426(2)(3)(4)(5)
- APPLICATIONS OF THE REDUCED DISTANCE
gi()(x,y,T) = ~cp~ (x,y,T)
0
!0
(x,y,T)§co(cp(x,y,T))
uX^2 uT
o-0 0-o
= ;::i<p. (x, y, T)! (x, y, T) §oo(x, y, 7)
uX^2 uT=-J:_of.T( 1 _2f _2Tof) (N ( 1 _2f)-
1
+R)
N OX^2 N N OT 2T N= -~ :; T ( 1 + 0 ( N-^1 )) ( ~ + 0 (1))
= -:; (x,T) + 0 (N-^1 ).
0-c 0-d
§iJ· (x,y,T) = :::.<p· (x,y,T) ;::i<p· (x,y,T)§cd(cp(x,y,T))
ux^2 uxJo-k o-e
= ;::i<p. ( X, y, T) ;::i <p. ( X, y, T) gkl', ( X, y, T)
ux^2 uxJ
0-o o-0
+ ;::i<p· (x,y,T) ;::i<p· (x,y,T)§oo(x,y,T)
uX^2 uxJ(2T)
2
of of (N ( 2f)-1
=gij(x,y,T)+ N oxioxj 2T l-N +R )= 9ij (x,T) + 0 (N-^1 ).
0-c a-d
§1;13 (x, y, T) = o:a (x, y, T) o:f3 (x, y, T) §cd (cp (x, y, T))=gaf3 ( x,y,T ) = (l - 2f(x,T))-N 9a(3 ( x,y,T. )
0-c 0-d
g~(x,y,T) = o:i (x,y,T) o:a (x,y,T)§cd(cp(x,y,T))
o-0
= §ia(x, y, f') + o:i (x, y, T) §oa(x, y, f')