Influence of magnetic quantization on the effective electron mass in Kane-type semiconductors

Summary We study the effective electron mass at the Fermi level in Kane-type semiconductors on the basis of fourth order in effective mass theory and taking into account the interactions of the conduction electrons, heavy holes, light holes and split-off holes, respectively. The results obtained are then compared to those derived on the basis of the well-known three-band Kane model. It is found, takingn-Hg_1−x Cd _x Te as an example, that the effective electron mass at the Fermi level in accordance with fourth-order model depends on the Fermi energy, magnetic quantum number and the electron spin respectively due to the influence of band nonparabolicity only. The dependence of effective mass on electron spin is due to spin-orbit splitting parameter of the valence band in three-band Kane model and the Fermi energy due to band nonparabolicity in two-band Kane model. The same mass exhibits an oscillatory magnetic-field dependence for all the band models as expected since the origin of oscillations in the effective mass in nonparabolic compounds is the same as that of the Shubnikov-de Hass oscillations. In addition, the corresponding results for parabolic energy bands have been obtained from the generalized expressions under certain limiting conditions.     

An explicit analytical expression for bed-load layer thickness based on maximum entropy principle

The present study aims to derive an analytical model on bed-load layer thickness in an open channel turbulent flow carrying sediments. Determination of the thickness of the bed-load layer is of utmost importance in the study of bed-load transport as it is required to determine the bed-load transport rate, as well as in the study of suspended load transport as it acts as reference level for the particles in suspension. Apart from the several deterministic approaches available in the literature, the work adopts probabilistic approach based on entropy theory to determine the bed-load layer thickness. The concept of entropy theory developed by Shannon is used and the method of Lagrange multipliers is employed for the maximization of entropy function to find the least biased probability distribution. To calculate the Lagrange multipliers, present in the probabilistic model of dimensionless bed-load layer thickness, two different methodologies are presented. The model of bed-load layer thickness is a function of dimensionless shear stress and also depends on three other parameters which are found to be functions of specific gravity of sediment particle and dimensionless particle diameter from a non-linear regression analysis. The proposed model is validated with wide sets of experimental data available in literature and a good agreement is achieved. Apart from comparison with data, the model is also compared with existing deterministic model and computation of relative percentage error proves the better efficiency of the present model.     

Detection of maximum loadability limits and weak buses using Chaotic PSO considering security constraints

In the current research chaotic search is used with the optimization technique for solving non-linear complicated power system problems because Chaos can overcome the local optima problem of optimization technique. Power system problem, more specifically voltage stability, is one of the practical examples of non-linear, complex, convex problems. Smart grid, restructured energy system and socio-economic development fetch various uncertain events in power systems and the level of uncertainty increases to a great extent day by day. In this context, analysis of voltage stability is essential. The efficient method to assess the voltage stability is maximum loadability limit (MLL). MLL problem is formulated as a maximization problem considering practical security constraints (SCs). Detection of weak buses is also important for the analysis of power system stability. Both MLL and weak buses are identified by PSO methods and FACTS devices can be applied to the detected weak buses for the improvement of stability. Three particle swarm optimization (PSO) techniques namely General PSO (GPSO), Adaptive PSO (APSO) and Chaotic PSO (CPSO) are presented for the comparative study with obtaining MLL and weak buses under different SCs. In APSO method, PSO-parameters are made adaptive with the problem and chaos is incorporated in CPSO method to obtain reliable convergence and better performances. All three methods are applied on standard IEEE 14 bus, 30 bus, 57 bus and 118 bus test systems to show their comparative computing effectiveness and optimization efficiencies.     

More Efficient Palladium Catalyst for Hydrogenolysis of Benzyl Groups

Organic halides absorbed without solvent onto sodium phenylsulfinate on alumina (1) gave phenylsulfones (2) under microwave or ultrasound activation.     

Thermodynamic investigations of uranium-rich binary and ternary alloys

Uranium–zirconium, uranium niobium, and uranium–zirconium–niobium alloys were synthesized by the arc melting technique and their phase transition temperatures were determined using a high temperature calorimeter. Heat capacities of U–7 wt%Zr, U–7 wt%Nb, U–5 wt%Zr–2 wt%Nb, U–3.5 wt%Nb–3.5 wt%Zr, and U–2 wt%Zr–5 wt%Nb were measured using a differential scanning calorimeter in the temperature range 303–921 K. A set of self-consistent thermodynamic functions such as entropy, enthalpy, and Gibbs energy function data for these binary and ternary alloys were reported for the first time using heat capacity data obtained in this study and required literature data.     

Numerical solution of a system of coupled non-linear integro-differential equations of Fredholm type

A method, based on a generalization of Runge-Kutta's method, is applied to a system of coupled integro-differenital equations of Fredholm type. It is shown that, under certain conditions, the related integral, containing an unknown variable, in each integro-differential equation can be approximated by a contraction operator, converging in the respective space concerned. Therefore they may be found by the method of iteration, starting from arbitrary values, and hence the given system may be solved, with a high degree of accuracy.     

Structural diversity in manganese squarate frameworks using N,N-donor chelating/bridging ligands: syntheses, crystal structures and magnetic properties

Three new polymeric squarato-bridged manganese complexes {[Mn(H(2)O)(2)(bpe)(sq)].bpe.H(2)O}(n) (1), [Mn(2)(H(2)O)(4)(phen)(2)(sq)(2)](n) (2) and [Mn(2)(H(2)O)(2)(phen)(4)(sq)].(sq).8(H(2)O) (3) [bpe, 1,2-bis(4-pyridyl)ethane; phen, 1,10-phenanthroline; sq, squarate dianion] have been synthesized and characterized by single crystal X-ray diffraction analysis and variable temperature magnetic studies. Complex 1 is a 2D rectangular grid-like structure, achieved through flexible bpe bridging ligands and squarate dianions. On the other hand the use of chelating phen instead of bpe gives rise to a 1D polymeric chain in complex 2 and to a dinuclear entity in 3. In all the three complexes weak interactions play a vital role in stabilizing the solid-state structure. Variable temperature (2-300 K) magnetic studies indicate weak antiferromagnetic coupling between the metal centres in all the complexes.