Stability of Model and Selection of Parameters: Application to Metrology in Optical Microscopy

Abstract

In optical microscopy, the a priori knowledge of the nature of the object to be imaged and of the transfer function of the optical system allows the improvement of the limit of resolution beyond classical bounds derived from consideration of the optical transfer only. This paper presents a quantitative study of this improvement as a function of the object model and of the image noise. The method is derived from recent studies about the limit of resolution in image restoration. An application to linewidth measurement on integrated circuits is shown.     

Model simplification of stable discrete‐time systems by the squared magnitude Padé approximation

Abstract

A squared magnitude Padé approximation technique is presented for the model simplification of stable discrete‐time systems. The simplification is started from the squared magnitude function M(e^jTω ) =G(e^jTω )G(e^–jTω ), where G(z) is the z‐transfer function of a given high order discrete‐time system. The method is fully computer‐oriented and leads to a satisfactory approximation while preserving stability and minimum‐phase characteristics.     

Evaporation heat and mass transfer in natural convection pipe flow

Abstract

A numerical analysis has been performed to examine film evaporation on natural convection heat and mass transfer in a vertical pipe. Coupled governing equations for liquid film and induced gas flow were simultaneously solved by the implicit finite difference method. Results for interfacial heat and mass transfer coefficients are specifically presented for ethanol film and water film vaporization. The predicted results indicate that the heat transfer from gas‐liquid interface to the gas flow is predominated by the transport of latent heat in association with film evaporation. The results are also contrasted with those of zero film thickness and show that the assumption of extremely thin film thickness made by Chang et al. [5] and Yan and Lin [19] is only valid for a system with a low liquid Reynolds number Re _l1. But as the liquid Reynolds number is high, the assumption becomes inappropriate.     

The vertical beam quality of GaInP/AlGaInP strained multiple quantum well laser

Abstract

The waveguided mode of the visible GaInP/AlGaInP compressive strained multiple quantum well laser is calculated by using transfer matrix method. On the basis of the nonparaxial vectorial moment theory of light beam propagation, the vertical (perpendicular to junction plane) optical beam quality factor M ²? of the waveguided mode is shown to be smaller than unity. This result may be useful for the design of semiconductor lasers and analysis of nonparaxial beam propagating characteristics.     

Effects of Aberrations on Transfer Functions Used in High Angular Resolution Astronomical Imaging

Abstract

In this paper we present the results of the effect of aberrations on the transfer functions used in the high-angular resolution astronomical imaging techniques of speckle interferometry, Knox-Thompson and bispectral imaging. The analyses are based on a computer simulation of imaging through atmospheric turbulence. The results show that as the seeing becomes worse, its effect dominates the behaviour of the transfer functions which tend to be independent of (small) optical aberrations. However, if the wavefront variation due to fixed aberrations is significant over r ₀-sized regions in the pupil (where r ₀ is the Fried parameter), the above transfer functions do depend on the aberration: in particular, the bispectral transfer function is relatively sensitive to odd aberrations, such as coma.     

Effects of substrate protection and intraparticle diffusion on the stability of immobilized glucose isomerase

Abstract

The objective of this study is to investigate the adsorption of a chlorinated pesticide; lindane, with the presence of humic acid, has been found in a number of surface water supplies. This study includes developing equilibrium data and performing the adsorption column on lindane in the presence of different concentrations of humic acid with different pH conditions. A multicomponent model is used for data synthesis and for simulation and prediction of dynamic performance of carbon beds for removing lindane from the water containing humic acid. The film transfer coefficients (K_f ) and surface diffusivities (D_s ) used for predictive modeling are determined by micro‐column method.     

LQG/LTR loop shaping design with an application to position control

Abstract

In contrast to the conventional LQG method using calculus of variations, this paper presents an alternative approach based on operator theory and spectrum factorization. This approach, which works toward transfer function domain, has merits in its simple and straightforward development. The novelty of this method is not the results achieved, but rather in their derivation. A loop shaping design procedure which incorporates the classical loop shaping into LQG/LTR synthesis is developed such that the robustness properties of the optimal full state feedback are guaranteed at both the plant input and the plant output. The design procedure is applied to a position controller design in a servo system, and the performance is evaluated by a digital signal processor, the TMS320C30. Experimental results have shown effectiveness of this design method.     

