The Alpha-Method Direct Transcription In Path Constrained Dynamic Optimization

Numerically discretized dynamic optimization problems having active inequality and equality path constraints that along with the dynamics induce locally high index differential algebraic equations often cause the optimizer to fail in convergence or to produce degraded control solutions. In many applications, regularization of the numerically discretized problem in direct transcription schemes by perturbing the high index path constraints helps the optimizer to converge to usefulm control solutions. For complex engineering problems with many constraints it is often difficult to find effective nondegenerat perturbations that produce useful solutions in some neighborhood of the correct solution. In this paper we describe a numerical discretization that regularizes the numerically consistent discretized dynamics and does not perturb the path constraints. For all values of the regularization parameter the discretization remains numerically consistent with the dynamics and the path constraints specified in the, original problem. The regularization is quanti. able in terms of time step size in the mesh and the regularization parameter. For full regularized systems the scheme converges linearly in time step size.The method is illustrated with examples.

Stream power criterion and design of sand bed channels at incipient motion

The critical stream power criterion may be used to describe the incipient motion of cohesionless particles of plane sediment beds. The governing equation relating ``critical stream power'' to ``shear Reynolds number'' is developed by using the present experimental data as well as the data from several other sources. Simultaneously, a resistance equation, relating the ``particle Reynolds number'' to the``shear Reynolds number'' is developed for plane sediment beds in wide channels with little or no transport. By making use of these relations, a procedure is developed to design plane sediment beds such that any two of the four design variables, including particle size, energy/friction slope, flow depth, and discharge per unit width in the channel should be known to predict the remaining two variables. Finally, a straightforward design procedure using design tables/design curves and analytical methods is presented to solve six possible design problems.

Insoluble anode of porous lead dioxide for electrosynthesis: preparation and characterization

Preparation of a novel type of titanium-substrate lead dioxide anode with enhanced electrocatalytic activity for electrosynthesis is described. It has been demonstrated that in the presence of a suitable surfactant in the coating solution, an adherent and mainly tetragonal form of lead dioxide is deposited on a platinized titanium surface such that the solution side of the coating is porous while the substrate side is compact. By an analysis of anodic charging curves and steady-state Tafel plots with such porous electrodes in contact with sodium sulphate solution, it has been proved that the electrochemically active area of these anodes is higher by more than an order of magnitude when compared to the area of conventional titanium-substrate lead dioxide anodes. The electrocatalytic activity is also thereby enhanced to a significant degree.

Alfven Surface-Waves Along Coronal Streamers

The dispersive characteristics of Alfvdn Surface Waves (ASW) along a moving plasma surrounded by a stationary plasma is discussed. The stability curves for the symmetric and the asymmetric modes are also discussed.

Kinetic studies on thermal decomposition of polystyrene peroxide

Polystyrene peroxide has been synthesized and its decomposition has been studied by thermogravimetry and differential thermal analysis. Polystyrene peroxide has been found to decompose exothermically at about 110°C. The activation energy for the decomposition was estimated to be 30 kcal/mole both by the Jacobs and Kureishy method and by fitting the α versus time curves to the first-order kinetic equation. This suggests that the rate-controlling step in the decomposition of polystyrene peroxide is cleavage of the O---O bond.

A simple and inexpensive technique to study the flammability of polymers

A simple and inexpensive technique is described for the study of flammability of polymers, wherein the samples can be weighed continuously during their combustion in controlled atmosphere. The mass versus time curves for burning and quenching process in polystyrene samples are discussed. The experimental data indicates the efficiency of Monoammonium phosphate and ammonium halides in quenching of polystyrene.

Computer-aided analysis of the structure of kinematic chains

Using the link-link incidence matrix to represent a simple-jointed kinematic chain algebraic procedures have been developed to determine its structural characteristics such as the type of freedom of the chain, the number of distinct mechanisms and driving mechanisms that can be derived from the chain. A computer program incorporating these graph theory based procedures has been applied successfully for the structural analysis of several typical chains.

