Spectroscopic and morphological study of laser ablated Titanium

The optical characteristics of biological tissues sampled from the anterior abdominal wall of laboratory rats are for the first time experimentally studied in a wide wavelength range (350-2500 nm). The experiments have been performed in vitro using a LAMBDA 950 (PerkinElmer, United States) spectrophotometer. Inverse Monte Carlo simulation is used to restore the spectral dependences for scattering and absorption coefficients, as well as the scattering anisotropy factor for biological tissue based on the recorded spectra of diffuse reflection and total and collimated transmissions.     

Time-stepping algorithms for semidiscretized linear parabolic PDEs based on rational approximants with distinct real poles

Time dependent problems in Partial Differential Equations (PDEs) are often solved by the Method Of Lines (MOL). For linear parabolic PDEs, the exact solution of the resulting system of first order Ordinary Differential Equations (ODEs) satisfies a recurrence relation involving the matrix exponential function. In this paper, we consider the development of a fourth order rational approximant to the matrix exponential function possessing real and distinct poles which, consequently, readily admits a partial fraction expansion, thereby allowing the distribution of the work in solving the corresponding linear algebraic systems in essentially Backward Euler-like solves on concurrent processors. The resulting parallel algorithm possesses appropriate stability properties, and is implemented on various parabolic PDEs from the literature including the forced heat equation and the advection-diffusion equation.Dedicated to Professor J. Crank on the occasion of his 80th birthday     

Fiber-optic liquid-level sensor using a long-period grating

A liquid-level sensor based on the refractive-index sensitivity of long-period fiber-optic gratings is proposed and demonstrated. The form of the transmission spectrum of the long-period grating is dependent on the fraction of the length of the long-period grating that is surrounded by the liquid. The sensor shows a large linear range, with sensitivity of 4.8% change in transmission per millimeter, for a long-period grating with a length of 40 mm and a periodicity of 400mu;m .     

One-step multiderivative methods for first order ordinary differential equations

A family of one-step multiderivative methods based on Padé approximants to the exponential function is developed. The methods are extrapolated and analysed for use inPECE mode.Error constants, stability intervals and stability regions are given in two associated Technical Reports.Comparisons are made with well-known linear multi-step combinations and combinations using high accuracy Newton-Cotes quadrature formulas as correctors.     

Smoothing schemes for reaction-diffusion systems with nonsmooth data

Cox and Matthews [S.M. Cox, P.C. Matthews, Exponential time differencing for stiff systems, J. Comput. Phys. 176 (2002) 430–455] developed a class of Exponential Time Differencing Runge–Kutta schemes (ETDRK) for nonlinear parabolic equations; Kassam and Trefethen [A.K. Kassam, Ll. N. Trefethen, Fourth-order time stepping for stiff pdes, SIAM J. Sci. Comput. 26 (2005) 1214–1233] have shown that these schemes can suffer from numerical instability and they proposed a modified form of the fourth-order (ETDRK4) scheme. They use complex contour integration to implement these schemes in a way that avoids inaccuracies when inverting matrix polynomials, but this approach creates new difficulties in choosing and evaluating the contour for larger problems. Neither treatment addresses problems with nonsmooth data, where spurious oscillations can swamp the numerical approximations if one does not treat the problem carefully. Such problems with irregular initial data or mismatched initial and boundary conditions are important in various applications, including computational chemistry and financial engineering. We introduce a new version of the fourth-order Cox–Matthews, Kassam–Trefethen ETDRK4 scheme designed to eliminate the remaining computational difficulties. This new scheme utilizes an exponential time differencing Runge–Kutta ETDRK scheme using a diagonal Padé approximation of matrix exponential functions, while to deal with the problem of nonsmooth data we use several steps of an ETDRK scheme using a sub-diagonal Padé formula. The new algorithm improves computational efficiency with respect to evaluation of the high degree polynomial functions of matrices, having an advantage of splitting the matrix polynomial inversion problem into a sum of linear problems that can be solved in parallel. In this approach it is only required that several backward Euler linear problems be solved, in serial or parallel. Numerical experiments are described to support the new scheme.     

Determination of oil contents from eight varieties of olea europaea (Olive) grown in Pakistan

Abstract

The olive (Olea europaea L.) is a worldwide famous tree crop having valuable commercial role due to nutritional as well as therapeutic benefits obtained from its edible oil. Eight varieties of Olea europaea L. fruits were obtained from three Agricultural research institutes located in different areas of Pakistan including Quetta, Lorallia and Zhob to extract and determine their oil contents by conventional method as solvent extraction (soxhlet apparatus). Statistical analysis showed significant (p?=?0.002) difference in oil composition of collected plants. Highest amount (percentage) of oil was obtained from Gemlik variety (65%) from Lorallia and lowest oil content from Dolece-agogia variety (17.5%) collected from Quetta. Further research is under consideration to rule out best suitable factors including some soil and environmental factors to obtained more potential cultivars of Olea europaea in Pakistan.     

A fourth‐order compact algorithm for nonlinear reaction‐diffusion equations with Neumann boundary conditions

In this article, we discuss a scheme for dealing with Neumann and mixed boundary conditions using a compact stencil. The resulting compact algorithm for solving systems of nonlinear reaction‐diffusion equations is fourth‐order accurate in both the temporal and spatial dimensions. We also prove that the standard second‐order approximation to zero Neumann boundary conditions provides fourth‐order accuracy when the nonlinear reaction term is independent of the spatial variables. Numerical examples, including an application of this algorithm to a mathematical model describing frontal polymerization process, are presented in the article to demonstrate the accuracy and efficiency of the scheme. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

A compound adaptive approach to degenerate nonlinear quenching problems

Quenching phenomena play important roles in both steady and unsteady combustion processes. This article studies a compound finite difference method for solving a nonlinear degenerate combustion model problem. The approach combines procedures of semidiscretization, adaptive ODE solver, and highly stable rational approximation for handling the spatial degeneracy and quenching singularity involved. A second‐order adaptive scheme is constructed, which provides monotone convergence of the numerical solution and direct computations of critical quenching values. It has a simple, yet accurate and reliable, structure and is easy to use. We further demonstrate advantages of the scheme by comparing it to existing algorithms. Numerical examples are presented to further strengthen our results. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 29–47, 1999