Analytical and numerical study on grating depth effects in grating coupled waveguide sensors

The in-coupling process for grating-coupled planar optical waveguide sensors is investigated in the case of TE waves. A simple analytical model based on the Rayleigh–Fourier–Kiselev method is applied to take into account the depth of the grating coupler, which is usually neglected in the modeling. Analytical expressions are derived both for the position and width of the in-coupling peaks to illustrate the effects of grating depth on the guided mode resonances in grating coupled waveguide sensors. Numerical computations verify the model for shallow gratings both in terms of peak shape and position and provide the limitations for the analytical formulas.     

Enantioselective synthesis of the carbacephem antibiotic loracarbef via Mitsunobu and Dieckmann cyclization from an unnatural amino acid

The nucleus of the carbacephem antibiotic loracarbef was synthesized in a highly efficient and enantioselective fashion from 2S,3S-2-amino-3-hydroxy-6-heptenoic acid (AHHA), which was derived from enzyme-catalyzed condensation of glycine and 4-pentenaldehyde. The bicyclic framework of this compound was established through sequential Mitsunobu reaction and aldol condensations.     

Finite difference representations of non-linear waves

The work concerns cnoidal and solitary wave solutions of the Boussinesq equations in the context of finite difference methods. The existence of permanent wave-forms is discussed and approximate solutions are found for one particular discrete formulation by perturbation techniques. These techniques can be applied to most difference and regular element discretizations of equations describing weakly non-linear and dispersive waves. No proof of convergence of the perturbation expansions is established, but the appropriateness of the solutions is confirmed through comparison with the results of computer simulations. From the perturbation series it is found that the phase speed of solitons is useless for the evaluation of numerical methods and that asymmetries in the discrete equations may ruin the soliton solution. The availability of a discrete closed-form solution is especially important for discussions concerning the existence and accuracy of permanent wave-forms with oblique orientations relative to the grid.     

On the basic algebraic operations in solvable Lie groups

Summary For a simply connected solvable Lie group we specify the structure of the product, the inverse and the exponential map expressed in suitable coordinates (canonical coordinates of the second kind), and point out that in these coordinates the product and inverse are expressed entirely in terms of polynomials, exponential functions and trigonometric functions. We devise algorithms for computing the product, the inverse and the exponential map.     

Magnetic interaction between ultrafine amorphous Fe1-xCx alloy particles in ferrofluids

Ferrofluids with ultrafine magnetic particles of amorphous Fe_1-xC_x were studied by Mössbauer spectroscopy, transmission electron microscopy and magnetic measurements. Magnetic measurements showed that the initial susceptibility follows a Curie-Weiss law, indicating magnetic interaction between the particles. The influence of the magnetic interaction on the estimation of the particle size, made from the field dependence of the induced hyperfine splitting, is discussed.     

Model of contact between rollers and sprockets in chain-drive systems

A model of a roller-chain drive is developed and applied to the simulation and analysis of roller-chain drives of large marine diesel engines. Two different ways of modelling the contact between the rollers and sprockets are presented; one using a circular shaped tooth profile and the other using the shape of a real tooth profile. The main components of the roller-chain drive model include the sprockets with different sizes and the chain made of rollers and links, which are represented by rigid bodies, mass particles and spring-damper assemblies, respectively. The contact between the rollers and the sprockets are represented by a continuous contact force. The models proposed effectively represent the polygonal effect always present in this type of drive. The numerical results from the simulations are compared with analytical results, for simplified models. The model with a real tooth profile proves superior to the model with a circular tooth profile.The applications represent the ongoing work that resulted from many fruitful discussions with Per Rønnedal, Mikkel Preem et al. of MAN B&W Diesel A/S, Copenhagen, Denmark.     

Influence of boundary conditions on the stability of a column under non-conservative load

The cantilever follower force problem with external damping is extended to a three-parameter case, including a concentrated mass, a linear elastic spring, and a partial follower force at the free end. As a result of the study an unexpected, hitherto unrecognized feature of stability/vibration is identified.Normally, the boundary conditions have great influence on the stability limits. However, it is proved that there exists a force at which the critical frequency is independent of all three boundary parameters. The characteristics of this force/frequency combination are discussed in detail, especially in relation to the corresponding eigenfunctions.Also a direct study of the onset of flutter as a function of the boundary parameters is included.