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

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

Stress and Fracture Analyses Under Elastic-plastic and Creep Conditions: Some Basic Developments and Computational Approaches

A new hybrid-stress finite element algorith, suitable for analyses of large quasi-static deformations of inelastic solids, is presented. Principal variables in the formulation are the nominal stress-rate and spin. A such, a consistent reformulation of the constitutive equation is necessary, and is discussed. The finite element equations give rise to an initial value problem. Time integration has been accomplished by Euler and Runge-Kutta schemes and the superior accuracy of the higher order schemes is noted. In the course of integration of stress in time, it has been demonstrated that classical schemes such as Euler's and Runge-Kutta may lead to strong frame-dependence. As a remedy, modified integration schemes are proposed and the potential of the new schemes for suppressing frame dependence of numerically integrated stress is demonstrated. The topic of the development of valid creep fracture criteria is also addressed

Generalized Solutions for Quantum Mechanical Oscillator on K\"{a}hler Conifold

We study the possible generalized boundary conditions and the corresponding solutions for the quantum mechanical oscillator model on K\"{a}hler conifold. We perform it by self-adjoint extension of the the initial domain of the effective radial Hamiltonian. Remarkable effect of this generalized boundary condition is that at certain boundary condition the orbital angular momentum degeneracy is restored! We also recover the known spectrum in our formulation, which of course correspond to some other boundary condition.Comment: 7 pages, latex, no figur

Tidal Dissipation in WASP-12

WASP-12 is a hot Jupiter system with an orbital period of $P= 1.1\textrm{ day}$, making it one of the shortest-period giant planets known. Recent transit timing observations by Maciejewski et al. (2016) and Patra et al. (2017) find a decreasing period with $P/|\dot{P}| = 3.2\textrm{ Myr}$. This has been interpreted as evidence of either orbital decay due to tidal dissipation or a long term oscillation of the apparent period due to apsidal precession. Here we consider the possibility that it is orbital decay. We show that the parameters of the host star are consistent with either a $M_\ast \simeq 1.3 M_\odot$ main sequence star or a $M_\ast \simeq 1.2 M_\odot$ subgiant. We find that if the star is on the main sequence, the tidal dissipation is too inefficient to explain the observed $\dot{P}$. However, if it is a subgiant, the tidal dissipation is significantly enhanced due to nonlinear wave breaking of the dynamical tide near the star's center. The subgiant models have a tidal quality factor $Q_\ast'\simeq 2\times10^5$ and an orbital decay rate that agrees well with the observed $\dot{P}$. It would also explain why the planet survived for $\simeq 3\textrm{ Gyr}$ while the star was on the main sequence and yet is now inspiraling on a 3 Myr timescale. Although this suggests that we are witnessing the last $\sim 0.1\%$ of the planet's life, the probability of such a detection is a few percent given the observed sample of $\simeq 30$ hot Jupiters in $P1.2 M_\odot$ hosts.Comment: 6 pages, 3 figures, accepted to ApJ Letter

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

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