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By Gerald Warnecke

The concern examine software research and Numerics for Conservation legislation used to be funded by means of the German examine starting place Deutsche Forschungsgemeinschaft (DFG) for a interval of six years beginning in 1997. the range of issues, represented within the current booklet, used to be one of many energy of the examine application. learn teams of very various history, such a lot of which have been interacting for the 1st time, contributed to this interdisciplinary paintings. the current publication comprises contributions from interlinked engaging tasks starting from the research of hyperbolic platforms of first order partial differential equations, the improvement of better numerical equipment for those equations to purposes in astrophysics and engineering. It goals at conveying their effects accomplished within the software to readers outdoors in their personal specific box. The ebook features a huge variety of figures and a couple of colour plates. The reader can locate an up to date presentation of many present learn issues within the box.

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Because nuclear reactors have a compact design and because of the great distance from the sun, nuclear power is the only reasonable energy source for interplanetary flights to the outer solar system so that MPD self–field engines – besides nuclear thermal rockets – represent an advantageous propulsion concept due to their high exhaust velocity and high thrust density. Since the 1980s MPD thrusters have been investigated experimentally [Weg94, ABH98], theoretically [Wag94, Kae91] and numerically [Sle92, Sle98, Boi99] at IRS.

Notice that H(η, ξ) = H(η, Rn ξ) for n ∈ Z. The set of hexagons H(η, ξ) is denoted as H. ( a) Fig. 3. Some regular hexagons in Gh . 2 A hexagonal collision model Assume H ∈ H to be given by the six-tupel H = H(η, ξ)=(g ˆ 0 , . . , g5 ) (44) with gi = η + Ri ξ . (45) A binary hexagonal collision model is given by the collision relation (gi , gi+3 ) → (gj , gj+3 ) (46) which maps opposite pairs (gi , gi+3 ) of velocities with equal probability into one of the other opposite pairs. The corresponding collision operator reads ⎞ ⎛ 2 1 (47) JH,bin [fH , fH ]i = γH,bin ⎝ · fj fj+3 − fi f(i+3) mod 6 ⎠ , 3 j=0 where the indices 0, .

51) 56 H. Babovsky Then π, Jbin [f , f ] = v,w∈Gh kh (v, w) ( π, µ(v, w) − π(v)) f (v)f (w) (52) Unfortunately, Jbin contains – besides the physically correct invariants mass, momenta and kinetic energy – a further invariant sign, f . To suppress this, we are forced to introduce an additional ternary collision operator. Its restriction onto one single hexagon H ∈ H reads JH,ter [fH , fH , fH ]i = γter · (−1)i (f1 f3 f5 − f0 f2 f4 ) , (53) and its weak version is πH , JH,ter [fH , fH , fH ] = γH,ter ·sign(g0 )· πH , sign ·(f1 f3 f5 −f0 f2 f4 ) .

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