Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

Heat transfer in a MHD flow between eccentric disks rotating at different speeds

Heat transfer in a MHD flow between two infinite eccentric disks rotating with different speeds is considered when the plates are maintained at different temperatures. The results for the corresponding nonmagnetic case presented wrongly by Banerjee and Borkakati [7] are corrected. It is observed that the eccentric rotation reduces the heat transfer on the disks.

Elastic analysis of pin joints in plates under some combined pin and plate loads

Joints are primary sources of weakness in structures. Pin joints are very common and are used where periodic disassembly of components is needed. A circular pin in a circular hole in an infinitely large plate is an abstraction of such a pin joint. A two-dimensional plane-stress analysis of such a configuration is carried out, here, subjected to pin-bearing and/or biaxial-plate loading. The pin is assumed to be rigid compared to the plate material. For pin load the reactive stresses at the edges of the infinite plate tend to zero though their integral over the external boundary equals to the pin load. The pin-hole interface is unbonded and so beyond some load levels the plate separates from the pin and the extent of separation is a non-linear function of load level. The problem is solved by inverse technique where the extent of contact is specified and the causative loads are evaluated directly. In the situations where combined load is acting the separation-contact zone specification generally needs two parameters (angles) to be specified. The present report deals with analysing such a situation in metallic (or isotropic) plates. Numerical results are provided for parametric representation and the methodology is demonstrated.

Thermal Overstability Of Hydromagnetic Surface-Waves

We investigate the effects of radiative heat losses and thermal conductivity on the hydromagnetic surface waves along a magnetic discontinuity in a plasma of infinite electrical conductivity. We show that the effects of radiative heat losses on such surface waves are appreciable only when values of the plasma pressure on the two sides of the discontinuity are substantially different. Overstability of a surface wave requires that the medium in which it gives larger first-order compression should satisfy the criterion of Field (1965). Possible applications of the study to magnetic discontinuities in solar corona are briefly discussed.

On the magnetohydrodynamic flow between eccentrically rotating disks

The steady flow of an incompressible, viscous, electrically conducting fluid between two parallel, infinite, insulated disks rotating with different angular velocities about two noncoincident axes has been investigated; under the application of a uniform magnetic field in the axial direction. The solutions for the symmetric and asymmetric velocities are presented. The interesting feature arising due to the magnetic field is that in the central region the flow attains a uniform rotation with mean angular velocity at all rotation speeds for sufficiently large Hartmann number. In this case the flow adjusts to the rotational velocities of the disks mainly in the boundary layers near the disks. The forces on the disks are found to increase due to the presence of the applied magnetic field.

Evolution of sex ratios in social hymenoptera: consequences of finite brood size

Evolutionarily stable sex ratios are determined for social hymenoptera under local mate competition (LMC) and when the brood size is finite. LMC is modelled by the parameter d. Of the reproductive progeny from a single foundress nest, a fraction d disperses (outbreeding), while (1-d) mate amongst themselves (sibmating). When the brood size is finite, d is taken to be the probability of an offspring dispersing, and similarly, r, the proportion of male offspring, the probability of a haploid egg being laid. Under the joint influence of these two stochastic processes, there is a nonzero probability that some females remain unmated in the nest. As a result, the optimal proportion of males (corresponding to the evolutionarily stable strategy, ESS) is higher than that obtained when the brood size is infinite. When the queen controls the sex ration, the ESS becomes more female biased under increased inbreeding (lower d), However, the ESS under worker control shows an unexpected pattern, including an increase in the proportion of males with increased inbreeding. This effect is traced to the complex interaction between inbreeding and local mate competition.

