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.

Instabilities and Waves in Thin Films of Living Fluids

We formulate the thin-film hydrodynamics of a suspension of polar self-driven particles and show that it is prone to several instabilities through the interplay of activity, polarity, and the existence of a free surface. Our approach extends, to self-propelling systems, the work of Ben Amar and Cummings [Phys. Fluids 13 1160 (2001)] on thin-film nematics. Based on our estimates the instabilities should be seen in bacterial suspensions and the lamellipodium, and are potentially relevant to the morphology of biofilms. We suggest several experimental tests of our theory.

Magnetic superconductors: Model theories and experimental properties of rare-earth compounds

Superconducting and magnetically long-range ordered states were believed to be mutually exclusive phenomena. The discovery of rare-earth compounds in recent years, which exhibit both superconductivity and magnetic ordering (ferromagnetic, antiferromagnetic or sinusoidal), has led to considerable theoretical and experimental work on such systems. In the present article, we give a review of various theoretical models and important experimental results. In the theoretical sections, we start with the Abrikosov-Gorkov pair breaking theory for dilute alloys and discuss its improvement in the work of Müller-Hartmann and Zittartz. Then, in the context of magnetic superconductors, various microscopic theories that have been advanced are presented. These predict re-entrant behaviour in some systems (ferromagnetic superconductors) and coexistence regions in others (particularly antiferromagnetic superconductors). Following this, phenomenological generalized Ginzburg-Landau theories for two kinds of orders (superconducting and magnetic) are presented. A section dealing with renormalization group analysis of phase diagrams in magnetic superconductors is given. In experimental sections, the properties of each rare-earth compounds (ternary as well as some tetranery) are reviewed. These involve susceptibility, heat capacity, resistivity, upper critical field, neutron scattering and magnetic resonance measurements. The anomalous behaviour of the upper critical field of antiferromagnetic superconductors near the Néel temperature is discussed both in theory sections and experimental section for various systems.

Critical-point Properties of Liquids and the Born-Green Theory

Recent work of Jones et al. giving the long-range behaviour of the pair correlation function is used to confirm that the critical ratio Pc/nckBTc = 1/2 in the Born-Green theory. This deviates from experimental results on simple insulating liquids by more than the predictions of the van der Waals equation of state. A brief discussion of conditions for thermodynamic consistency, which the Born-Green theory violates, is then given. Finally, the approach of the Ornstein-Zernike correlation function to its critical point behaviour is discussed within the Born-Green theory.

Assessment of accuracies of some approximate solutions

The classic work of Richardson and Gaunt [1 ], has provided an effective means of extrapolating the limiting result in an approximate analysis. From the authors' work on "Bounds for eigenvalues" [2-4] an interesting alternate method has emerged for assessing monotonically convergent approximate solutions by generating close bounds. Whereas further investigation is needed to put this work on sound theoretical foundation, we intend this letter to announce a possibility, which was confirmed by an exhaustive set of examples.

Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

On an asymptotic method of Krylov-Bogoliubov for overdamped nonlinear systems

A general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems. A second-order system with both roots real is treated first and the method is then extended to higher-order systems. Two illustrative examples show good agreement with results obtained by numerical integration.

Oxidation of vitamin A1 and vitamin A2 aldehydes to the corresponding acids by enzymes from pig and rat livers

VITAMIN A is stored in rat liver largely as its ester with small amounts of the alcohol, but is transported in the normal circulating blood in the latter form1. Although it was generally believed that the alcohol form is the more physiological state of the vitamin, since the work of Dowling and Wald2, it is being recognized that vitamin A acid and not the alcohol may be nearer to the 'active vitamin A'. If this were to be so, it would be important to demonstrate that a mechanism exists in the rat for the production of vitamin A acid from vitamin A alcohol through the intermediate, the aldehyde. Regarding the formation of the aldehyde, it has been well established that the alcohol dehydrogenase can bring about the conversion of vitamin A alcohol to retinene3. The presence of an enzyme in rat and pig liver catalysing the oxidation of retinene1 and retinene2 to the corresponding acids has been demonstrated in the present work and the partially purified enzyme preparation shown to be completely devoid of alcohol dehydrogenase activity.

