A study of symbolic processing and computational aspects in helicopter dynamics

Even research models of helicopter dynamics often lead to a large number of equations of motion with periodic coefficients; and Floquet theory is a widely used mathematical tool for dynamic analysis. Presently, three approaches are used in generating the equations of motion. These are (1) general-purpose symbolic processors such as REDUCE and MACSYMA, (2) a special-purpose symbolic processor, DEHIM (Dynamic Equations for Helicopter Interpretive Models), and (3) completely numerical approaches. In this paper, comparative aspects of the first two purely algebraic approaches are studied by applying REDUCE and DEHIM to the same set of problems. These problems range from a linear model with one degree of freedom to a mildly non-linear multi-bladed rotor model with several degrees of freedom. Further, computational issues in applying Floquet theory are also studied, which refer to (1) the equilibrium solution for periodic forced response together with the transition matrix for perturbations about that response and (2) a small number of eigenvalues and eigenvectors of the unsymmetric transition matrix. The study showed the following: (1) compared to REDUCE, DEHIM is far more portable and economical, but it is also less user-friendly, particularly during learning phases; (2) the problems of finding the periodic response and eigenvalues are well conditioned.

Padé approach to potential transients: Part 1. Electron transfer without and with coupling to first-order homogeneous reactions at planar electrodes

Potential transients are obtained by using “Padé approximants” (an accurate approximation procedure valid globally — not just perturbatively) for all amplitudes of concentration polarization and current densities. This is done for several mechanistic schemes under constant current conditions. We invert the non-linear current-potential relationship in the form (using the Lagrange or the Ramanujan method) of power series appropriate to the two extremes, namely near reversible and near irreversible. Transforming both into the Pad́e expressions, we construct the potential-time profile by retaining whichever is the more accurate of the two. The effectiveness of this method is demonstrated through illustrations which include couplings of homogeneous chemical reactions to the electron-transfer step.

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.

Income inequality in the process of economic development : An empirical approach

This thesis studies the effect of income inequality on economic growth. This is done by analyzing panel data from several countries with both short and long time dimensions of the data. Two of the chapters study the direct effect of inequality on growth, and one chapter also looks at the possible indirect effect of inequality on growth by assessing the effect of inequality on savings. In Chapter two, the effect of inequality on growth is studied by using a panel of 70 countries and a new EHII2008 inequality measure. Chapter contributes on two problems that panel econometric studies on the economic effect of inequality have recently encountered: the comparability problem associated with the commonly used Deininger and Squire s Gini index, and the problem relating to the estimation of group-related elasticities in panel data. In this study, a simple way to 'bypass' vagueness related to the use of parametric methods to estimate group-related parameters is presented. The idea is to estimate the group-related elasticities implicitly using a set of group-related instrumental variables. The estimation results with new data and method indicate that the relationship between income inequality and growth is likely to be non-linear. Chapter three incorporates the EHII2.1 inequality measure and a panel with annual time series observations from 38 countries to test the existence of long-run equilibrium relation(s) between inequality and the level of GDP. Panel unit root tests indicate that both the logarithmic EHII2.1 inequality measure and the logarithmic GDP per capita series are I(1) nonstationary processes. They are also found to be cointegrated of order one, which implies that there is a long-run equilibrium relation between them. The long-run growth elasticity of inequality is found to be negative in the middle-income and rich economies, but the results for poor economies are inconclusive. In the fourth Chapter, macroeconomic data on nine developed economies spanning across four decades starting from the year 1960 is used to study the effect of the changes in the top income share to national and private savings. The income share of the top 1 % of population is used as proxy for the distribution of income. The effect of inequality on private savings is found to be positive in the Nordic and Central-European countries, but for the Anglo-Saxon countries the direction of the effect (positive vs. negative) remains somewhat ambiguous. Inequality is found to have an effect national savings only in the Nordic countries, where it is positive.

