Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Analysis of Paschen Curves for air, N2 and SF6 Using the Townsend Breakdown Equation

It has been shown that it is possible to extend the validity of the Townsend breakdown criterion for evaluating the breakdown voltages in the complete pd range in which Paschen curves are available. Evaluation of the breakdown voltages for air (pd=0.0133 to 1400 kPa · cm), N2(pd=0.0313 to 1400 kPa · cm) and SF6 (pd=0.3000 to 1200 kPa · cm) has been done and in most cases the computed values are accurate to ±3% of the measured values. The computations show that it is also possible to estimate the secondary ionization coefficient ¿ in the pd ranges mentioned above.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Evaluation Of Diffusion-Coefficient And Ionic Mobility In (Nh4)4fe(Cn)6.1.5 H2o

The diffusion coefficient, D, and the ionic mobility, μ, in the protonic conductor ammonium ferrocyanide hydrate have been determined by the isothermal transient ionic current method. D is also determined from the time dependence of the build up of potential across the samples and theretical expressions describing this build up in terms of double exponential dependence on time are obtained. The values obtained are D=3.875×10−11m2s−1 and μ=1.65×10−9 m2V−1s−1.

Diffusion Parameters in the Nb-Mo System: Revisited

The variation of the interdiffusion coefficient with the change in composition in the Nb-Mo system is determined in the temperature range of 1800 °C to 1900 °C. It was found that the activation energy has a minimum at around 45 at. pct Nb. The values of the pre-exponential factor and the activation energy for diffusion are compared with the data available in the literature. Further, the impurity diffusion coefficients of Nb in Mo and Mo in Nb are calculated.

Swarm intelligence-based solver for parameter estimation of laboratory through-diffusion transport of contaminants

Theoretical approaches are of fundamental importance to predict the potential impact of waste disposal facilities on ground water contamination. Appropriate design parameters are generally estimated be fitting theoretical models to data gathered from field monitoring or laboratory experiments. Transient through-diffusion tests are generally conducted in the laboratory to estimate the mass transport parameters of the proposed barrier material. Thes parameters are usually estimated either by approximate eye-fitting calibration or by combining the solution of the direct problem with any available gradient-based techniques. In this work, an automated, gradient-free solver is developed to estimate the mass transport parameters of a transient through-diffusion model. The proposed inverse model uses a particle swarm optimization (PSO) algorithm that is based on the social behavior of animals searching for food sources. The finite difference numerical solution of the forward model is integrated with the PSO algorithm to solve the inverse problem of parameter estimation. The working principle of the new solver is demonstrated and mass transport parameters are estimated from laboratory through-diffusion experimental data. An inverse model based on the standard gradient-based technique is formulated to compare with the proposed solver. A detailed comparative study is carried out between conventional methods and the proposed solver. The present automated technique is found to be very efficient and robust. The mass transport parameters are obtained with great precision.

Convenient construction of tetrahedral finite elements for the quasi-harmonic equation

It is shown that in the finite-element formulation of the general quasi-harmonic equation using tetrahedral elements, for every member of the element family there exists just one numerical universal matrix indpendent of the size, shape and material properties of the element. Thus the element matrix is conveniently constructed by manipulating this single matrix along with a set of reverse sequence codes at the same time accounting for the size, shape and material properties in a simple manner.

An Analysis of a Boundary Layer Diffusion Flame Over a Porous Flat Plate in a Confined Flow

A numerical analysis of the gas dynamic structure of a two-dimensional laminar boundary layer diffusion flame over a porous flat plate in a confined flow is made on the basis of the familiar boundary layer and flame sheet approximations neglecting buoyancy effects. The governing equations of aerothermochemistry with the appropriate boundary conditions are solved using the Patankar-Spalding method. The analysis predicts the flame shape, profiles of temperature, concentrations of variousspecies, and the density of the mixture across the boundary layer. In addition, it also predicts the pressure gradient in the flow direction arising from the confinement ofthe flow and the consequent velocity overshoot near the flame surface. The results of thecomputation performed for an n-pentane-air system are compared with experimental data andthe agreement is found to be satisfactory.

Electrochemical phase formation (ECPF) and macrogrowth Part II. Two-rate models

A general theory is evolved for a class of macrogrowth models which possess two independent growth-rates. Relations connecting growth-rates to growth geometry are established and some new growth forms are shown to result for models with passivation or diffusion-controlled rates. The corresponding potentiostatic responses, their small and large time behaviours and peak characteristics are obtained. Numerical transients are also presented. An empirical equation is derived as a special case and an earlier equation is corrected. An interesting stochastic result pertaining to nucleation events in the successive layers is proved.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

nvestigations on the Stability and Extinction of a Laminar Diffusion Flame Over a Porous Flat Plate

The limits of stability and extinction of a laminar diffusion flame have been experimentally studied in a two-dimensional laminar boundary layer over a porous flat plate through which n-pentane vapour was uniformly injected. The stability and extinction boundaries are mapped on a plot of free stream oxidant velocity versus fuel injection velocity. Effects of free stream temperature and of dilution of fuel and oxidant on these boundaries have been examined. The results show that there exists a limiting oxidant flux beyond which the diffusion flame cannot be sustained. This limiting oxidant flux has been found to depend_on the free stream oxygen concentration, fuel concentration and injection'velocity of the fuel.