Performance analysis of a k‐nearest neighbor searching technique

Abstract

A transfer admittance is treated as a two‐terminal network driven by cascaded dependent sources. By complex‐curve fitting, each of the four admittances of a conventional two‐port model can be approximated over a wideband with a rational function of frequency. A SPICE2‐acceptable R‐L‐C two‐port model can then be derived by applying continued fractions to the rational functions. Examples are included to demonstrate the applications of this method.     

Planar silver nanowire,carbon nanotube and PEDOT:PSS nanocomposite transparent electrodes

Abstract

Highly conductive, transparent and flexible planar electrodes were fabricated using interwoven silver nanowires and single-walled carbon nanotubes (AgNW:SWCNT) in a PEDOT:PSS matrix via an epoxy transfer method from a silicon template. The planar electrodes achieved a sheet resistance of 6.6 ± 0.0 Ω/□ and an average transmission of 86% between 400 and 800 nm. A high figure of merit of 367 Ω^?1 is reported for the electrodes, which is much higher than that measured for indium tin oxide and reported for other AgNW composites. The AgNW:SWCNT:PEDOT:PSS electrode was used to fabricate low temperature (annealing free) devices demonstrating their potential to function with a range of organic semiconducting polymer:fullerene bulk heterojunction blend systems.     

A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method

The Element free Galerkin method, which is based on the Moving Least Squares approximation, requires only nodal data and no element connectivity, and therefore is more flexible than the conventional finite element method. Direct imposition of essential boundary conditions for the element free Galerkin (EFG) method is always difficult because the shape functions from the Moving Least Squares approximation do not have the delta function property. In the prior literature, a direct collocation of the fictitious nodal values & u circ; used as undetermined coefficients in the MLS approximation, u ^h (x) [u ^h (x)=Φ·& u circ;], was used to enforce the essential boundary conditions. A modified collocation method using the actual nodal values of the trial function u ^h (x) is presented here, to enforce the essential boundary conditions. This modified collocation method is more consistent with the variational basis of the EFG method. Alternatively, a penalty formulation for easily imposing the essential boundary conditions in the EFG method with the MLS approximation is also presented. The present penalty formulation yields a symmetric positive definite system stiffness matrix. Numerical examples show that the present penalty method does not exhibit any volumetric locking and retains high rates of convergence for both displacements and strain energy. The penalty method is easy to implement as compared to the Lagrange multiplier method, which increases the number of degrees of freedom and yields a non-positive definite system matrix.     

General formalism of interaction of a three-level atom with cavity fields in the Kerr-like medium

Abstract

A general formalism of a three-level atom interacting with one-mode or two-mode cavity fields in a Kerr-like medium is presented. Dynamic behaviours of the atomic occupation probabilities and the transfer phenomena are investigated numerically in two typical cases. Our results show that the transfer phenomena may depend on the initial conditions.     

Improved Multiple Comparisons With a Control in Response Surface Analysis

Quadratic response surface methodology often focuses on finding the levels of some (coded) predictor variables x = (x ₁, x ₂,…, x _k) that optimize the expected value of a response variable y. Typically the experimenter starts from some best guess or “control” combination of the predictors (usually coded to x = 0) and performs an experiment varying them in a region around this center point. The question of interest addressed here is whether any x in the experimental region provides a long-run mean response E(y) preferable to that of the control, and if so, by what amount? This article approaches this question via simultaneous confidence intervals for δ(x) = E(y|x) = E(y|0) for all x within a specified distance of 0. A new method for two or more predictors is introduced that gives sharper intervals than the Scheffé method and also the Sa and Edwards adaptation of the Casella and Strawderman method. The new method does not require a rotatable design and allows for one-sided simultaneous bounds for δ(x). Approximate sample-size savings of the improved method over the Sa and Edwards adaptation of the Casella and Strawderman method ranged from 12%–45% for two-sided intervals and 19%–40% for one-sided intervals for designs with two or three predictors. Approximate sample-size savings of the improved method over the Scheffe method ranged from 14%–47% for two-sided intervals and 22%–62% for one-sided intervals.     

Effects of wetted wall on laminar natural convection in vertical annular ducts

Abstract

A detailed numerical analysis is performed to investigate the effects of latent heat exchange, in connection with evaporation of the liquid film on the wall, on the natural convection heat transfer in vertical concentric annuli. Major governing parameters identified are Gr_T, Gr_M, Pr, Sc, and N. Results are specifically presented for an air‐water system under various heating conditions to illustrate the latent heat transport during the evaporation process. The effects of the channel length, ratio of radii N and wetted wall temperature on the momentum, heat and mass transfer are examined in detail. Tremendous enhancement in heat transfer due to the exchange of latent heat was clearly demonstrated.     

