Propagation attenuation factor

In order to compute the thermal radiation effects produced by a burning vapor cloud, it is necessary to know the flame s temperature, size, and dynamics during its propagation through the cloud. Thermal radiation intercepted by an object in the vicinity is determined by the emissive power of the flame (determined by the flame temperature), the flame s emissivity, the view factor, and an atmospheric-attenuation factor. The fundamentals of heat-radiation modeling are described in Section 3.5. 

The real and imaginary parts of the complex propagation constant are called attenuation factor (Np m ) and the phase factor (Rad m ), respectively. They are given by Eqs (64) and (65) ... 

The attenuation factor leads to attenuation of electric field and power during propagation along the z coordinate as described by Eqs. (68) and (69) ... 

The imaginary part of the propagation constant, accounts for the attenuation factor exp (—jSjz) of the modal fields in Table 11-2. If Pj z) is the modal power distance z along the waveguide, then, by substituting these fields into Eq. (1 l-21a), we obtain the expression for power attenuation in terms of the power attenuation coefficient jj, and the initial power Pj 0). 

The imaginary part gives a (hnear) attenuation factor in the propagation of a plane optical wave exp( co/c)n(co)/, where / is the propagation length into the medium. The attenuation constant (co/c)n is usually referred to as the linear absorption constant in units of (length). o( ) is the dispersion of the medium (see Fig. 10.6a). n (co) gives the hnear absorption spectral line shape which is a Lorentzian (see Fig. 10.6b). 

Laser communication systems based on free-space propagation through the atmosphere suffer drawbacks because of factors like atmospheric turbulence and attenuation by rain, snow, haze, or fog. Nevertheless, free-space laser communication systems were developed for many appHcations (89—91). They employ separate components, such as lasers, modulators, collimators, and detectors. Some of the most promising appHcations are for space communications, because the problems of turbulence and opacity in the atmosphere are absent. 

Normalizing the attenuation in this way enables it to be used as an imaginary component of a factor multiplying a real wavenumber in an expression for wave propagation. 

The loss factor r is an important quantity for sound attenuating materials. Eg.11 shows that r is directly related to the attenuation per wavelength for a harmonic wave propagating through the material. An alternate expression for r can be derived in terms of the energy dissipated per one cycle (period) of the sound wave. 

In most of the cases, an ultrasonic wave propagates adiabatically, so the (20) looks more naturally its right-hand side represents the adiabatic (non-relaxed) modulus and non-adiabatic contribution to the dynamic modulus. Recall that the relaxed (or isothermal) modulus should be regarded as quasi-static one. Figure 1 shows the frequency-dependent factor of non-adiabatic contribution as function of cox. One can see that transformation from isothermal-like to adiabatic-like propagation occurs in the vicinity cox = 1. The velocity of ultrasound is increased in this region, while the attenuation reaches its maximum value. 

The amplitude of the SAW is dependent upon time t and propagation path x. The dependency is assumed as exp (i(o)t - /3x)). A complex propagating factor 3 is defined by the wave number k and attenuation a as... 

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