Mean spectral distribution

From the wavelet coefficients Ttl,[x](a, b) one can calculate the energy density Ethree-dimensional surface E(l,[x](a, t). Sections of this surface at fixed time moments t = b define the local energy spectrum Ev[x](f, t) with / = a 1. Finally, in order to obtain the mean spectral distribution of the time series x t) we may consider a so-called scalogram, i.e., the time-averaged energy spectrum. This is analogous to the classic Fourier spectrum. 

A means for describing the volumetric efficiency of a flare is the radiant energy per steradian per unit flare volume (W-sec/ster cm3), the RED (Ref 133, p 227), such that the RED, the bum time of the flare and the curve of the spectral distribution constitutey for most purposes, 2 full description of a flare... 

As a result, the basic problem - that of spectral distribution of the radiation - could not be attacked with.the new equipment. The tests were conducted, however, with an improved apparatus described in Progr Repts No 10 11 and the following mean results were obtd 4900°K for Tetryl and 4000°K for NG... 

The spectral distribution of the radiation at the earth surface Is only weakly related to the spectral distribution outside the atmosphere. This means that a measurement of the spectral distribution and spaclal distribution will usually be required at a site to determine the available energy flux. 

Fig. 1. The theoretical extraterrestrial solar spectral distribution (at the top of the Earth s atmosphere at the mean Earth-Sun distance of one astronomical unit) of Kurucz at high and low...

Figure 5. Spectral distribution of radiant energy from the sun at Sunspot, N. M. Mean for 4 clear days In June 1955...

In order to imderstand this important property of Fourier transform spectroscopy, let us consider a broad spectrum over a wide wave number range with one narrow absorption line in it (cf. Fig. 12). Then, according to the rules of Fourier transformation, the broad spectrum produces an interferogram with highly damped oscillation. The maximum amplitude of the oscillation and also the mean value of the interferogram are equal to the total intensity or to the area under the spectral distribution [see Appdx 1 and Eqs. (A 1.1) and (A 1.2)] ... 

Fig. 4. Hole spectral function for different momenta below fcp. As in a finite nucleus, one observes that the closer a sp state is to the mean-field Fermi energy, the sharper peaked the spectral distribution becomes.

M series lines can also be used for initial identification or verification, but unlike the majority of the K and L series, the spectral distribution and specific line intensities of M series lines are variable. This is because many M lines originate from partially filled atomic orbitals or in some cases from molecular orbitals. Although this problem is by no means unique to the M line series, it can be particularly severe in this case. 

Amplitudes of density fluctuations at different wavelengths follow independent Gaussian (also called normal) statistics (see Sect. 9.3.6, Chap. 9, Vol. 1), and their mean spectral power is distributed in an almost scale-invariant manner, described above. The absolute normalization was determined by the COBE satellite to be 1 part in 100,000. Their evolution can be analyzed initially with the help of the linearized gravitational equations. The classical analysis, originally performed by Jeans (1902), leads to the conclusion that fluctuations above the Jeans-scale are unstable and they are at the origin of the formation of the oldest structures (for a modern textbook on the subject, see Peacock 1999). 

An excited atom can emit its excitation energy as spontaneous radiation (Sect. 2.7). In order to investigate the spectral distribution of this spontaneous emission on a transition Ei Ek, v/t shall describe the excited atomic electron by the classical model of a damped harmonic oscillator with frequency co, mass m, and restoring force constant k. The radiative energy loss results in a damping of the oscillation described by the damping constant y. We shall see, however, that for real atoms the damping is extremely small, which means that y 0). ... 

The spectral distribution of the light can be measured by means of the fluorescence generated by the VUV light in a thin layer of sodium salicylate facing the monochromator exit slit. A photomultiplier is used to detect the fluorescence at 420 nm. For the estimation of the energy threshold, the normalized current is fitted to the photon energy by an empirical power function of the form... 

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