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3 Numerical Results
All simulations in this section were obtained using a hexagonal lattice with 2500
individuals and
ρ
0
= 2 with an object oriented code C++ code[5,6] running on
a single processor with CPU clock at 700MHz under Linux.
3.1 Lane Formation
The formation of lanes in two crowds moving in opposite directions is one of the
macroscopic observations of interests to validate our approach. Fig. 1 shows the
three types of states the model is able to produce. The first is a state with no
lanes, individuals do not consider deviation form their favorite direction (
λ ≈
0)
and create high density cells where movement is reduced. The second is a dense
lane formation with individuals strongly following each other(
λ ≈
1
,η≈
2
)even
when no obstacles are present. The third is a sparse configuration of individuals
where individuals have optimized the space occupation, (
λ ≈
0
,η ≈
1). The
ability of the crowd to optimize its total mobility
µ
=
r
µ
(
r
,t
) under the
three above conditions is shown in fig. 2. We see that the global behavior of
the crowd is highly dependent of
η
and
ξ
which leads us to conclude that a
realistic simulation must most probably include a mechanism which dynamically
sets the values of
η
and
ξ
with regards to circumstances. However, without this
sophistication, the system qualitatively behaves in a correct way.
3.2 Door Oscillations
We now look at the oscillations at a door between two crowds moving in opposite
directions. The door serves as a bottleneck and jamming naturally ensues at the
door. Oscillations appear when, for noise fluctuations reasons, a population on
one side of the door wins access through the door thus increasing mobility for
people behind. This results in a burst of one population through the door until
fluctuations will inverse the situation.
In order to shows the bursts, we measure the total mobility at the door and
compare it with a test simulation where no interaction (
ρ
0
>ρ,η
= 0) occurs
between individuals. In order to outline the oscillations, we look at the Fourier
transform of the signal, see fig. 3. We thus observe that the Fourier transform
of the signal for interacting crowd possess higher amplitudes at low frequencies.
This shows that the throughput across the door oscillates over periods of time
significantly higher than an iteration.
3.3 Evacuation Problem
In the third experiment we look at the influence of the disorder parameter
ξ
on
the time needed for a crowd to evacuate a room. The
ξ
parameter statistically
determines how much an individual will search in other directions to find mo-
bility. By doing so however we increase the diffusion of individuals and should
