Advances in kinetic theory and computing : selected papers by Perthame B. (ed.)

By Perthame B. (ed.)

This paintings comprises 36 brief papers on development in various topics in mathematical and theoretical physics, written for the complaints of a symposium in honor of the seventieth birthday of Professor F.Y. Wu, held on the Nankai Institute of arithmetic, October 7-11, 2001. the gathering of papers is aimed toward researchers, together with graduate scholars, with an interdisciplinary curiosity and provides a short creation to a number of the subject matters of present curiosity. those contain effects on precisely solvable types in statistical mechanics, integrable in the course of the Yang-Baxter equations, quantum teams, fractional information, random matrices, index theorems at the lattice, and different comparable issues I. Vlasov-Poisson in plasma physics -- II. Quantum mechanics and semiconductors -- III. Boltzmann equations and fuel dynamics

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31) i f n(X{t,y))J(t,y) does not depend on t. ((,J/} be a smooth function on O, which vanishes on a neighbourhood of the boundary dO a n d let %X~ We have : J ftMX(t y))J(t,y)} (t,y)dtdS(y). y)) - (t,y). y)eO. 54) does not depend on (. y). 57) 0 mai we have, by the Green formula: J^n{X(t,y))J{t )^(t,y)dtdS(y) >y = - j n(X(0,»)) J ( 0 , y ) v ( 0 , y) dS(y). 45) f JTO (M(&,Ks))#*)<&Ce) = " f n(X(Q,y))J(0,y) (0,y)dS(y). 60). 5. The multidimensional laminar Child-Langmuir problem We now summarize the m u l t i d i m e n s i o n a l C h i l d - L a n g m u i r problem under the ass u m p t i o n of laminar beam.

3 (1931). pp 191-257. [20) J. D. Lawson, The physics of charged-particle beams. International Series of monographs on physics n75, Oxford University Press, Oxford, 1983[21] F. Poupaud, Boundary Value Problems for the stationary Vlasov-Maxwell System, Forum Mathematicum, 777. |22| T . Weisterman, A particle-in-cetl method as a tool for diode simulations, Nuclear Instruments and Methods in Physics Research A 260 (1988), pp. 271-279. 45 EULERIAN CODES FOR THE VLASOV EQUATION 2 M R. F E L X ' . P .

V) = / " ( r - v > A / / 2 . 6) It must be pointed out that substituting successively Eqs. (2 5) and (2 4) into (2 6), we obtain f*'(x,v) with x-x-v&i/2. 7) Thus we find that Eq. (2 7) is equivalent to the following integrated equations o f the characteristics o f Eq. e. 5) Different methods can be used. Cubic spline interpolation in the v-space and Fourier interpolation in x-space (without using Fast Fourier Transform) have been used by Cheng and Knorr [12], which requires, in the x direction, an execution time proportional to N, (where is the number o f points in the spatial direction).

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