Ab initio molecular orbital calculations on ion-molecule and ion pair-molecule complexes of the water-lithium cyanide system

Ab initio molecular orbital (MO) calculations with the 3-21G and 6-31G basis sets were performed on a series of ion-molecule and ion pair-molecule complexes for the H2O + LiCN system. Stabilisation energies (with counter-poise corrections), geometrical parameters, internal force constants and harmonic vibrational frequencies were evaluated for 16 structures of interest. Although the interaction energies are smaller, the geometries and relative stabilities of the monohydrated contact ion pair are reminiscent of those computed for the complexes of the individual ions. Thus, interaction of the oxygen lone pair with lithium leads to a highly stabilised C2v structure, while the coordination of water to the cyanide ion involves a slightly non-linear hydrogen bond. Symmetrical bifurcated structures are computed to be saddle points on the potential energy surface, and to have an imaginary frequency for the rocking mode of the water molecule. On optimisation the geometries of the solvent shared ion pair structures (e.g. Li+cdots, three dots, centered OH2cdots, three dots, centered CN−) revealed a proton transfer from the water molecule leading to hydrogen bonded forms such as Li-O-Hcdots, three dots, centered HCN. The variation in the force constants and harmonic frequencies in the various structures considered are discussed in terms of ion-molecular and ion pair-molecule interactions.

AC impedance spectroscopic characterization of 10 mol% MgO doped ZnO varistors

The performance parameters e.g. non-linear coefficient (α) and breakdown electric field (Eb1mA/cm2) of ZnO based ceramic varistors were found to improve after the addition of 10 mol% MgO. The improvement in the varistor properties is examined by ac impedance spectroscopy technique in the frequency range (1 Hz–10 MHz) between temperature 25–250°C and understood in terms of differing contributions from the equivalent electrical circuit elements.

Effect of microstructure and hardness on the grinding abrasive wear resistance of a ball bearing steel

Grinding media wear appears to be non-linear with the time of grinding in a laboratory-scale ball mill. The kinetics of wear can be expressed as a power law of the type w=atb, where the numerical constant a represents wear of a particular microstructure at time t = 1 min and b is the wear exponent which is independent of the particle size prevailing inside a ball mill at any instant of time of grinding. The wear exponent appears to be an indicator of the cutting wear mechanism in dry grinding: a plot of the inverse of the normalised wear exponent (Image ) versusHs (where Hs is the worn surface hardness of the media) yields a curve similar to that of a wear resistance plot obtained in the case of two-body sliding abrasive wear. This method of evaluating the cutting wear resistance of media is demonstrated by employing 15 different microstructures of AISI-SAE 52100 steel balls in dry grinding of quartz in a laboratory-scale ball mill.

Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x greater-or-equal, slanted 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as var epsilon → 0 is obtained.

Pulsatile flow of a viscous fluid in elliptical pipe of variable cross-section

The pulsatile flow of an incompressible viscous fluid in an elliptical pipe of slowly varying cross-section is considered. Asymptotic series solutions for the velocity distribution and pressure gradient are obtained in terms of Mathieu functions for a low Reynold number flow in which the volume flux is prescribed. An expression for shear stress on the boundary is derived. The physically significant quantities governing the flow are computed numerically and analysed for different types of constrictions. The effect of eccentricity and Womerslay parameter on the flow is discussed.

Interior Photon Absorption Based Adaptive Regularization Improves Diffuse Optical Tomography

An adaptive regularization algorithm that combines elementwise photon absorption and data misfit is proposed to stabilize the non-linear ill-posed inverse problem. The diffuse photon distribution is low near the target compared to the normal region. A Hessian is proposed based on light and tissue interaction, and is estimated using adjoint method by distributing the sources inside the discretized domain. As iteration progresses, the photon absorption near the inhomogeneity becomes high and carries more weightage to the regularization matrix. The domain's interior photon absorption and misfit based adaptive regularization method improves quality of the reconstructed Diffuse Optical Tomographic images.

Piezoelectrically actuated insect scale flapping wing

An energy method is used in order to derive the non-linear equations of motion of a smart flapping wing. Flapping wing is actuated from the root by a PZT unimorph in the piezofan configuration. Dynamic characteristics of the wing, having the same size as dragonfly Aeshna Multicolor, are analyzed using numerical simulations. It is shown that flapping angle variations of the smart flapping wing are similar to the actual dragonfly wing for a specific feasible voltage. An unsteady aerodynamic model based on modified strip theory is used to obtain the aerodynamic forces. It is found that the smart wing generates sufficient lift to support its own weight and carry a small payload. It is therefore a potential candidate for flapping wing of micro air vehicles.

