Microchanneled chirped fibre Bragg gratings for simultaneous refractive index and temperature measurements

We report here the fabrication, charaterisation and refractive index sensing of two microchanneled chirped fiber Bragg gratings (MCFBGs) with different channel sizes (~550µm and ~1000µm). The chirped grating structures were UV-inscribed in optical fibre and the microchannels were created in the middle of the CFBGs by femtosecond (fs) laser assisted chemical etching method. The creation of microchannels in the CFBG structures gives an access to the external index liquid, thus inducing refractive index (RI) sensitivity to the structure. In comparison with previously reported FBG based RI sensors, for which the cladding layers usually were removed, the MCFBGs represent a more ideal solution for robust devices as the microchannel will not degrade the structure strength. The two MCFBGs were spectrally charaterised for their RI and temperature responses and both gratings exhibited unique thermal and RI sensitivities, which may be utilised for implementation of bio-chemical sensors with capability to eliminate temperature crosssensitivity.

Microchanneled chirped fibre Bragg gratings for simultaneous refractive index and temperature measurements

We report here the fabrication, charaterisation and refractive index sensing of two microchanneled chirped fiber Bragg gratings (MCFBGs) with different channel sizes (~550µm and ~1000µm). The chirped grating structures were UV-inscribed in optical fibre and the microchannels were created in the middle of the CFBGs by femtosecond (fs) laser assisted chemical etching method. The creation of microchannels in the CFBG structures gives an access to the external index liquid, thus inducing refractive index (RI) sensitivity to the structure. In comparison with previously reported FBG based RI sensors, for which the cladding layers usually were removed, the MCFBGs represent a more ideal solution for robust devices as the microchannel will not degrade the structure strength. The two MCFBGs were spectrally charaterised for their RI and temperature responses and both gratings exhibited unique thermal and RI sensitivities, which may be utilised for implementation of bio-chemical sensors with capability to eliminate temperature crosssensitivity.

Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Case-based reasoning enabling database mining for cryo-preserving algae applications

Case-based Reasoning's (CBR) origins were stimulated by a desire to understand how people remember information and are in turn reminded of information, and that subsequently it was recognized that people commonly solve problems by remembering how they solved similar problems in the past. Thus CBR became an appropriate way to find out the most suitable solution method for a new problem based on the old methods for the same or even similar problems. The research highlights how to use CBR to aid biologists in finding the best method to cryo preserve algae. The study found CBR could be used successfully to find the similarity percentage between the new algae and old cases in the case base. The prediction result showed approximately 93.75% accuracy, which proves the CBR system can offer appropriate recommendations for most situations. © 2011 IEEE.

Optimization of chemical plant simulation using double collocation

A method has been constructed for the solution of a wide range of chemical plant simulation models including differential equations and optimization. Double orthogonal collocation on finite elements is applied to convert the model into an NLP problem that is solved either by the VF 13AD package based on successive quadratic programming, or by the GRG2 package, based on the generalized reduced gradient method. This approach is termed simultaneous optimization and solution strategy. The objective functional can contain integral terms. The state and control variables can have time delays. Equalities and inequalities containing state and control variables can be included into the model as well as algebraic equations and inequalities. The maximum number of independent variables is 2. Problems containing 3 independent variables can be transformed into problems having 2 independent variables using finite differencing. The maximum number of NLP variables and constraints is 1500. The method is also suitable for solving ordinary and partial differential equations. The state functions are approximated by a linear combination of Lagrange interpolation polynomials. The control function can either be approximated by a linear combination of Lagrange interpolation polynomials or by a piecewise constant function over finite elements. The number of internal collocation points can vary by finite elements. The residual error is evaluated at arbitrarily chosen equidistant grid-points, thus enabling the user to check the accuracy of the solution between collocation points, where the solution is exact. The solution functions can be tabulated. There is an option to use control vector parameterization to solve optimization problems containing initial value ordinary differential equations. When there are many differential equations or the upper integration limit should be selected optimally then this approach should be used. The portability of the package has been addressed converting the package from V AX FORTRAN 77 into IBM PC FORTRAN 77 and into SUN SPARC 2000 FORTRAN 77. Computer runs have shown that the method can reproduce optimization problems published in the literature. The GRG2 and the VF I 3AD packages, integrated into the optimization package, proved to be robust and reliable. The package contains an executive module, a module performing control vector parameterization and 2 nonlinear problem solver modules, GRG2 and VF I 3AD. There is a stand-alone module that converts the differential-algebraic optimization problem into a nonlinear programming problem.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Mechanisms of chemical and physical transdermal penetration enhancement

The underlying theme of this thesis is one of exploring the processes involved in the enhancement of percutaneous absorption. The development of an attenuated total reflectance Fourier-Transform infrared (ATR-FTIR) spectroscopic method to analyse diffusion of suitable topically applied compounds in membrane is described. Diffusion coefficients (D/h2) and membrane solubility (AO) for topically applied compounds were determined using a solution to Fick's second law of diffusion. This method was employed to determine the diffusional characteristics of a model permeant, 4-cyanophenol (CP), across silicone membrane as a function of formulation applied and permeant physicochemical properties. The formulations applied were able to either affect CP diffusivity and/or its membrane solubility in the membrane; such parameters partially correlated with permeant physicochemical properties in each formulation. The interplay during the diffusion process between drug, enhancer and vehicle in stratum corneum (SC) was examined. When enhancers were added to the applied formulations, CP diffusivity and solubility were significantly enhanced when compared to the neat propylene glycol (PG) application. Enhancers did not affect PG diffusivity in SC but enhancers did affect PG solubility in SC. PG diffusion closely resembled that of CP, implying that the respective transport processes were inter-related. Additionally, a synergistic effect, which increases CP diffusivity and membrane solubility in SC, was found to occur between PG and water. Using 12-azidooleic acid (AOA) as an IR active probe for oleic acid, the simultaneous penetration of CP, AOA and PG into human stratum corneum was determined. It was found that the diffusion profiles for all three permeants were similar. This indicated that the diffusion of each species through SC was closely related and most likely occurred via the same route or SC microenvironment.

SQUID magnetometry as a tool for following a clock reaction in solution

SQUID magnetometry, normally used to characterise the properties of solids, was used to follow a clock reaction in solution, namely the auto-catalytic oxidation of [Co(ii)EDTA] by HO, in real time and it was shown that, in combination with other methods (e.g., magnetic resonance proton relaxation studies and UV-vis absorption analysis), SQUID magnetometry can be a powerful method in elucidating and interpreting the time-profile of chemical reactions so as long as reactants, intermediates and products have suitably large differences in their respective magnetic susceptibilities. © 2009 The Royal Society of Chemistry.

A finite-element method for the solution of turbine-generation end-zone fields

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Furnace chemical vapor deposition (FCVD) method for special optical fibers fabrication

The features of the Furnace Chemical Vapor Deposition (FCVD) method of manufacturing preforms for special optical fibers are considered. It is shown that misalignment of substrate silica tube and furnace hole axes has a negative effect on the quality of fabricated preforms, leading to angular and radial asymmetry of the refractive index profile. Ways of getting rid of this and other disadvantages of the FCVD method are described. Some advantages of the FCVD method over the MCVD method are shown. It was demonstrated that the FCVD method, despite some drawbacks, allows to manufacture high-quality fiber preforms with good symmetry of the refractive index profile, and thus it is promising for fabrication of dispersion, dispersion varying and active fibers. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.