Ultrahigh-temperature metamorphism from an unusual corundum plus orthopyroxene intergrowth bearing Al-Mg granulite from the Southern Marginal Zone, Limpopo Complex, South Africa

The Southern Marginal Zone of the Limpopo Complex is composed of granite-greenstone cratonic rocks reworked by a Neoarchean high-grade tectono-metamorphic event. Petrographic and mineral chemical characterization of an Al-Mg granulite from this zone is presented here. The granulite has a gneissic fabric with distinct Al-rich and Si-rich layers, with the former preserving the unusual lamellar (random and regular subparallel) intergrowths of corundum and symplectic intergrowth of spinel with orthopyroxene. The Al-rich layer preserves mineral assemblages such as rutile with orthopyroxene + sillimanite +/- A quartz, Al-rich orthopyroxene (similar to 11 wt%), spinel + quartz, and corundum in possible equilibrium with quartz, while the Si-rich layer preserves antiperthites and orthopyroxene + sillimanite +/- A quartz, all considered diagnostic of ultrahigh-temperature metamorphism. Application of Al-in-opx thermometry, ternary feldspar thermometry and construction of suitable pressure-temperature phase diagrams, compositional and model proportion isopleth results indicate P-T conditions as high as similar to 1,050-1,100 A degrees C, and similar to 10-12 kbars for the Al-Mg granulite. Our report of ultrahigh-temperature conditions is significant considering that the very high temperature was reached during decompression of an otherwise high-pressure granulite complex (clockwise P-T path), whereas most other ultrahigh-temperature granulites are linked to magma underplating at the base of the crust (counterclockwise P-T path).

Application of scaled particle theory to alkyl-aryl surfactants: a two zone model of micellar core

Scaled Particle Theory (SPT) has been applied to predict the total free energies of micellization of ionic as well as nonionic micellar systems containing an aryl ring. A modification of the previously developed model has been made, proposing a two-zone model of micellar core which corroborates with the structural information available for such systems. The results are in good agreement with experimental data and also confirm the dictating role of cavity forming free energies for such systems

An elementary introduction to solar dynamo theory

The cyclically varying magnetic field of the Sun is believed to be produced by the hydromagnetic dynamo process. We first summarize the relevant observational data pertaining to sunspots and solar cycle. Then we review the basic principles of MHD needed to develop the dynamo theory. This is followed by a discussion how bipolar sunspots form due to magnetic buoyancy of flux tubes formed at the base of the solar convection zone. Following this, we come to the heart of dynamo theory. After summarizing the basic ideas of a turbulent dynamo and the basic principles of its mean field formulation, we present the famous dynamo wave solution, which was supposed to provide a model for the solar cycle. Finally we point out how a flux transport dynamo can circumvent some of the difficulties associated with the older dynamo models.

A nonlinear theory of wake development

A simple new series, using an expansion of the velocity profile in parabolic cylinder functions, has been developed to describe the nonlinear evolution of a steady, laminar, incompressible wake from a given arbitrary initial profile. The first term in this series is itself found to provide a very satisfactory prediction of the decay of the maximum velocity defect in the wake behind a flat plate or aft of the recirculation zone behind a symmetric blunt body. A detailed analysis, including higher order terms, has been made of the flat plate wake with a Blasius profile at the trailing edge. The same method yields, as a special case, complete results for the development of linearized wakes with arbitrary initial profile under the influence of arbitrary pressure gradients. Finally, for purposes of comparison, a simple approximate solution is obtained using momentum integral methods, and found to predict satisfactorily the decay of the maximum velocity defect. © 1970 Wolters-Noordhoff Publishing.

Simplified theory of carrier back-scattering in semiconducting carbon nanotubes: A Kane's model approach

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane's nonparabolic energy subband model.The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi's golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 mu m long nanotube at 105 V m(-1) has been exhibited. The analytical results are in good agreement with the available experimental data. (c) 2010 American Institute of Physics.

Theory of the non-Fermi-liquid transition point in the two-impurity Kondo model

We present an explicit solution of the problem of two coupled spin-1/2 impurities, interacting with a band of conduction electrons. We obtain an exact effective bosonized Hamiltonian, which is then treated by two different methods (low-energy theory and mean-field approach). Scale invariance is explicitly shown at the quantum critical point. The staggered susceptibility behaves like ln(T(K)/T) at low T, whereas the magnetic susceptibility and [S1.S2] are well behaved at the transition. The divergence of C(T)/T when approaching the transition point is also studied. The non-Fermi-liquid (actually marginal-Fermi-liquid) critical point is shown to arise because of the existence of anomalous correlations, which lead to degeneracies between bosonic and fermionic states of the system. The methods developed in this paper are of interest for studying more physically relevant models, for instance, for high-T(c) cuprates.

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.