Critical behavior of the aqueous electrolytic system 3-methylpyridine+D2O+NaBr

The system 3-methylpyridine(3MP)+water(H2O)+NaBr has been the subject of an intense scientific debate since the work of Jacob [Phys. Rev. E. 58, 2188 (1988)] and Anisimov [Phys. Rev. Lett. 85, 2336 (2000)]. The crossover critical behavior of this system seemed to show remarkable sensitivity to the weight fraction (X) of the ionic impurity NaBr. In the range X <= 0.10 the system displayed Ising behavior and a pronounced crossover to mean-field behavior in the range 0.10 <= X <= 0.16. A complete mean-field behavior was observed at X=0.17, a result that was later attributed to the existence of long-living nonequilibrium states in this system [Kostko , Phys. Rev. E. 70, 026118 (2004)]. In this paper, we report the near-critical behavior of osmotic susceptibility in the isotopically related ternary system, 3MP+heavy water(D2O)+NaBr. Detailed light-scattering experiments performed at exactly the same NaBr concentrations as investigated by Jacob reveal that the system 3MP+D2O+NaBr shows a simple Ising-type critical behavior with gamma similar or equal to 1.24 and nu similar or equal to 0.63 over the entire NaBr concentration range 0 <= X <= 0.1900. The crossover behavior is predominantly nonmonotonic and is completed well outside the critical domain. An analysis in terms of the effective susceptibility exponent (gamma(eff)) reveals that the crossover behavior is nonmonotonic for 0 <= X <= 0.1793 and tends to become monotonic for X > 0.1793. The correlation length amplitude xi(o), has a value of similar or equal to 2 A for 0.0250 <= X <= 0.1900, whereas for X=0, xi(o)similar or equal to 3.179 A. Since isotopic H -> D substitution is not expected to change the critical behavior of the system, our results support the recent results obtained by Kostko [Phys. Rev. E. 70, 026118 (2004)] that 3MP+H2O+NaBr exhibits universal Ising-type critical behavior typical for other aqueous solutions.

Thermodynamics of Phosphorus and Sulphur Removal during Basic Oxygen Steelmaking

Removal of impurity elements from hot metal is essential in basic oxygen steelmaking. Oxidation of phosphorus from hot metal has been studied by several authors since the early days of steelmaking. Influence of different parameters on the distribution of phosphorus, seen during the recent work of the authors, differs somewhat from that reported earlier. On the other hand, removal of sulphur during steelmaking has drawn much less attention. This may be due to the magnitude of desulphurisation in oxygen steelmaking being relatively low and desulphurisation during hot metal pre-treatment or in the ladle furnace offering better commercial viability Further, it is normally accepted that sulphur is removed to steelmaking slag in the form of sulphide only However, recent investigations have indicated that a significant amount of sulphur removed during basic oxygen steelmaking can exist in the form of sulphate in the slag under oxidising conditions. The distribution of sulphur during steelmaking becomes more important in the event of carry-over of sulphur-rich blast-furnace slag, which increases sulphur load in the BOF. The chemical nature of sulphur in this slag undergoes a gradual transition from sulphide to sulphate as the oxidative refining progresses.

Gauge-invariant reformulation of theories with second-class constraints

Given a classical dynamical theory with second-class constraints, it is sometimes possible to construct another theory with first-class constraints, i.e., a gauge-invariant one, which is physically equivalent to the first theory. We identify some conditions under which this may be done, explaining the general principles and working out several examples. Field theoretic applications include the chiral Schwinger model and the non-linear sigma model. An interesting connection with the work of Faddeev and Shatashvili is pointed out.

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T Wpropx lambda and surface injectionv Wpropx(lambda–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

Steady compressible flow of cohesionless granular materials through a wedge-shaped bunker

