By Bhowmick D., Davison A.C.
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E. p(E» = p(1:,T). The problem to find stationary distribution functions p('t,T) is rather complex and solutions are not available in integratable form. Therefore evaluation ofV(1:,T) can only be made numerically. 4 COMPUTER SIMULATIONS Due to the complexity of the problem and to the impossibility of analytical treatments computer simulation of dislocation movement are an attractive alternative. In the early 70's computer power become sufficiently large to consider array of the order of 104 obstacles in 2D.
We must now take account of the fact that we have steady-state conditions. When the kinks annihilate after a lifetime tk and the formation rate of kinkpairs per unit length is r, the steady-state concentration of kinks obviously is (40) The kink may now be annihilated after moving a distance La. The lifetime tk of a kink is then (41 ) This leads to the general relation under steady-state conditions 48 V=2 hfLa . (42) The annihilation distance La is now given either by the distance L between sinks (or insurmountable obstacles), or else by the mutual annihilation of kinks of opposite sign with an average separation X= lick, whichever is smaller.
Pineau, A. (1996) Effect of inhomogeneities in the modelling of mechanical behaviour and damage of metallic materials, in La Mise en Forme des Materiaux: Vingt Ans de Recherche aux CEMEF, Ecole des Mines de Paris, Paris. 34a. KrOner, E. (1958) Kontinuumstheories der Versetzungen und Eigenspannungen. Springer, Berlin. 35. G. (1998) Mechanical behaviour ofnanostructured materials, Vol. 2 ofM. H. ) Materials Science Foundations, TransTech Publications, Uetikon-ZOrich. 36. A. C. (1998) On the 'anomalous' hardness of nanocrystalline materials, NanoStructured Materials 10, 1111-1118.
A Laplace mixture model for identification of differential expression in microarray experiments (200 by Bhowmick D., Davison A.C.