<s>
Computer	B-Application
simulation	I-Application
is	O
the	O
process	O
of	O
mathematical	O
modelling	O
,	O
performed	O
on	O
a	O
computer	O
,	O
which	O
is	O
designed	O
to	O
predict	O
the	O
behaviour	O
of	O
,	O
or	O
the	O
outcome	O
of	O
,	O
a	O
real-world	O
or	O
physical	O
system	O
.	O
</s>
<s>
Computer	B-Application
simulations	I-Application
have	O
become	O
a	O
useful	O
tool	O
for	O
the	O
mathematical	O
modeling	O
of	O
many	O
natural	O
systems	O
in	O
physics	O
(	O
computational	B-Algorithm
physics	I-Algorithm
)	O
,	O
astrophysics	O
,	O
climatology	O
,	O
chemistry	O
,	O
biology	O
and	O
manufacturing	O
,	O
as	O
well	O
as	O
human	O
systems	O
in	O
economics	O
,	O
psychology	O
,	O
social	O
science	O
,	O
health	O
care	O
and	O
engineering	O
.	O
</s>
<s>
Computer	B-Application
simulations	I-Application
are	O
realized	O
by	O
running	O
computer	B-Application
programs	I-Application
that	O
can	O
be	O
either	O
small	O
,	O
running	O
almost	O
instantly	O
on	O
small	O
devices	O
,	O
or	O
large-scale	O
programs	O
that	O
run	O
for	O
hours	O
or	O
days	O
on	O
network-based	O
groups	O
of	O
computers	O
.	O
</s>
<s>
The	O
scale	O
of	O
events	O
being	O
simulated	O
by	O
computer	B-Application
simulations	I-Application
has	O
far	O
exceeded	O
anything	O
possible	O
(	O
or	O
perhaps	O
even	O
imaginable	O
)	O
using	O
traditional	O
paper-and-pencil	O
mathematical	O
modeling	O
.	O
</s>
<s>
a	O
complete	O
simulation	O
of	O
the	O
life	O
cycle	O
of	O
Mycoplasma	O
genitalium	O
in	O
2012	O
;	O
and	O
the	O
Blue	O
Brain	O
project	O
at	O
EPFL	O
(	O
Switzerland	O
)	O
,	O
begun	O
in	O
May	O
2005	O
to	O
create	O
the	O
first	O
computer	B-Application
simulation	I-Application
of	O
the	O
entire	O
human	O
brain	O
,	O
right	O
down	O
to	O
the	O
molecular	O
level	O
.	O
</s>
<s>
A	O
computer	B-Application
model	I-Application
is	O
the	O
algorithms	O
and	O
equations	O
used	O
to	O
capture	O
the	O
behavior	O
of	O
the	O
system	O
being	O
modeled	O
.	O
</s>
<s>
By	O
contrast	O
,	O
computer	B-Application
simulation	I-Application
is	O
the	O
actual	O
running	O
of	O
the	O
program	O
that	O
contains	O
these	O
equations	O
or	O
algorithms	O
.	O
</s>
<s>
Computer	B-Application
simulation	I-Application
developed	O
hand-in-hand	O
with	O
the	O
rapid	O
growth	O
of	O
the	O
computer	O
,	O
following	O
its	O
first	O
large-scale	O
deployment	O
during	O
the	O
Manhattan	O
Project	O
in	O
World	O
War	O
II	O
to	O
model	O
the	O
process	O
of	O
nuclear	O
detonation	O
.	O
</s>
<s>
It	O
was	O
a	O
simulation	O
of	O
12	O
hard	O
spheres	O
using	O
a	O
Monte	B-Algorithm
Carlo	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Computer	B-Application
simulation	I-Application
is	O
often	O
used	O
as	O
an	O
adjunct	O
to	O
,	O
or	O
substitute	O
for	O
,	O
modeling	O
systems	O
for	O
which	O
simple	O
closed	O
form	O
analytic	O
solutions	O
are	O
not	O
possible	O
.	O
</s>
<s>
There	O
are	O
many	O
types	O
of	O
computer	B-Application
simulations	I-Application
;	O
their	O
common	O
feature	O
is	O
the	O
attempt	O
to	O
generate	O
a	O
sample	O
of	O
representative	O
scenarios	O
for	O
a	O
model	O
in	O
which	O
a	O
complete	O
enumeration	O
of	O
all	O
possible	O
states	O
of	O
the	O
model	O
would	O
be	O
prohibitive	O
or	O
