The name is absent

89

and space-varying solution can be integrated over time for a step of current delivered at a
point in spaee(i(ʃ. t) = w(t)ʌ(ʃ)) at t=∞ to yield the steady state solution for a point source:

Where space constant λ, the dimensionless quantity of cell lengths, is given by the fol-

7 = 21 cosh — - 1

T ^^ R_c∣ Rm

When λ » D [69] :

(5.6)

These general solutions G*(x,t') and G*(aj)_oo are known in Mathematics as Green’s
functions^ for the cable equation, but they are equivalent to the engineering concept of an
impulse response. The steady-state solution G*(x)_x can be convolved (superimposed) with
any other distribution of current i(ʃ) to yield the steady-state solution for that distribution.
Likewise, the time-dependent solution G*(x,t) can also be convolved through space and

≠Green⅛ functions are named after George Green, the who was a miller who taught himself mathemat-
ics mathematician. He studied the idea of fundamental solutions to particular partial differential equations
(PDEs) in the early 19th century [72]. His work was (not surprisingly) very influential for Lord Kelvin

<<   95   96   97   98   99   100   101   >>

More intriguing information