Introduction to molecular beams gas dynamics

Introduction to Molecular Beams Gas Dynamics

Volumn , Issue , 2005, Pages 1-383

  Sanna, Giovanni ^a   Tomassetti, Giuseppe ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

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Indexed keywords

EID: 84967663219     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/P387     Document Type: Book

References (142)

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12. z only.
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21. The function f(r, v, t) satisfying to the Boltzmann equation is generally normalised to the density n(r, t), while the Maxwellian distribution [Eq. (1.8.3)] is normalised to the unity. This is why we use the term n(r, t) in Eq. (1.14.11).
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56. The density p here introduced is the mass density. This latter is related to the numeric density n by the relation p = nm, where m is the molecular mass. From the macroscopic point of view, the density p can be defined by where ΔM is the mass of fluid contained in the element ΔV. Practically, the limit ΔV→0 must be substituted by the limit ΔV→δV, δV is the smallest volume satisfying to the continuum condition.
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59. Also in this case it holds for the limit ΔV→0 the observation made in, The density p here introduced is the mass density. This latter is related to the numeric density n by the relation p = nm, where m is the molecular mass. From the macroscopic point of view, the density p can be defined by where ΔM is the mass of fluid contained in the element ΔV. Practically, the limit ΔV→0 must be substituted by the limit ΔV→δV, δV is the smallest volume satisfying to the continuum condition.
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68. The subject of the “shock waves” will be extensively discussed in Chap. 6.
69. In the four cases corresponding to the possible combinations of u > 0 or < 0 and IUI > a or < a shown in the figure there are real characteristics. As we shall see later (see Secs. 5.2 and 5.3 Case ii), this comes from the circumstance that the differential equation system (4.6.1) is of “hyperbolic” type. From this fact it follows that the differential equations (4.6.8;9) of the characteristics have real solutions both for the subsonic and supersonic flows. In other cases [see the Case iii] of Sec. 5.31 the differential equations of the characteristics have real solutions only for the supersonic flow.
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77. i, and an averaged value of M in the same element. However, the differences between this value and those considered in the text vanish for n→∞.
78. + family can appear in the solution of the problem.
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