Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

Taylor series expansion based multidimensional image reconstruction for confocal and 4pi microscopy

We propose and experimentally demonstrate a three-dimensional (3D) image reconstruction methodology based on Taylor series approximation (TSA) in a Bayesian image reconstruction formulation. TSA incorporates the requirement of analyticity in the image domain, and acts as a finite impulse response filter. This technique is validated on images obtained from widefield, confocal laser scanning fluorescence microscopy and two-photon excited 4pi (2PE-4pi) fluorescence microscopy. Studies on simulated 3D objects, mitochondria-tagged yeast cells (labeled with Mitotracker Orange) and mitochondrial networks (tagged with Green fluorescent protein) show a signal-to-background improvement of 40% and resolution enhancement from 360 to 240 nm. This technique can easily be extended to other imaging modalities (single plane illumination microscopy (SPIM), individual molecule localization SPIM, stimulated emission depletion microscopy and its variants).

Integral Formulation of the Problem of Current Distribution in Compulsator Wires of Electromagnetic Launchers and Railguns

Compulsators are power sources of choice for use in electromagnetic launchers and railguns. These devices hold the promise of reducing unit costs of payload to orbit. In an earlier work, the author had calculated the current distribution in compulsator wires by considering the wire to be split into a finite number of separate wires. The present work develops an integral formulation of the problem of current distribution in compulsator wires which leads to an integrodifferential equation. Analytical solutions, including those for the integration constants, are obtained in closed form. The analytical solutions present a much clearer picture of the effect of various input parameters on the cross-sectional current distribution and point to ways in which the desired current density distribution can be achieved. Results are graphically presented and discussed, with particular reference to a 50-kJ compulsator in Bangalore. Finite-element analysis supports the results.

Optimum Evaluation of Reactive Power Requirements in Power Distribution-Systems

This paper presents three methodologies for determining optimum locations and magnitudes of reactive power compensation in power distribution systems. Method I and Method II are suitable for complex distribution systems with a combination of both radial and ring-main feeders and having different voltage levels. Method III is suitable for low-tension single voltage level radial feeders. Method I is based on an iterative scheme with successive powerflow analyses, with formulation and solution of the optimization problem using linear programming. Method II and Method III are essentially based on the steady state performance of distribution systems. These methods are simple to implement and yield satisfactory results comparable with the results of Method I. The proposed methods have been applied to a few distribution systems, and results obtained for two typical systems are presented for illustration purposes.

State space formulation of ammonia reactor dynamics

The specific objective of this paper is to develop a state space model of a tubular ammonia reactor which is the heart of an ammonia plant in a fertiliser complex. A ninth order model with three control inputs and two disturbance inputs is generated from the nonlinear distributed model using linearization and lumping approximations. The lumped model is chosen such that the steady state temperature at the exit of the catalyst bed computed from the simplified state space model is close enough to the one computed from the nonlinear steady state model. The model developed in this paper is very useful for the design of continuous/discrete versions of single variable/multivariable control algorithms.

Optimal hydrothermal load flow: Formulation and a successive approximation solution for fixed head systems

This paper deals with the optimal load flow problem in a fixed-head hydrothermal electric power system. Equality constraints on the volume of water available for active power generation at the hydro plants as well as inequality constraints on the reactive power generation at the voltage controlled buses are imposed. Conditions for optimal load flow are derived and a successive approximation algorithm for solving the optimal generation schedule is developed. Computer implementation of the algorithm is discussed, and the results obtained from the computer solution of test systems are presented.

A computerized methodology for structural synthesis of kinematic chains: Part 1- Formulation

In an effort to develop a fully computerized approach for structural synthesis of kinematic chains the steps involved in the method of structural synthesis based on transformation of binary chains [38] have been recast in a format suitable for implementation on a digital computer. The methodology thus evolved has been combined with the algebraic procedures for structural analysis [44] to develop a unified computer program for structural synthesis and analysis of simple jointed kinematic chains with a degree of freedom 0. Applications of this program are presented in the succeeding parts of the paper.

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.

Some Unique Features of Egg Laying and Reproduction in Ichthyophis Malabarensis (Taylor) (Apoda:Amphibia)

The paper describes egg laying and reproduction in ICHTHYOPHIS MALABARENSIS. 100 eggs, the largest ever in Apoda, are laid in a single string and manipulated by the female into a massive clutch. The reproductive strategies in the species are discussed.

An algebraic formulation of static isotropy and design of statically isotropic 6-6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration. (C) 2008 Elsevier Ltd. All rights reserved.

The effect of viscosity and surface tension on the Taylor instability of the surface of a cavitation bubble*

This paper is devoted to a consideration of the following problem: A spherical mass of fluid of density varrho1, viscosity μ1 and external radius R is surrounded by a fluid of density varrho2 and viscosity μ2.The fluids are immiscible and incompressible. The interface is accelerated radially by g1: to study the effect of viscosity and surface tension on the stability of the interface. By analyzing the problem in spherical harmonics the mathematical problem is reduced to one of solution of the characteristic determinant equation. The particular case of a cavity bubble, where the viscosity μ1 of the fluid inside the bubble is negligible in comparison with the viscosity μ2 of the fluid outside the bubble, is considered in some detail. It is shown that viscosity has a stabilizing role on the interface; and when g1 > T(n − 1) (n + 2)/R2(varrho2 − varrho1) the stabilizing role of both viscosity and surface tension is more pronounced than would result when either of them is taken individually.

A self-consistent formulation for analysis and generation of non-uniform DNA structure

A fully self-consistent formulation is described here for the analysis and generation of base-pairs in non-uniform DNA structures, in terms of various local parameters. It is shown that the internal "wedge parameters" are mathematically related to the parameters describing the base-pair orientation with respect to an external helix axis. Hence any one set of three translation and three rotation parameters are necessary and sufficient to completely describe the relative orientation of the base-pairs comprising a step (or doublet). A general procedure is outlined for obtaining an average or global helix axis from the local helix axes for each step. A graphical representation of the local helix axes in the form of a polar plot is also shown and its application for estimating the curvature of oligonucleotide structures is illustrated, with examples of both A and B type structures.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.