Reduced‐order modelling of linear discrete‐time systems using cauer third continued‐fraction method

Abstract

In this paper a generalization of the Cauer third continued‐fraction expansion (CFE) is introduced for the reduced‐order modelling of linear time‐invariant discrete‐time systems. First, a new algorithm is presented for obtaining the Cauer third continued‐fraction expansion about z=1 and z=8 of the z‐transfer function of a discrete‐time system from its time‐moments and Markov parameters. Next, a realization of the Cauer third continued‐fraction expansion about z=1 and z=8, and the corresponding CFE canonical state‐space model are derived. Finally, an approximate aggregation matrix is constructed for relating the state‐vector of the reduced‐order CFE canonical state‐space model to that of the original system. An example is included to illustrate the use of the method.     

Possible ionization of mercury atoms by elastic reflection in hyperthermal surface ionization experiments

An elastic collision model baed on data given by Danon et al. [Phys. Rev. Lett. 65, 2038 (1990)] was used to calculate the ionization potential of mercury atoms (V′) at the critical charge transfer distance as a function of the kinetic energy of the atoms (E). The linear dependence V′(E) obtained supports the model of surface ionization of mercury atoms by elastic reflection from a surface. Pis’ma Zh. Tekh. Fiz. 25, 42–45 (July 26, 1999)     

g-Jitter mixed convection adjacent to a vertical stretching sheet

This paper studies the effect of periodical gravity modulation, or g-jitter induced mixed convection, on the flow and heat transfer characteristics associated with a stretching vertical surface in a viscous and incompressible fluid. The velocity and temperature of the sheet are assumed to vary linearly withx, wherex is the distance along the sheet. It is assumed that the gravity vector modulation is given byg*(t)=g_o [1+ɛ cos(πωt)]k, and the resulting non-similar boundary layer equations are solved numerically using an implicit finite-difference scheme. The effects of the amplitude of modulation, frequency of the single-harmonic component of oscillation, mixed convection parameter and Prandtl number on the skin friction and Nusselt number are discussed in detail.     

The Lie-Group Shooting Method for Solving Classical Blasius Flat-Plate Problem

In this paper, we propose a Lie-group shooting method to deal with the classical Blasius flat-plate problem and to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element$\mathbf G(T) and the formation of a generalized mid-point Lie group element$\mathbf G(r). Then, by imposing G(T) = G(r) we can derive some algebraic equations to recover the missing initial conditions. It is the first time that we can apply the Lie-group shooting method to solve the classical Blasius flat-plate problem. Numerical examples are worked out to persuade that the novel approach has better efficiency and accuracy with a fast convergence speed by searching a suitable r ∈(0, 1) with the minimum norm to fit the targets.     

Laminar forced convection in wedge flow with separation

Abstract

A perturbation method is used to study the steady and unsteady laminar boundary layer heat transfer from a wedge with separation for a step‐discontinuity in the surface temperature. The analytic solutions obtained can be used to calculate the steady and unsteady heat transfer rate with arbitrary surface temperature. The effects of the Prandtl number on the temperature distribution and the heat transfer rate are discussed in detail. The solution is valid for large or moderate Prandtl number.     

The study of α in GM(1,1) model

Abstract

The purpose of this paper is to analyze a predicted error in using the GM(1, 1) model based on the parameter α. The transfer function for the predicted error with the parameter α in the GM(1, 1) model is presented. The algorithm of solving equations in calculus is used to analyze whether the α is adaptive or not. The criterion of α is applied to describe the adaptive criterion of α. Finally, an example of the cagenet amounts of fish in the Peng‐hu area is used to demonstrate the small prediction error due to the optimal α value. The result shows that the criterion for α is applicable for minimizing the predicted error easily.     

Numerical solution of Cauchy type singular integral equations with logarithmic weight,based on arbitrary collocation points

Singular integral equations with a Cauchy type kernel and a logarithmic weight function can be solved numerically by integrating them by a Gauss-type quadrature rule and, further, by reducing the resulting equation to a linear system by applying this equation at an appropriate number of collocation points x _k. Until now these x _k have been chosen as roots of special functions. In this paper, an appropriate modification of the original method permits the arbitrary choice of x _k without any loss in the accuracy. The performance of the method is examined by applying it to a numerical example and a plane crack problem.