Raleigh line

The probability of Raman scattering is quite small. This normally requires the use of intense laser sources and concentrated samples. A high-resolution double or triple monochromator is used to separate the Raman lines from the intense Raleigh line. 

Extension of the hydrodynamic theory to explain the variation of detonation velocity with cartridge diameter takes place in two stages. First, the structure of the reaction zone is studied to allow for the fact that the chemical reaction takes place in a finite time secondly, the effect of lateral losses on these reactions is studied. A simplified case neglecting the effects of heat conduction or diffusion and of viscosity is shown in Fig. 2.5. The Rankine-Hugoniot curves for the unreacted explosive and for the detonation products are shown, together with the Raleigh line. In the reaction zone the explosive is suddenly compressed from its initial state at... 

The p(V) diagram shows the shock adiabat of the explosive, which is also called the Hugoniot curve or Hugoniot adiabat (see Fig. 1.22). The shock adiabat can be calculated for both the non-reacted explosive as well as for the reaction products (see Fig. 1.22). The C-J point, which represents the point where the C-J conditions are fulfilled, is therefore the point where the shock adiabat of the reaction products touches the Raleigh line (tangent), which is described by the following equation ... 

At the point where the Raleigh line touches the schock adiabate of the reaction products the slope of both functions is the same, and the following relationship, where U is the velocity of the products, is valid ... 

Since the Hugoniot represents the locus of all possible states behind the shock front, then a line joining the initial and final states on the P-v Hugoniot represents the jump condition. This line is called the Raleigh line and is shown in Figure 17.3. If we eliminate the particle velocity term u by manipulating the mass- and momentum-jump equations, and let mq = 0, we get... 

This is the equation of the Raleigh line, and we see that the slope of this line is - V lvl, or -poU. If we know the initial and final P-v states of a shock, then we can calculate the shock velocity by taking the slope of the Raleigh line U = -(slope) %o-... 

The second wavelet drops the pressure from P to P3 (ambient or Pq)- These two steps are shown on the P-v plane in Figure 19.2. We allow wavelet 1 to jump from Pi to P2, likewise wavelet 2 from P2 to P3. Look at the Raleigh lines for each of these jumps. Remembering that the slope of the Raleigh line is - (f/ /uo) we see that wavelet I has a higher slope than at the shock front it is traveling faster than the shock The slope of wavelet 2 Raleigh line is lower than... 

Here, po is the material density of the unreacted explosive, u is the impact velocity and V and are the specific volumes. The Raleigh line is a straight line with the slope D l V connecting (16,Po), VuPi) and (V2,p2) in thep V) diagram. 

Ljungkvist ASE, Bussink J, Kaanders JHAM, Rijken PFJW, Begg AC, Raleigh JA, van der Kogel AJ (2005) Hypoxic cell turnover in different solid tumor lines. Int J Radiat Oncol Biol Phys 62 1157-1168... 

A. Hamid and W.F. McClure, Software for an on-line computerized spectrometer. NCARS Bulletin No. 252, North Carolina State University, Raleigh, NC (1978). 

Eq. (3.45), then the slopes dS /dq and d5 /dcm of the two lines at the origin would give i g/3 and 2A2] the limiting value S q = 0, Cm = 0) would furnish N. Actually, in experiments directly measurable quantities such as the Raleigh ratio E and the weight concentration are usually employed, rather than S and Cm- Corresponding substitutions can be carried out in Eq. (3.45) which is then converted to... 

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