By Perthame B. (ed.)

ISBN-10: 9810216718

ISBN-13: 9789810216719

This paintings comprises 36 brief papers on development in various matters in mathematical and theoretical physics, written for the court cases 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 geared toward researchers, together with graduate scholars, with an interdisciplinary curiosity and provides a quick advent to some of the subject matters of present curiosity. those comprise effects on precisely solvable versions in statistical mechanics, integrable throughout the Yang-Baxter equations, quantum teams, fractional records, random matrices, index theorems at the lattice, and different comparable themes I. Vlasov-Poisson in plasma physics -- II. Quantum mechanics and semiconductors -- III. Boltzmann equations and gasoline dynamics

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**Extra info for Advances in kinetic theory and computing : selected papers**

**Example text**

T h e p r o b l e m is to find 7l(x), l i ( i ) , f{x), satisfying the equations : + V . 61) x E 0. 66) i e r „ - 0 . 68) is made t o insure t h a t i f a characteristics h i t s the b o u n d a r y r , „ , i t docs i t tangentially, so t h a t no particle flow crosses t h i s boundary. I t is a consequence of the laminar beam assumption. 69). 40). 69) may be easier and cheeper, because more standard fluid dynamical tools can be used. O n the other hand, i t cannot yield non-laminar solutions. I t is well established t h a t , in particular i n the case of large space-charge beams, non-laminar flows are produced.

37) 33 and ip is the solution of *- *%) { r - „(r) = - ^ = , „ ( ! ) = 0, * , ) - ! 38) w i t h a vanishing derivative (dip/dr)(r = 1) = 0. 39) is shown i n [11]. p)- is defined by : 3 2 icUp) = X[p)~ ' . p>0,p*l. 16 o fort • Ifi • If i > ich- problem (4-38) has no solution such that

e f>,i). < icL, problem (4-38) kas a unique solution suck that ip(r) > 0 forr e (PM • Furthermore, dip/dr{\) i = icL(p) is the unique value ofi such that the solution satisfies = 0. C o n t r a r y t o the c y l i n d r i c a l case, there is no difference between the cases p < 1 and p > 1.

S k e t c h of proof of T h e o r e m 4 . 1). I t is thus possible t o chose the functions F,, F , F n o n negative such t h a t the r e s t r i c t i o n of F to the b o u n d a r y ) r = 1 [ dominates the b o u n d a r y profile 7. *,(*,«,) Now, when £ < F*(r,tV,W,B,). 18) 0, all the mass o f the upper-solution P* concentrates on the characteristics defined by : v 2 =

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