique. The study reveals significant reductions in the electron density and TEC that persisted up to 2 h past the last contact even during early morning eclipse. These observations imply that during the early morning eclipse, the production and loss of ionization dominate over the plasma transport processes.     

Thermosolutal-convective instability of a composite plasma in a stellar atmosphere including the effects of finite larmor radius and Hall currents

Thermosolutal-convective instability of a composite plasma in a stellar atmosphere is considered to include the effects, separately, due to finite Larmor radius (FLR) and Hall currents in the presence of a uniform horizontal magnetic field. The sufficient conditions for the existence of monotonic instability are derived and are found to hold good both in the presence, separately, of FLR and Hall current effects.     

Evidence of decay of flux ratio of Fe to Fe-Ni line features with electron temperature in solar flares

We report observational evidence of the decay of the flux ratio of Fe to Fe-Ni line features as a function of plasma electron temperature in solar flares in comparison to that theoretically predicted by Phillips (2004). We present the study of spectral analysis of 14 flares observed by the Solar X-ray Spectrometer (SOXS) — Low Energy Detector (SLD) payload. The SLD payload employs the state-of-the-art solid state detectors, viz., Si PIN and Cadmium-Zinc-Telluride (CZT) devices. The sub-keV energy resolution of Si PIN detector allows us to study the Fe-line and Fe-Ni line features appearing at 6.7 and 8 keV, respectively, in greater detail. In order to best-fit the whole spectrum at one time in the desired energy range between 4 and 25 keV we considered Gaussian-line, the multi-thermal power-law and broken power-law functions. We found that the flux ratio of Fe to Fe-Ni line features decays with flare electron temperature by the asymptotic form of polynomial of inverse third order. The relative flux ratio is ∼30 at temperature 12 MK which drops to half, ∼15 at 20 MK, and at further higher temperatures it decreases smoothly reaching to ∼8 at ∼50 MK. The flux ratio, however, at a given flare plasma temperature, and its decrease with temperature is significantly lower than that predicted theoretically. We propose that the difference may be due to the consideration of higher densities of Fe and Fe-Ni lines in the theoretical model of Phillips (2004). We suggest revising the Fe and Fe-Ni line densities in the corona. The decay of flux ratio explains the variation of equivalent width and peak energy of these line features with temperature.     

Nonlinear model to study filamentation instability of circularly polarized dispersive Alfvén waves in solar wind plasmas

This paper examines the small-scale solar wind turbulence driven in view of the Alfvén waves subjected to ponderomotive nonlinearity. Filamentation instability is known to take place for the case of dispersive Alfvén wave (DAW) propagating parallel to the ambient magnetic field. The ponderomotive force associated with DAW is responsible for wave localization and these webs of filaments become more intense and irregular as one proceeds along the spatial domain. The ponderomotive force associated with pump changes with pump parameters giving rise to different evolution patterns. This paper studies in detail the nonlinear evolution of filamentation instability introduced by dispersive Alfven waves (DAWs) which becomes dispersive on account of the finite frequency of DAW i.e., pump frequency is comparable to the ion cyclotron frequency. We have explicitly obtained the perturbation dynamics and then examined the impact of pump magnitude on the driven magnetic turbulence using numerical simulation. The results show steepening at small scales with increasing pump amplitude. The compressibility associated with acoustic fluctuations may explain the variation in spectral scaling of solar wind turbulence as observed by Alexandrova et al. (Astrophys. J. 674:1157, 2008).