impossible	O
.	O
</s>
<s>
For	O
some	O
,	O
the	O
input	O
might	O
be	O
just	O
a	O
few	O
numbers	O
(	O
for	O
example	O
,	O
simulation	O
of	O
a	O
waveform	O
of	O
AC	O
electricity	O
on	O
a	O
wire	O
)	O
,	O
while	O
others	O
might	O
require	O
terabytes	O
of	O
information	O
(	O
such	O
as	O
weather	O
and	O
climate	B-Application
models	I-Application
)	O
.	O
</s>
<s>
data	O
can	O
be	O
entered	O
into	O
the	O
simulation	O
when	O
it	O
starts	O
up	O
,	O
for	O
example	O
by	O
reading	O
one	O
or	O
more	O
files	O
,	O
or	O
by	O
reading	O
data	O
from	O
a	O
preprocessor	B-General_Concept
;	O
</s>
<s>
Because	O
of	O
this	O
variety	O
,	O
and	O
because	O
diverse	O
simulation	O
systems	O
have	O
many	O
common	O
elements	O
,	O
there	O
are	O
a	O
large	O
number	O
of	O
specialized	O
simulation	B-Language
languages	I-Language
.	O
</s>
<s>
The	O
best-known	O
may	O
be	O
Simula	B-Language
.	O
</s>
<s>
Computer	B-Application
models	I-Application
can	O
be	O
classified	O
according	O
to	O
several	O
independent	O
pairs	O
of	O
attributes	O
,	O
including	O
:	O
</s>
<s>
Dynamic	B-Application
system	I-Application
simulation	I-Application
,	O
e.g.	O
</s>
<s>
Local	O
or	O
distributed	B-Architecture
.	O
</s>
<s>
Simulations	O
which	O
store	O
their	O
data	O
in	O
regular	O
grids	O
and	O
require	O
only	O
next-neighbor	O
access	O
are	O
called	O
stencil	B-Application
codes	I-Application
.	O
</s>
<s>
If	O
the	O
underlying	O
graph	O
is	O
not	O
a	O
regular	O
grid	O
,	O
the	O
model	O
may	O
belong	O
to	O
the	O
meshfree	B-Algorithm
method	I-Algorithm
class	O
.	O
</s>
<s>
Such	O
models	O
are	O
often	O
used	O
in	O
simulating	O
physical	O
systems	O
,	O
as	O
a	O
simpler	O
modeling	O
case	O
before	O
dynamic	B-Application
simulation	I-Application
is	O
attempted	O
.	O
</s>
<s>
Dynamic	B-Application
simulations	I-Application
model	O
changes	O
in	O
a	O
system	O
in	O
response	O
to	O
(	O
usually	O
changing	O
)	O
input	O
signals	O
.	O
</s>
<s>
A	O
discrete	B-General_Concept
event	I-General_Concept
simulation	I-General_Concept
(	O
DES	O
)	O
manages	O
events	O
in	O
time	O
.	O
</s>
<s>
A	O
continuous	O
dynamic	B-Application
simulation	I-Application
performs	O
numerical	O
solution	O
of	O
differential-algebraic	O
equations	O
or	O
differential	O
equations	O
(	O
either	O
partial	O
or	O
ordinary	O
)	O
.	O
</s>
<s>
Applications	O
include	O
flight	B-Application
simulators	I-Application
,	O
construction	B-Application
and	I-Application
management	I-Application
simulation	I-Application
games	I-Application
,	O
chemical	O
process	O
modeling	O
,	O
and	O
simulations	O
of	O
electrical	O
circuits	O
.	O
</s>
<s>
By	O
the	O
late	O
1980s	O
,	O
however	O
,	O
most	O
"	O
analog	O
"	O
simulations	O
were	O
run	O
on	O
conventional	O
digital	O
computers	O
that	O
emulate	B-Application
the	O
behavior	O
of	O
an	O
analog	O
computer	O
.	O
</s>
<s>
Distributed	B-Architecture
models	O
run	O
on	O
a	O
network	O
of	O
interconnected	O
computers	O
,	O
possibly	O
through	O
the	O
Internet	O
.	O
</s>
<s>
Simulations	O
dispersed	O
across	O
multiple	O
host	O
computers	O
like	O
this	O
are	O
often	O
referred	O
to	O
as	O
"	O
distributed	B-Architecture
simulations	O
"	O
.	O
</s>
<s>
There	O
are	O
several	O
standards	O
for	O
