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_- - -- then give the totpl number of displacements per primary recoil. Although the primary recoils all move into the forward hemisphere, the secondaries , and so f o r t h w i l l not and we may assume that the flux o i atoms will be roqhly isotropic. j Then this f l u is given by: [C N(RL>~ ) = J n ~ , d 3 dx atoms/cm? sec. For a flux of n 1 MeV. neutrons/cm2/sec we find the following value of j: j = 10-5 n dx atoms/cm2 sec. J.

Thus t h e epergy of t h e e l e c t r o n s i s given up cm. (1) Mot$ and Jones, Theory of Metals and A l l o y s . -Chap. VI1 . . -. (50) Using Eq. (50) we f i n d a valye To t h e l a t t i c e i n a d i s t a n c e of t h e order of * - Atomic Displacements Produced by Fiss,an Neutrons The p r i n c i p a l mode by which f i s s $ o n neutrons l o s e energy i s e l a s t i c scattering. For enereies, such as w e consider here, 2 MeV. - SypmetTic. 8= 0 or s-wave i s scatteredb pe consider first some f e a t u r e s of an e l a s t i c c o l l i s i o n of a neutron of energy E with an atom of mas6 A a t rest.

Then t b e solutiop is; H $= H2 q t U e $ y f i For small t, t h e term e C st H dt t -HZ will be nearly u n i t y and . . (47) i s then given by: I, Thus f o r small t and $p4Hlt, t h e r a t i o of t h e temperatures is: 9 i s much smaller than Y i n i t i a l l y . see i n a q u a l i t a t i v e way t h a t , i n t h e times when 2/4Hlt $ -H2 a result which shows t h a t - Re can w i l l not be an 'appreciable f r a c t i o n of h a s i t s l a r g e i n i t i a l values. Thus we can con- clude that $he temperature of t h e l a t t i c e nowhere rises s u f f i c i e n t l y high t o produce d5splacgments of atoms; t h i g conclusion would hold even with Nrly large c t would es i n our choice of c o n s t a n t be more for r c$ t o solve <5 go( ) w i t h the condition t h a t I n d y = 0 for r > 5'1s -Hlk ' 2t k dk .

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Numerical Anal. of Lattice Boltzmann Methods for the Heat Eqn on a Bounded Interval by J. Weiss


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