Some studies on free vibration of composite laminates

Free vibration analysis is carried out to study the vibration characteristics of composite laminates using the modified shear deformation, layered, composite plate theory and employing the Rayleigh-Ritz energy approach. The analysis is presented in a unified form so as to incorporate all different combinations of laminate boundary conditions and with full coverage with regard to the various design parameters of a laminated plate. A parametric study is made using a beam characteristic function as the admissible function for the numerical calculations. The numerical results presented here are for an example case of fully clamped boundary conditions and are compared with previously published results. The effect of parameters, such as the aspect ratio of plates, ply-angle, number of layers and also the thickness ratios of plies in laminates on the frequencies of the laminate, is systematically studied. It is found that for anti-symmetric angle-ply or cross-ply laminates unique numerical values of the thickness ratios exist which improve the vibration characteristics of such laminates. Numerical values of the non-dimensional frequencies and nodal patterns, using the thickness ratio distribution of the plies, are then obtained for clamped laminates, fabricated out of various commonly used composite materials, and are presented in the form of the design curves.

"Central Atoms" models for ternary silicate and alumino-silicate melts

The �Central Atoms� model presented by the authors in an earlier paper is extended to ternary silicate and alumino-silicate melts. The model is applied to the CaO-FeO-SiO2 and the CaO-Al2O3-SiO2 system. Use is made of the parameters from the relevant binaries only. The agreement between experimental and calculated isoactivity curves is good in all cases.

A Gaussian quadrature analysis of linear sweep voltammetry

The application of Gaussian Quadrature (GQ) procedures to the evaluation of i—E curves in linear sweep voltammetry is advocated. It is shown that a high degree of precision is achieved with these methods and the values obtained through GQ are in good agreement with (and even better than) the values reported in literature by Nicholson-Shain, for example. Another welcome feature with GQ is its ability to be interpreted as an elegant, efficient analytic approximation scheme too. A comparison of the values obtained by this approach and by a recent scheme based on series approximation proposed by Oldham is made and excellent agreement is shown to exist.

Studies on Thermal Polymerization of Acrylamide

Thermal polymerization of acrylamide has been followed by the DSC technique, and the activation energy (E) values at different stages of the fraction polymerized (a) have been determined from the exotherm of the thermograms obtained. The trend of variation of E with agr shows that E remains constant up to agr = 0.5 and decreases with a further increase in agr. A close look at the composite nature of the exotherms, agr-t, and agr-T curves shows that the polymerization of acrylamide involves two processes. The first process is the formation of linear polyacrylamide and the second is the simultaneous cross-linking of the linear chains together with the formation of linear polyacrylamide. Experiments such as NH3 detection by differential thermal analysis techniques and annealing studies have been made to shed further light on the polymerization process.

Kinetics of thermal decomposition of barium zirconyl oxalate

Kinetics of the thermal decomposition of anhydrous barium zirconyl oxalate and a carbonate intermediate have been studied. Decomposition of the anhydrous oxalate, though it could be explained based on a contracting-cube model, is quite complex. Kinetics of decomposition of the intermediate carbonate Ba2Zr2O5CO3 is greatly influenced by thermal effects during its formation. (agr-t) curves are sigmoidal and obey a power law equation followed by first order decay. Presence of carbon in the vacuum-prepared carbonate has a strong deactivating effect. Decomposition of the carbonate is accompanied by growth in particle size of the product barium zirconate.

Monte Carlo simulation of mictomagnets

Monte Carlo simulations of a binary alloy with impurity concentrations between 20 and 45 at.% have been carried out. The proportion of large clusters relative to that of small clusters increases with the number of MC diffusion steps as well as impurity concentration. Magnetic susceptibility peaks become more prominent and occur at higher temperatures with increasing impurity concentration. The different peaks in the susceptibility and specific heat curves seem to correspond to different sized clusters. A freezing model would explain the observed behaviour with the large clusters freezing first and the small clusters contributing to susceptibility (specific heat) peaks at lower temperatures.

Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

The mechanism of manganese electrodeposition

The mechanism of manganese electrodeposition from a sulphate bath on to a stainless-steel substrate has been studied by using current efficiency data to resolve the totali-E curves. A simple, two-step electron transfer mechanism:is proposed to explain the following experimentally obtained parameters: cathodic and anodic transfer coefficients, reaction order and stoichiometric number. The mechanism also explains the effect of pH oni o,Mn and on the corrosion currents.