distributed	B-Architecture
simulation	O
,	O
including	O
Aggregate	B-Operating_System
Level	I-Operating_System
Simulation	I-Operating_System
Protocol	I-Operating_System
(	O
ALSP	B-Operating_System
)	O
,	O
Distributed	B-Operating_System
Interactive	I-Operating_System
Simulation	I-Operating_System
(	O
DIS	O
)	O
,	O
the	O
High	B-Operating_System
Level	I-Operating_System
Architecture	I-Operating_System
(	O
simulation	O
)	O
(	O
HLA	O
)	O
and	O
the	O
Test	O
and	O
Training	O
Enabling	O
Architecture	O
(	O
TENA	O
)	O
.	O
</s>
<s>
Formerly	O
,	O
the	O
output	O
data	O
from	O
a	O
computer	B-Application
simulation	I-Application
was	O
sometimes	O
presented	O
in	O
a	O
table	O
or	O
a	O
matrix	O
showing	O
how	O
data	O
were	O
affected	O
by	O
numerous	O
changes	O
in	O
the	O
simulation	O
parameters	O
.	O
</s>
<s>
Today	O
,	O
weather	B-Application
forecasting	I-Application
models	I-Application
tend	O
to	O
balance	O
the	O
view	O
of	O
moving	O
rain/snow	O
clouds	O
against	O
a	O
map	O
that	O
uses	O
numeric	O
coordinates	O
and	O
numeric	O
timestamps	O
of	O
events	O
.	O
</s>
<s>
Similarly	O
,	O
CGI	O
computer	B-Application
simulations	I-Application
of	O
CAT	O
scans	O
can	O
simulate	O
how	O
a	O
tumor	O
might	O
shrink	O
or	O
change	O
during	O
an	O
extended	O
period	O
of	O
medical	O
treatment	O
,	O
presenting	O
the	O
passage	O
of	O
time	O
as	O
a	O
spinning	O
view	O
of	O
the	O
visible	O
human	O
head	O
,	O
as	O
the	O
tumor	O
changes	O
.	O
</s>
<s>
Other	O
applications	O
of	O
CGI	O
computer	B-Application
simulations	I-Application
are	O
being	O
developed	O
to	O
graphically	O
display	O
large	O
amounts	O
of	O
data	O
,	O
in	O
motion	O
,	O
as	O
changes	O
occur	O
during	O
a	O
simulation	O
run	O
.	O
</s>
<s>
Generic	O
examples	O
of	O
types	O
of	O
computer	B-Application
simulations	I-Application
in	O
science	O
,	O
which	O
are	O
derived	O
from	O
an	O
underlying	O
mathematical	O
description	O
:	O
</s>
<s>
a	O
numerical	B-Application
simulation	I-Application
of	O
differential	O
equations	O
that	O
cannot	O
be	O
solved	O
analytically	O
,	O
theories	O
that	O
involve	O
continuous	O
systems	O
such	O
as	O
phenomena	O
in	O
physical	O
cosmology	O
,	O
fluid	O
dynamics	O
(	O
e.g.	O
,	O
climate	B-Application
models	I-Application
,	O
roadway	O
noise	O
models	O
,	O
roadway	O
air	O
dispersion	O
models	O
)	O
,	O
continuum	O
mechanics	O
and	O
chemical	O
kinetics	O
fall	O
into	O
this	O
category	O
.	O
</s>
<s>
Phenomena	O
in	O
this	O
category	O
include	O
genetic	B-Application
drift	I-Application
,	O
biochemical	O
or	O
gene	O
regulatory	O
networks	O
with	O
small	O
numbers	O
of	O
molecules	O
.	O
</s>
<s>
(	O
see	O
also	O
:	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
)	O
.	O
</s>
<s>
Techniques	O
used	O
for	O
such	O
simulations	O
are	O
Molecular	O
dynamics	O
,	O
Molecular	O
mechanics	O
,	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
,	O
and	O
Multiscale	O
Green	O
's	O
function	O
.	O
</s>
<s>
Specific	O
examples	O
of	O
computer	B-Application
simulations	I-Application
include	O
:	O
</s>
<s>
agent	O
based	O
simulation	O
has	O
been	O
used	O
effectively	O
in	O
ecology	O
,	O
where	O
it	O
is	O
often	O
called	O
"	O
individual	O
based	O
modeling	O
"	O
and	O
is	O
used	O
in	O