Molecular theory for the effects of specific solute-solvent interaction on the diffusion of a solute particle in a molecular liquid

An understanding of the effect of specific solute-solvent interactions on the diffusion of a solute probe is a long standing problem of physical chemistry. In this paper a microscopic treatment of this effect is presented. The theory takes into account the modification of the solvent structure around the solute due to this specific interaction between them. It is found that for strong, attractive interaction, there is an enhanced coupling between the solute and the solvent dynamic modes (in particular, the density mode), which leads to a significant increase in the friction on the solute. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of the attractive interaction. An interesting observation is that specific solute-solvent interaction can induce a crossover from a sliplike to a sticklike diffusion. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. On the other hand, for repulsive interaction, the diffusion coefficient of the solute increases. These results are in qualitative agreement with recent experimental observations.

Ultrafast Solvation Dynamics of an Ion in the gamma-Cyclodextrin Cavity: The Role of Restricted Environment

A detailed study of the solvation dynamics of a charged coumarin dye molecule in gamma-cyclodextrin/water has been carried out by using two different theoretical approaches. The first approach is based on a multishell continuum model (MSCM). This model predicts the time scales of the dynamics rather well, provided an accurate description of the frequency-dependent dielectric function is supplied. The reason for this rather surprising agreement is 2-fold. First, there is a cancellation of errors, second, the two-zone model mimics the heterogeneous microenvironment surrounding the ion rather well. The second approach is based on the molecular hydrodynamics theory (MI-IT). In this molecular approach, the solvation dynamics has been studied by restricting the translational motion of the solvent molecules enclosed within the cavity. The results from the molecular theory are also in good agreement with the experimental results. Our study indicates that, in the present case, the restricted environment affects only the long time decay of the solvation time correlation function. The short time dynamics is still governed by the librational (and/or vibrational) modes present in bulk water.

Effects of the filling process on the evolution of the mushy zone and macrosegregation in alloy casting

A numerical model of the entire casting process starting from the mould filling stage to complete solidification is presented. The model takes into consideration any phase change taking place during the filling process. A volume of fluid method is used for tracking the metal–air interface during filling and an enthalpy based macro-scale solidification model is used for the phase change process. The model is demonstrated for the case of filling and solidification of Pb–15 wt%Sn alloy in a side-cooled two-dimensional rectangular cavity, and the resulting evolution of a mushy region and macrosegregation are studied. The effects of process parameters related to filling, namely degree of melt superheat and filling velocity on macrosegregation in the cavity, are also investigated. Results show significant differences in the progress of the mushy zone and macrosegregation pattern between this analysis and conventional analysis without the filling effect.

An eigenproblem approach to classical screw theory

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.

Biomethanation of herbaceous biomass residues using 3-zone plug flow like digesters - A case study from India

Biomethanation of herbaceous biomass feedstock has the potential to provide clean energy source for cooking and other activities in areas where such biomass availability predominates. A biomethanation concept that involves fermentation of biomass residues in three steps, occurring in three zones of the fermentor is described. This approach while attempting take advantage of multistage reactors simplifies the reactor operation and obviates the need for a high degree of process control or complex reactor design. Typical herbaceous biomass decompose with a rapid VFA flux initially (with a tendency to float) followed by a slower decomposition showing balanced process of VFA generation and its utilization by methanogens that colonize biomass slowly. The tendency to float at the initial stages is suppressed by allowing previous days feed to hold it below digester liquid which permits VFA to disperse into the digester liquid without causing process inhibition. This approach has been used to build and operate simple biomass digesters to provide cooking gas in rural areas with weed and agro-residues. With appropriate modifications, the same concept has been used for digesting municipal solid wastes in small towns where large fermentors are not viable. With further modifications this concept has been used for solid-liquid feed fermentors. Methanogen colonized leaf biomass has been used as biofilm support to treat coffee processing wastewater as well as crop litter alternately in a year. During summer it functions as a biomass based biogas plants operating in the three-zone mode while in winter, feeding biomass is suspended and high strength coffee processing wastewater is let into the fermentor achieving over 90% BOD reduction. The early field experience of these fermentors is presented.

Simplified dispersion curves for circular cylindrical shells using shallow shell theory.

An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.

New Look at Kirchhoff's Theory of Plates

KIRCHHOFF’S theory [1] and the first-order shear deformation theory (FSDT) [2] of plates in bending are simple theories and continuously used to obtain design information. Within the classical small deformation theory of elasticity, the problem consists of determining three displacements, u, v, and w, that satisfy three equilibrium equations in the interior of the plate and three specified surface conditions. FSDT is a sixth-order theory with a provision to satisfy three edge conditions and maintains, unlike in Kirchhoff’s theory, independent linear thicknesswise distribution of tangential displacement even if the lateral deflection, w, is zero along a supported edge. However, each of the in-plane distributions of the transverse shear stresses that are of a lower order is expressed as a sum of higher-order displacement terms. Kirchhoff’s assumption of zero transverse shear strains is, however, not a limitation of the theory as a first approximation to the exact 3-D solution.