A continuum model based on the critical-state theory of soil mechanics is used to generate stress, density, and velocity profiles, and to compute discharge rates for the flow of granular material in a mass flow bunker. The bin–hopper transition region is idealized as a shock across which all the variables change discontinuously. Comparison with the work of Michalowski (1987) shows that his experimentally determined rupture layer lies between his prediction and that of the present theory. However, it resembles the former more closely. The conventional condition involving a traction-free surface at the hopper exit is abandoned in favour of an exit shock below which the material falls vertically with zero frictional stress. The basic equations, which are not classifiable under any of the standard types, require excessive computational time. This problem is alleviated by the introduction of the Mohr–Coulomb approximation (MCA). The stress, density, and velocity profiles obtained by integration of the MCA converge to asymptotic fields on moving down the hopper. Expressions for these fields are derived by a perturbation method. Computational difficulties are encountered for bunkers with wall angles θw [gt-or-equal, slanted] 15° these are overcome by altering the initial conditions. Predicted discharge rates lie significantly below the measured values of Nguyen et al. (1980), ranging from 38% at θw = 15° to 59% at θw = 32°. The poor prediction appears to be largely due to the exit condition used here. Paradoxically, incompressible discharge rates lie closer to the measured values. An approximate semi-analytical expression for the discharge rate is obtained, which predicts values within 9% of the exact (numerical) ones in the compressible case, and 11% in the incompressible case. The approximate analysis also suggests that inclusion of density variation decreases the discharge rate. This is borne out by the exact (numerical) results – for the parameter values investigated, the compressible discharge rate is about 10% lower than the incompressible value. A preliminary comparison of the predicted density profiles with the measurements of Fickie et al. (1989) shows that the material within the hopper dilates more strongly than predicted. Surprisingly, just below the exit slot, there is good agreement between theory and experiment.

Seismic Microzonation of Bangalore - Preliminary Maps

This paper presents an overview of the seismic microzonation and the grade/level based study along with methods used for estimating hazard. The principles of seismic microzonation along with some current practices are discussed. Summary of seismic microzonation experiments carried out in India is presented. A detailed work of seismic microzonation of Bangalore has been presented as a case study. In this case study, a seismotectonic map for microzonation area has been developed covering 350 km radius around Bangalore, India using seismicity and seismotectonic parameters of the region. For seismic microzonation Bangalore Mahanagar Palike (BMP) area of 220 km2 has been selected as the study area. Seismic hazard analysis has been carried out using deterministic as well as probabilistic approaches. Synthetic ground motion at 653 locations, recurrence relation and peak ground acceleration maps at rock level have been generated. A detailed site characterization has been carried out using borehole with standard penetration test (SPT) ―N‖ values and geophysical data. The base map and 3-dimensional sub surface borehole model has been generated for study area using geographical information system (GIS). Multichannel analysis of surface wave (MASW)method has been used to generate one-dimensional shear wave velocity profile at 58 locations and two- dimensional profile at 20 locations. These shear wave velocities are used to estimate equivalent shear wave velocity in the study area at every 5m intervals up to a depth of 30m. Because of wider variation in the rock depth, equivalent shear for the soil overburden thickness alone has been estimated and mapped using ArcGIS 9.2. Based on equivalent shear wave velocity of soil overburden thickness, the study area is classified as ―site class D‖. Site response study has been carried out using geotechnical properties and synthetic ground motions with program SHAKE2000.The soil in the study area is classified as soil with moderate amplification potential. Site response results obtained using standard penetration test (SPT) ―N‖ values and shear wave velocity are compared, it is found that the results based on shear wave velocity is lower than the results based on SPT ―N‖ values. Further, predominant frequency of soil column has been estimated based on ambient noise survey measurements using instruments of L4-3D short period sensors equipped with Reftek 24 bit digital acquisition systems. Predominant frequency obtained from site response study is compared with ambient noise survey. In general, predominant frequencies in the study area vary from 3Hz to 12Hz. Due to flat terrain in the study area, the induced effect of land slide possibility is considered to be remote. However, induced effect of liquefaction hazard has been estimated and mapped. Finally, by integrating the above hazard parameters two hazard index maps have been developed using Analytic Hierarchy Process (AHP) on GIS platform. One map is based on deterministic hazard analysis and other map is based on probabilistic hazard analysis. Finally, a general guideline is proposed by bringing out the advantages and disadvantages of different approaches.

Thermodynamics of oxygen in liquid copper-tin alloys

The activity coefficients of oxygen in copper-tin alloys at 1 1 00°C have been measured by two different equilibrium methodsthe cell Pt, Ni + NiO I ZrOz solid electrolyte I O[Cu + Sn], cermet. Pt and the equilibrium between Cu + Sn alloys and SnO + SiO, slags established via SnO vapour. The results from both types of measurement confirm the work of Block and co-workers and show that other data are in error. The deoxidation equilibria for Sn in liquid copper, with solid SnO, as deoxidation product, have been evaluated at temperatures of interest in copper smelting.