By Baxter G.P., Hartmann M.L.

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L E TALLEC, P . , AND PERTHAME, B. Microreversible collisions for polyatomic gases and Boltzmann's theorem. European J. Mech. B Fluids 13, 2 (1994), 237-254. 4. CONFORTO, F . , SCHURRER, F . , AND ZIEGLER, I. Steady det- onation waves via the Boltzmann equation for a reacting mixture. J. Phys. : Math. Gen. 36 (2003), 5381-5398. 5. , AND SALVARANI, F . A kinetic model allow- ing to obtain the energy law of polytropic gases in the presence of chemical reactions. Europ. J. Mech. B/Fluids 24 (2005), 219-236.

1) we obtain for v the equation vt = - a A 2 v - Av-2v-3v2-v3. 1) to the u = 1 solution thereof. 2) and also of its derivatives. Using these estimates together with a new interpolation inequality, we then estimate ||v|| in a way that only involves the parameter of our equation and interpolation constants whose values are explicitly known and sharp (which is very important). 3) JQ where the dot denotes differentiation with respect to time. To simplify the notation, from now on we drop the subscript Q in all the integrals but it is understood that all the integrations are done on the unit square Q,.

More details on the numerical schemes and more numerical results can be found in 1. 2. + . If rti(t,x) is the number density of particles of the species i at time t in position x, the link with the probability density function fi is the following: r m(t,x)- / r+00 / JwN Jo fi(t,x,v,l)dvdl. (fu fi) + J2 Q%, (fi} f^ + Qrrct- (2) The left-hand-side of (2) is the classical advection term. In the right-handside, Q^iQ^a and Qleact are the operators corresponding to different kinds of collisions between molecules: mechanical mono-species, mechanical bispecies and chemical collisions, respectively (see 5 for details).

### A Revision of the Atomic Weight of Cadmium (1914)(en)(4s) by Baxter G.P., Hartmann M.L.

by Kenneth

4.2