L
fil
=
Ö
(
k
/
l
)
k
is effective diffusivity
l
is strain rate
For exponential growth,
final width of filament is independent of
growth rate
identical to that for an inert
tracer
Typical values:
k
=5m
2
s
-1
,
l
=5x10
-6
s
-1
L
fil
~1km
Converges in ~ 1-2 days
For limited growth,
(McLeod et al., 2001)
2 regimes:
m
/
l
<2.5:
as exponentially growing/inert tracer
m
/
l
>2.5:
width dependent on growth rate
larger than for exponential growth
L
fil
~
Ö
(
k
m
/
l
2
)
Go through
Counter-intuitive that growth is irrelevant except for time.
Solution allows for time varying growth rate
Obvious extension to explicitly include limitation
EXPLAIN LIMITATION
- if less near exponential
- if greater decay
Regimes
Confirms earlier model for beta<2.5
For beta>2.5
- biology now important
- width larger than for exponential growth
- counter-intuitive
All nice theory, but what use?