Reversible Water Intercalation Accompanied by Coordination and Color Changes in a Layered Metal-Organic Framework

A new two-dimensional 3d-4f mixed-metal mixed dicarboxylate (homocyclic and heterocyclic) of the formula [Gd2(H2O)2Ni(H2O)2(1,2-bdc)2(2,5-pydc)2] 3 8H2O (1; 1,2-H2bdc = 1,2-benzenedicarboxylic acid and 2,5-H2pydc = 2,5- pyridinedicarboxylic acid) has been prepared by employing the hydrothermal method. The structure has infinite onedimensional-Gd-O-Gd- chains formed by the edge-shared GdO9 polyhedral units, resulting exclusively from the connectivity between the Gd3+ ions and the 1,2-bdc units. The chains are connected by the [Ni(H2O)2(2,5-pydc)2]2- metalloligand, forming the two-dimensional layer arrangements. The stacking of the layers creates hydrophilic and hydrophobic spaces in the interlamellar region. A one-dimensional water ladder structure, formed by the extraframework water molecules, occupies the hydrophilic region while the benzene ring of 1,2-bdc occupies the hydrophobic region. To the best of our knowledge, the present compound represents the first example of a 3d-4f mixed-metal carboxylate in which two different aromatic dicarboxylate anions act as the linkers. The stabilization energies of the water clusters have been evaluated using density functional theory calculations. The water molecules in 1 are fully reversible accompanied by a change in color (greenish blue to brown) and coordination around Ni2+ ions (octahedral to distorted tetrahedral).

Alfven surface waves along cylindrical plasma columns

The properties of Alfven surface waves along a cylindrical plasma column surrounded by vacuum or by another plasma medium are discussed. Both symmetric (m=0) and asymmetric (m=+or-1) modes are found to be dispersive in nature. The interfacial symmetric modes propagate in a certain frequency window ( omega A1, omega As), where omega As is the Alfven surface wave frequency along the interface of two semi-infinite media; when nu A1> nu A2 these modes propagate as backward waves and when nu A1< nu A2 as forward waves. The asymmetric modes change from backward to forward waves at a critical wave number kTr approximately=1.59/a when nu A1< nu A2 or vice versa when nu A1> nu A2.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

A Novel Approach for Designing Generator Excitation controllers Using the IDA-PBC Technique

This paper presents a novel approach for designing of generator excitation controllers using Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) technique for a Single Machine Infinite Bus (SMIB) system that can also be directly used in a multi-machine environment. The generator system equations are modified by referencing the rotor angle with respect to the secondary of the transformer bus instead of the infinite bus. For the modified system equations, IDA-PBC is applied to stabilize the system around an operating condition. The IDA-PBC design results in a Lyapunov function for the modified system. The new control law is practically feasible and can be applied directly to multi-machine system without referring to external system parameters. The effectiveness of the proposed controller is tested on a SMIB and a 10 generator 39 bus test system for a range of operating conditions. The Proposed excitation controller has shown good performance for both small and large disturbances when compared to the performance of a conventional static exciter with power system stabilizer.

An account of chronological developments in control of distributed parameter systems

Control systems arising in many engineering fields are often of distributed parameter type, which are modeled by partial differential equations. Decades of research have lead to a great deal of literature on distributed parameter systems scattered in a wide spectrum.Extensions of popular finite-dimensional techniques to infinite-dimensional systems as well as innovative infinite-dimensional specific control design approaches have been proposed. A comprehensive account of all the developments would probably require several volumes and is perhaps a very difficult task. In this paper, however, an attempt has been made to give a brief yet reasonably representative account of many of these developments in a chronological order. To make it accessible to a wide audience, mathematical descriptions have been completely avoided with the assumption that an interested reader can always find the mathematical details in the relevant references.

On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

A class of exact solutions for the flow of a micropolar fluid

The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

Flow between torsionally oscillating disks rotating about different axes at different speeds

The flow of an incompressible viscous fluid confined between two parallel infinite disks performing torsional oscillations with the same frequency, but rotating about different axes with different speeds has been studied. The solutions are presented for the symmetric and asymmetric first harmonic and steady streaming. The interesting features of the symmetric and asymmetric flow are discussed for the cases of small and large Womersley parameter at different ratios of the rotation speeds. The forces acting on one of the disks are also calculated.

Comparison of Elasticity, Shell Core, and Sandwich Shell Theories

The problem of an infinite circular sandwich shell subjected to an a\isymmetric radial line load is investigated using three-dimensional elasticity theory, shell core method, and sandwich shell theory due to Fulton and Schmidt. A comparison of the stresses and displacements with an exact elasticity solution is carried out for various shell parameters in order to clearly bring out the limitations of sandwich shell theories of Fulton and Schmidt as well as the shell core solution.