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Unformatted text preview: C 4 exp , 2 Ï€ ( ) âˆ« âˆž âˆ’ = = Dt x u s s du e C Dt x C t x C 2 2 2 2 erfc , Show that a Gaussian profile remains Gaussian after further diffusion. That is, If : (âˆž < x < + âˆž ) Then after additional time t at the same temperature: Please use the method similar to below for derivation. Here apparently C is not a constant â€“ it is a function of x i as C(x i ,t ) ( ) âˆ’ = 2 4 exp 2 , Dt x Dt Q t x C Ï€ ( ) + âˆ’ + = + ) ( 4 exp ) ( 2 , 2 t t D x t t D Q t t x C ( ) ( ) âˆ‘ = âˆ’ âˆ’ âˆ† = n i i i Dt x x x Dt C t x C 1 2 4 exp 2 ,...
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 Spring '10
 Bo
 Normal Distribution, dt, Error function

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