poly: Seeking StarFlight Functional Forms

Hi. I'm working on a paper, tentatively titled "Burning the
Cosmic Commons: Evolutionary Strategies for Interstellar
Colonization," building on Carl's insight that we can derive
colonization behavior from the selection effect of what it
takes to stay on the frontier.

Part of the paper proves some general results independent
of specific functional forms, but I also want to include
computer simulations of specific cases. For such specific
cases I need to pick specific functional forms, which I'd like
your advice on choosing.

The basic functions in the model are these:
R(s) = the resources available after growing at an oasis for
       time s. R(0) = 1. R'(s) > 0
1/A(x*b(v,h)) = the fraction of probes that survive traveling
       distance x at velocity v, with hardness h. A(0) = 1.
       A'(x) > 0.
C(v,h) = the resource cost to make one probe with v,h.
Q(P) = the fraction of probes which land at open oases, given
       a fraction P of them are occupied.

I'm considering these choices:
Q(P) = 1 - P.
R(s) = exp(lnR(s)), lnR'(s) = lnR0 - lnRd*s.
A(x) = exp(lnA(x)), lnA'(x) = lnA0 + lnAd*x.
b(v) = sqrt(1-v^2).
C(v) = 1 + k*v/sqrt(1-v^2).

Advice on functional forms, or on parameter values, welcome.
Published acknowledgements gratefully given.

Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614
Received on Thu Feb 5 19:57:10 1998