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Propagation of Radiation
Published in Ronald L. Snell, Stanley E. Kurtz, Jonathan M. Marr, Fundamentals of Radio Astronomy, 2019
Ronald L. Snell, Stanley E. Kurtz, Jonathan M. Marr
A medium's ability to attenuate radiation will depend on the nature of the particles in the medium and also on the density of these particles. It is often convenient to modify Equation 2.1 so that the dependence on the density is shown explicitly. The density can be expressed in terms of a number density (the number of particles per unit volume of space), n, or a mass density (the mass of particles per unit volume of space), ρ. In the former case, we can define another parameter σν which is related to κν by κν=σνn. Then, the decrease in intensity is given by dIν=−Iνoσνnds. Note that the units of σν must be a length squared or an area (e.g. cm2). In fact, in modeling the interactions between the photons and particles in the medium, the parameter σν, which is called the cross-section, Cross-section can be viewed as a measure of the cross-sectional area of a target, i.e., the particle, as viewed by the other interacting particle, in this case the photon, and is a function of frequency.
Gases: comparison with experiment
Published in Michael de Podesta, Understanding the Properties of Matter, 2020
Increasing the pressure of a gas at a fixed temperature implies an increase in the number density of molecules and hence a reduction in the average separation between molecules. This increases the frequency of molecular collisions and interactions, and these interactions restrict the motion of molecules. And so the associated degrees of freedom become inaccessible.
Mass Exchangers
Published in Anthony F. Mills, Heat and Mass Transfer, 2018
Figure 11.7 shows an elemental control volume Δx long, used to derive the equation governing particle concentration through a precipitator. The concentration of particles is expressed in terms of a number density N that has units [m−3] but as a conceptual aid can be assigned units [particles/m3]. The flow of gas in a commercial precipitator is always turbulent, and the characteristic turbulent mixing velocity is quite large compared with the electrical migration velocity, except very close to the electrodes. Thus, we will assume that the particle concentration N is uniform across the channel. The principle of conservation of particles applied to the elemental control volume requires that, at steady state, Rateofinflowofparticles=Rateofdepositionofparticles+RateofoutflowofparticlesNV˙|x=NVEPΔx+NV˙|x+Δx
Equation of state for dense gases from a self-consistent-field approach in the framework of kinetic theory
Published in Radiation Effects and Defects in Solids, 2020
D. Giusti, V. Molinari, D. Mostacci
The Vlasov equation for the distribution function – where r is the position and v the velocity of the generic particle of mass m subjected to the external force F – is written as follows (4, 5) In the above equation, the effect of molecule interaction is accounted through a self-consistent field F′, to be calculated as where is the force that a molecule located at position exerts on the molecule in r and is the local number density at r. It is worth recalling that the assumption that the total potential energy of the system may be expressed as the sum of the potentials between all pairs of molecules is basic to the derivation of Equation (3).
Metastable states and defect density waves in modulated ferroelectrics
Published in Phase Transitions, 2018
The number density of impurity ions is given by Equation (2):with the volume of unit cell V = abc. If all defects are located at DCs, their number per unit area of a DC is obtained as Equation (3):which leads to a decoration of about 0.5 Rb-ions per unit cell cross section ab on each DC for x = 1% and δ = 0.013. Hence, even small amounts of defects are able to hinder the displacements of DC’s efficiently and to affect the phase behaviour. Moreover, the temperature regime of the re-entrant IC-phase is observed to be larger (i.e. the transition temperature on heating is lower) if the misfit parameter δ is smaller. In view of Equation (3) this is due to the fact that the number of defects per DC is increased thus stabilizing the DC-pattern and hence, the INC-phase.
The pseudo-resonant-nuclide subgroup method based global–local self-shielding calculation scheme
Published in Journal of Nuclear Science and Technology, 2018
Zhouyu Liu, Qingming He, Tiejun Zu, Liangzhi Cao, Hongchun Wu, Qian Zhang
A pseudo background nuclide is defined as atomic weight ratio and potential scattering XS is identical to that of 1H. There is no absorption for the pseudo background nuclide. Then a pseudo resonant nuclide is defined for each pin cell in the lattice system or reactor core to be solved as: the energy-dependent XS of the pseudo resonant nuclide is averaged by number densities of all the resonant nuclides; the number density of the pseudo resonant nuclide is where R is the collection of resonant nuclides; is the volume averaged number density for resonant nuclide in fuel region. In the following derivation, the volume-averaged number density will be assumed for the resonant nuclides in fuel regions of the pin cell.