A Hybrid Mode Model of the Blazhko Effect, Shown to Accurately Fit Kepler Data for RR Lyr

The waveform for Blazhko stars can be substantially different during the ascending and descending parts of the Blazhko cycle. A hybrid model, consisting of two component oscillators of the same frequency, is proposed as a means to fit the data over the entire cycle. One component exhibits a sawtooth-like velocity waveform while the other is nearly sinusoidal. One method of generating such a hybrid is presented: a nonlinear model is developed for the first overtone mode, which, if excited to large amplitude, is found to drop strongly in frequency and become highly non-sinusoidal. If the frequency drops sufficiently to become equal to the fundamental frequency, the two can become phase locked and form the desired hybrid. A relationship is assumed between the hybrid mode velocity and the observed light curve, which is approximated as a power series. An accurate fit of the hybrid model is made to actual Kepler data for RR Lyr. The sinusoidal component may tend to stabilize the period of the hybrid which is found in real Blazhko data to be extremely stable. It is proposed that the variations in amplitude and phase might result from a nonlinear interaction with a third mode, possibly a nonradial mode at 3/2 the fundamental frequency. The hybrid model also applies to non-Blazhko RRab stars and provides an explanation for the light curve bump. A method to estimate the surface gravity is also proposed.Comment: No major changes. Emphasizes the ability of the hybrid mode to explain changes in the pulsation waveform throughout the Blazhko cycle that may otherwise be problematic. Notes that first-overtone/fundamental combination is just one possible means to generate the hybrid and suggests alternatives. Notes similarity of bump generation in this model to the resonance mechanism in bump Cepheid

Constant distortion embeddings of Symmetric Diversities

Diversities are like metric spaces, except that every finite subset, instead of just every pair of points, is assigned a value. Just as there is a theory of minimal distortion embeddings of finite metric spaces into $L_1$, there is a similar, yet undeveloped, theory for embedding finite diversities into the diversity analogue of $L_1$ spaces. In the metric case, it is well known that an $n$-point metric space can be embedded into $L_1$ with $\mathcal{O}(\log n)$ distortion. For diversities, the optimal distortion is unknown. Here, we establish the surprising result that symmetric diversities, those in which the diversity (value) assigned to a set depends only on its cardinality, can be embedded in $L_1$ with constant distortion.Comment: 14 pages, 3 figure

Diversities and the Geometry of Hypergraphs

The embedding of finite metrics in $\ell_1$ has become a fundamental tool for both combinatorial optimization and large-scale data analysis. One important application is to network flow problems in which there is close relation between max-flow min-cut theorems and the minimal distortion embeddings of metrics into $\ell_1$. Here we show that this theory can be generalized considerably to encompass Steiner tree packing problems in both graphs and hypergraphs. Instead of the theory of $\ell_1$ metrics and minimal distortion embeddings, the parallel is the theory of diversities recently introduced by Bryant and Tupper, and the corresponding theory of $\ell_1$ diversities and embeddings which we develop here.Comment: 19 pages, no figures. This version: further small correction

Large area solar cells from lunar materials

The first goal of the project was to produce polymers from materials available on the Moon. This, apparently simple, aim is made complicated by the fact that there is no carbon on the Moon and there are no polymers (with a couple of irrelevant exceptions) known which do not contain carbon. Because of the abundance of silicon and oxygen in the lunar regolith, it was decided to aim to produce siloxane polymers with the (-Si-O-) backbone found in silicones. A univalent side group is also needed but there are no univalent elements available in the regolith which could plausibly make stable structures. Failing this, hydrogen is a good choice for side group since it accounts for a small fraction of the total weight of the polymer. Thus, a group of target structures such as (-SiH2-O-)n, (-Si(OH)2-O-)n is determined. This goal was approached via a series of simpler syntheses. During the first year, polydimethylsiloxane (-Si(CH3)2-O-)n was made by controlled hydrolysis of SiCl2(CH3)2, which is a routine synthesis, and then an attempt was made to make polydichlorosiloxane by controlled hydrolysis of SiCl4. At the end of the first year, some infra-red spectra indicated that this product had been obtained

The development and use of off-shore mineral exploration techniques

Imperial Users onl

Proclivities of the Common Southern WASP

A hybrid collection of poems and creative nonfiction essays exploring the author\u27s relationship with his father and the American South