An alternate derivation of the Herman—Kluk (coherent state) semiclassical initial value representation of the time evolution operator

It is shown that the Herman—Kluk (or coherent state) initial value representation (IVR) of the semiclassical propagator (time evolution operator) can be obtained by application of a modified Filinov filtering procedure to the standard Van Vleck (coordinate space) expression for the propagator. This further illustrates the effective equivalence, semiclassically, of these various IVRs.     

DEVELOPMENT AND VALIDATION OF REACTION WHEEL DISTURBANCE MODELS: EMPIRICAL MODEL

Accurate disturbance models are necessary to predict the effects of vibrations on the performance of precision space-based telescopes, such as the Space Interferometry Mission (SIM). There are many possible disturbance sources on such spacecraft, but mechanical jitter from the reaction wheel assembly (RWA) is anticipated to be the largest. A method has been developed and implemented in the form of a MATLAB toolbox to extract parameters for an empirical disturbance model from RWA micro-vibration data. The disturbance model is based on one that was used to predict the vibration behaviour of the Hubble Space Telescope (HST) wheels and assumes that RWA disturbances consist of discrete harmonics of the wheel speed with amplitudes proportional to the wheel speed squared. The MATLAB toolbox allows the extension of this empirical disturbance model for application to any reaction wheel given steady state vibration data. The toolbox functions are useful for analyzing RWA vibration data, and the model provides a good estimate of the disturbances over most wheel speeds. However, it is shown that the disturbances are under-predicted by a model of this form over some wheel speed ranges. The poor correlation is due to the fact that the empirical model does not account for disturbance amplifications caused by interactions between the harmonics and the structural modes of the wheel. Experimental data from an ITHACO Space Systems E-type reaction wheel are used to illustrate the model development and validation process.     

On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis

A polynomial is said to be of type (p₁, p₂, p₃) relative tothe unit circle if it has p₁ zeros interior to, p₂ on, and p₃exterior to the unit circle. Stability criteria frequently arisewhere a polynomial or a family of polynomials must be shownto be of type (p₁, p₂, 0) or of type (p₁, 0, 0). Here we reconsiderthe practical problem of showing that a polynomial is of oneor other of these types, and we show that the testing of a polynomialof degree n may always be reduced to the testing of one of degreen–1. The simplicity of the method is illustrated by itsapplication to several well known difference schemes for partialdifferential equations.     

A Finite Element Moving Boundary Computation with an Adaptive Mesh

The finite element method is used to obtain an accurate approximationto the solution of a well-known moving boundary problem. Thealgorithm uses the projective nature of the approximate solutionto follow the movement of the boundary, and the element notesare adapted as the region of the solution changes.     

Monte Carlo simulations of an amphiphilic polymer at a hydrophobic/hydrophilic interface

Monte Carlo simulations have been carried out for an off-lattice model of an amphiphilic polymer at a hydrophobic/hydrophilic interface. The model system consists of a polynorbornene backbone with poly(ethylene oxide) (PEO) grafts modelled atomistically at an idealized interface between hydrophobic and hydrophilic regions, which are represented by external potentials. Results are presented for the distribution of PEO chain ends, and the density of PEO segments perpendicular to the surface. The latter is used to provide predictions for neutron reflectivity profiles normal to the surface as a function of the lateral confinement of the PEO grafts. At low surface coverage the simulation results are found to be in good agreement with experimental neutron scattering results from similar polymers studied at the water/air interface.