We discuss the solution of linear second order differential-algebraic equations (DAEs) with variable coefficients. Since index reduction and order reduction for higher order, higher index differential-algebraic systems do not commute, appropriate index reduction methods for higher order DAEs are required. We present an index reduction method based on derivative arrays that allows to determine a...

It is shown that by making straightforward approximations it is possible to simplify the analysis of the measurements of a well-established dual-waveguide interferometer for sensor applications. In particular we derive approximate algebraic formulae for the mode phase shifts that are measured in the interferometric sensor when a layer of the entity to be detected is deposited. Knowledge of the ...

1994 Abstract. We propose a new approach to diierential-algebraic systems based on the formal theory of partial diierential systems. This results in a new deenition of the index of the system, which is similar to but more general than the one proposed recently by Rabier and Rheinboldt. This index, however, is not related to the numerical diiculty of solving the system, but to the amount of symb...

The paper presents the results of numerical analyses of the structures of integrated optics in the form of planar waveguides made of materials with high values of the refractive index n = 2.00 and with an input-output system in the form of Bragg grating couplers. The numerical investigations were carried out by using the FDTD method (Finite Difference Time Domain method).

Stock market price index prediction is a challenging task for investors and scholars. Artificial neural networks have been widely employed to predict financial stock market levels thanks to their ability to model nonlinear functions. The accuracy of backpropagation neural networks trained with different heuristic and numerical algorithms is measured for comparison purpose. It is found that nume...

Numerical methods for design sensitivity analysis of multibody dynamics are presented. An analysis of the index-3 adjoint differential-algebraic equations is conducted and stability of the integration of the adjoint differential-algebraic equations in the backward direction is proven. Stabilized index-1 formulations are presented and convergence of backward differentiation formulas is shown for...

A numerical model based on a scalar beam propagation method is applied to study light transmission in photonic bandgap (PBG) waveguides. The similarity between a cylindrical waveguide with concentric layers of different indices and an analogous planar waveguide is demonstrated by comparing their transmission spectra that are numerically shown to have coinciding wavelengths for their respective ...

Large Eddy Simulations of the flow through a hydrocyclone are used to demonstrate that the Grid Convergence Index (GCI) is a practical method of accounting for numerical uncertainty. The small values of GCI (<7.2%) associated with the tangential velocity predictions suggest that numerical uncertainty due to discretization error does not greatly contribute to the disagreement between simulation ...

The design and experimental demonstration of an open cavity in the microwave region is presented. The resonance condition is achieved through the cancellation of lightpaths in positive and negative refractive index materials. The positive index material is a structured aluminium surface supporting a spoof surface plasmon mode, and the negative index material is a photonic crystal made of alumin...

We design an all-dielectric Lüneburg lens as an adiabatic space-variant lattice explicitly accounting for finite film thickness. We describe an all-analytical approach to compensate for the finite height of subwavelength dielectric structures in the pass-band regime. This method calculates the effective refractive index of the infinite-height lattice from effective medium theory, then embeds a ...