Radian

About: Radian is a research topic. Over the lifetime, 718 publications have been published within this topic receiving 3475 citations. The topic is also known as: rad.

On the flow due to a rotating disk

Abstract: The von Karman (1921) rotating disk problem is extended to the case of flow started impulsively from rest; also, the steady-state problem is solved to a higher degree of accuracy than previously by a simple analytical-numerical method which avoids the matching difficulties in Cochran's (1934) well-known solution. Exact representations of the non-steady velocity field and pressure are given by suitable power-series expansions in the angle of rotation, Ωt, with coefficients that are functions of a similarity variable. The first four equations for velocity coefficient functions are solved exactly in closed form, and the next six by numerical integration. This gives four terms in the series for the primary flow and three terms in each series for the secondary flow.The results indicate that the asymptotic steady state is approached after about 2 radians of the disk's motion and that it can be approximately obtained from the initial-value, time-dependent analysis. Furthermore, the non-steady flow has three phases, the first two of which are accurately and fully described with the terms computed. During the first-half radian (phase 1), the velocity field is essentially similar in time, with boundary-layer thickening the only significant effect. For 0·5 [lsim ] Ωt [lsim ] 1·5 (phase 2), boundary-layer growth continues at a slower rate, but simultaneously the velocity profiles adjust towards the shape of the ultimate steady-state profiles. At about Ωt = 1·5, some flow quantities overshoot the steady-state values by small amounts. In analogy with the ‘Greenspan-Howard problem’ (1963) it is believed that the third phase (Ωt > 1·5) consists of a small amplitude decaying oscillation about the steady-state solution.

High-accuracy waveforms for binary black hole inspiral, merger, and ringdown

Abstract: The first spectral numerical simulations of 16 orbits, merger, and ringdown of an equal-mass nonspinning binary black hole system are presented. Gravitational waveforms from these simulations have accumulated numerical phase errors through ringdown of <~0.1 radian when measured from the beginning of the simulation, and <~0.02 radian when waveforms are time and phase shifted to agree at the peak amplitude. The waveform seen by an observer at infinity is determined from waveforms computed at finite radii by an extrapolation process accurate to <~0.01 radian in phase. The phase difference between this waveform at infinity and the waveform measured at a finite radius of r=100M is about half a radian. The ratio of final mass to initial mass is Mf/M=0.951 62±0.000 02, and the final black hole spin is Sf/Mf^2=0.686 46±0.000 04.

X-ray phase imaging : demonstration of extended conditions with homogeneous objects

Abstract: We discuss contrast formation in a propagating x-ray beam. We consider the validity conditions for linear relations based on the transport-of-intensity equation (TIE) and on contrast transfer functions (CTFs). From a single diffracted image, we recover the thickness of a homogeneous object which has substantial absorption and a phase-shift of --0.37 radian.