Quenching across quantum critical points: Role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z(2) invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent nu being different in different sectors. Copyright (C) EPLA, 2010

Thermomechanical behaviour of pin joints subjected to sheet loads

An important problem regarding pin joints in a thermal environment is addressed. The motivation emerges from structural safety requirements in nuclear and aerospace engineering. A two-dimensional model of a smooth, rigid misfit pin in a large isotropic sheet is considered as an abstraction. The sheet is subjected to a biaxial stress system and far-field unidirectional heat flow. The thermoelastic analysis is complex due to non-linear load-dependent contact and separation conditions at the pin-hole interface and the absence of existence and uniqueness theorems for the class of frictionless thermoelastic contact problems. Identification of relevant parameters and appropriate synthesis of thermal and mechanical variables enables the thermomechanical generalization of pin-joint behaviour. This paper then proceeds to explore the possibility of multiple solutions in such problems, especially interface contact configuration.

Chloroplastic glutamine synthetase from normal and water stressed safflower (Carthamus tinctorius L.) leaves

The chloroplastic isoform of glutamine synthetase (GS(2), EC 6.3.1.2) from normal and water stressed safflower (Carthamus tinctorius L. cv.A-300) leaves has been purified to apparent electrophoretic homogeneity by a procedure involving anion-exchange, hydrophobic and size-exclusion chromatography followed by electroelution of the protein from preparative polyacrylamide gels. The observed molecular weight of the native protein varied from 305-330 kDa depending on the sizing column employed. The native protein is composed of 44 kDa subunits. Under conditions of saturating ammonium and at ATP levels of 0.1-10 mM, double-reciprocal plots with respect to glutamate are biphasic and concave downward at high concentrations of the varied substrate for normal enzyme but are linear for enzyme from water-stressed plants. Under subsaturating ATP levels, K-Glu is over 18-fold lower for enzyme from stressed leaves. The K-m, (ATP) varies with Mg2+ levels in the assay mixture. Double-reciprocal plots of initial velocity with respect to ATP at changing fixed levels of NH4+ are linear for normal enzyme but are curved upwards for enzyme from stressed leaves. Initial velocity data of 1/v vs. 1/ammonium for the enzyme from both the sources are non-linear (curved upwards) when ATP is saturating. At subsaturating ATP levels, the data are linear for normal enzyme but are still non-linear for the enzyme from stressed leaves. The results obtained suggest positively cooperative binding of NH4+ A V-max(/2) value of 3.6 mM for Mg2+ was obtained at 5 mM ATP. The isoelectric point of the native protein from normal and stressed leaves was determined to be, respectively, 5.6 and 6.1. The mixed competitive and competitive inhibitors, methionine sulfoximine and ADP and K-i values of 0.086 mM (0.017 for the enzyme from stressed leaves) and 2.15 mM (1.70 for the enzyme from stressed leaves), respectively. Enzyme from stressed leaves is not inhibited by 5 mM proline. The observed kinetic constants of GS(2) from normal and water stressed safflower seedlings are discussed in relation to the known water-stress tolerance of this crop plant.

Cracks emanating from pin-loaded lugs

Pin-loaded lugs were analysed in the presence of cracks emanating from circular holes. The analysis presents a unified treatment of interference, push or clearance fit pins. Both metallic (isotropic) and composite (orthotropic) plates were dealt with. The finite element model used special singular six-noded quadrilateral elements at the crack tip. The non-linear load contact behaviour at the pin-hole interface was dealt with by an inverse technique. A modified crack closure integral (MCCI) technique was used to evaluate the strain energy release rates (SERRs) and stress intensity factors (SIFs) at the crack tips. Numerical results are presented showing the non-linear variation of SIF with applied stress, and the influence of the amount of interference or clearance and the interfacial friction on SIF.