The Cauchy Problem for the Wave Equation in the Schwarzschild Geometry

The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. We derive an integral spectral representation for the solution and prove pointwise decay in time.Comment: 33 page

Impact of the tidal p-g instability on the gravitational wave signal from coalescing binary neutron stars

Recent studies suggest that coalescing neutron stars are subject to a fluid instability involving the nonlinear coupling of the tide to $p$-modes and $g$-modes. Its influence on the inspiral dynamics and thus the gravitational wave signal is, however, uncertain because we do not know precisely how the instability saturates. Here we construct a simple, physically motivated model of the saturation that allows us to explore the instability's impact as a function of the model parameters. We find that for plausible assumptions about the saturation, current gravitational wave detectors might miss $> 70\%$ of events if only point particle waveforms are used. Parameters such as the chirp mass, component masses, and luminosity distance might also be significantly biased. On the other hand, we find that relatively simple modifications to the point particle waveform can alleviate these problems and enhance the science that emerges from the detection of binary neutron stars.Comment: 15 pages, 12 figures, 1 tabl

On and Off-diagonal Sturmian operator: dynamic and spectral dimension

We study two versions of quasicrystal model, both subcases of Jacobi matrices. For Off-diagonal model, we show an upper bound of dynamical exponent and the norm of the transfer matrix. We apply this result to the Off-diagonal Fibonacci Hamiltonian and obtain a sub-ballistic bound for coupling large enough. In diagonal case, we improve previous lower bounds on the fractal box-counting dimension of the spectrum.Comment: arXiv admin note: text overlap with arXiv:math-ph/0502044 and arXiv:0807.3024 by other author

Providing value to a business using a lightweight design system to support knowledge reuse by designers

This paper describes an alternative approach to knowledge based systems in engineering than traditional geometry or explicit knowledge focused systems. Past systems have supported product optimisation rather than creative solutions and provide little benefit to businesses for bespoke and low volume products or products which do not benefit from optimisation. The approach here addresses this by supporting the creativity of designers through codified tacit knowledge and encouraging knowledge reuse for bespoke product development, in particular for small to medium sized enterprises. The implementation and evaluation of the approach is described within a company producing bespoke fixtures and tooling in shorter than average lead times. The active support of knowledge management in the company is intended to add value to the business by further reducing the lead times of the designs and creating a positive impact to business processes. The evaluation demonstrates a viable alternative framework to the traditional management of knowledge in engineering, which could be implemented by other small to medium enterprises

Some Hamiltonian Models of Friction

Mathematical results on some models describing the motion of a tracer particle through a Bose-Einstein condensate are described. In the limit of a very dense, very weakly interacting Bose gas and for a very large particle mass, the dynamics of the coupled system is determined by classical non-linear Hamiltonian equations of motion. The particle's motion exhibits deceleration corresponding to friction (with memory) caused by the emission of Cerenkov radiation of gapless modes into the gas. Precise results are stated and outlines of proofs are presented. Some technical details are deferred to forthcoming papers.Comment: 19 Pages, 1 figur

Wing/store flutter with nonlinear pylon stiffness

Recent wind tunnel tests and analytical studies show that a store mounted on a pylon with soft pitch stiffness provides substantial increase in flutter speed of fighter aircraft and reduces dependency of flutter on mass and inertia of the store. This concept, termed the decoupler pylon, utilizes a low frequency control system to maintain pitch alignment of the store during maneuvers and changing flight conditions. Under rapidly changing transient loads, however, the alignment control system may allow the store to momentarily bottom against a relatively stiff backup structure in which case the pylon stiffness acts as a hardening nonlinear spring. Such structural nonlinearities are known to affect not only the flutter speed but also the basic behavior of the instability. The influence of pylon stiffness nonlinearities or the flutter characteristics of wing mounted external stores is examined

The Upland Monitor: August 9, 1917

The August 9, 1917 edition of The Upland Monitor.https://pillars.taylor.edu/monitor-1917-1918/1021/thumbnail.jp

The Upland Monitor: November 22, 1917

The November 22, 1917 edition of The Upland Monitor.https://pillars.taylor.edu/monitor-1917-1918/1036/thumbnail.jp