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CE 561 Homework 6:
(assigned 10/01/09, due 10/12/09)
(1)
Suppose we wanted to model the behavior of undergraduate students on a Saturday night
at Molly's Pub in the same way we have been modeling chemical rate processes.
Let
N
M
be the number of male undergraduates in the bar, let
N
F
be the number of female
undergraduates in the bar, let
N
C
be the number of couples in the bar, let
N
X
be the
number of individuals (male or female) that have not yet come to the bar or have left
alone, and let
N
XC
be the number of couples that have left the bar together.
Then the rate
processes might be written in terms of the following list of "reactions"
(1)
M + F
→
C, with
r
1
=
k
hu
N
M
N
F
2
(2)
C
→
M + F, with
r
2
=
k
bu
N
C
N
F
(3)
M
→
X, with
r
3
=
k
la
N
M
(4)
F
→
X, with
r
4
=
k
la
N
F
(5)
X
→
M, with
r
5
=
k
ma
(6)
X
→
F, with
r
6
=
k
fa
(7)
C
→
XC, with
r
7
=
k
lt
N
C
The numerical values of the rate constants for these processes are
k
hu
= 0.2 events undergraduate
3
hr
1
k
bu
= 0.1 events couple
1
undergraduate
1
hr
1
k
la
= 0.3 events undergraduate
1
hr
1
k
ma
= 20 events hr
1
k
fa
= 10 events hr
1
k
lt
= 0.5 events couple
1
hr
1
The "initial conditions" for this problem are that at time = 0 (when the bar opens),
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 Fall '09

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