situations	O
for	O
which	O
individual	O
variability	O
in	O
the	O
agents	O
cannot	O
be	O
neglected	O
,	O
such	O
as	O
population	O
dynamics	O
of	O
salmon	B-Protocol
and	O
trout	O
(	O
most	O
purely	O
mathematical	O
models	O
assume	O
all	O
trout	O
behave	O
identically	O
)	O
.	O
</s>
<s>
computer	B-Application
simulations	I-Application
have	O
also	O
been	O
used	O
to	O
formally	O
model	O
theories	O
of	O
human	O
cognition	O
and	O
performance	O
,	O
e.g.	O
,	O
ACT-R	B-Language
.	O
</s>
<s>
computer	B-Application
simulation	I-Application
using	O
molecular	O
modeling	O
for	O
drug	O
discovery	O
.	O
</s>
<s>
computer	B-Application
simulation	I-Application
to	O
model	O
viral	O
infection	O
in	O
mammalian	O
cells	O
.	O
</s>
<s>
computer	B-Application
simulation	I-Application
for	O
studying	O
the	O
selective	O
sensitivity	O
of	O
bonds	O
by	O
mechanochemistry	O
during	O
grinding	O
of	O
organic	O
molecules	O
.	O
</s>
<s>
Notable	O
,	O
and	O
sometimes	O
controversial	O
,	O
computer	B-Application
simulations	I-Application
used	O
in	O
science	O
include	O
:	O
Donella	O
Meadows	O
 '	O
World3	O
used	O
in	O
the	O
Limits	O
to	O
Growth	O
,	O
James	O
Lovelock	O
's	O
Daisyworld	O
and	O
Thomas	O
Ray	O
's	O
Tierra	O
.	O
</s>
<s>
In	O
social	O
sciences	O
,	O
computer	B-Application
simulation	I-Application
is	O
an	O
integral	O
component	O
of	O
the	O
five	O
angles	O
of	O
analysis	O
fostered	O
by	O
the	O
data	O
percolation	O
methodology	O
,	O
which	O
also	O
includes	O
qualitative	O
and	O
quantitative	O
methods	O
,	O
reviews	O
of	O
the	O
literature	O
(	O
including	O
scholarly	O
)	O
,	O
and	O
interviews	O
with	O
experts	O
,	O
and	O
which	O
forms	O
an	O
extension	O
of	O
data	O
triangulation	O
.	O
</s>
<s>
Computer	B-Application
simulations	I-Application
are	O
used	O
in	O
a	O
wide	O
variety	O
of	O
practical	O
contexts	O
,	O
such	O
as	O
:	O
</s>
<s>
simulation	O
of	O
other	O
computers	O
is	O
emulation	B-Application
.	O
</s>
<s>
urban	B-Application
simulation	I-Application
models	I-Application
that	O
simulate	O
dynamic	O
patterns	O
of	O
urban	O
development	O
and	O
responses	O
to	O
urban	O
land	O
use	O
and	O
transportation	O
policies	O
.	O
</s>
<s>
The	O
reliability	O
and	O
the	O
trust	O
people	O
put	O
in	O
computer	B-Application
simulations	I-Application
depends	O
on	O
the	O
validity	O
of	O
the	O
simulation	O
model	O
,	O
therefore	O
verification	B-Application
and	I-Application
validation	I-Application
are	O
of	O
crucial	O
importance	O
in	O
the	O
development	O
of	O
computer	B-Application
simulations	I-Application
.	O
</s>
<s>
Another	O
important	O
aspect	O
of	O
computer	B-Application
simulations	I-Application
is	O
that	O
of	O
reproducibility	O
of	O
the	O
results	O
,	O
meaning	O
that	O
a	O
simulation	O
model	O
should	O
not	O
provide	O
a	O
different	O
answer	O
for	O
each	O
execution	O
.	O
</s>
<s>
Vehicle	O
manufacturers	O
make	O
use	O
of	O
computer	B-Application
simulation	I-Application
to	O
test	O
safety	O
features	O
in	O
new	O
designs	O
.	O
</s>
<s>
Computer	O
graphics	O
can	O
be	O
used	O
to	O
display	O
the	O
results	O
of	O
a	O
computer	B-Application
simulation	I-Application
.	O
</s>
<s>
Animations	O
can	O
be	O
used	O
to	O
experience	O
a	O
simulation	O
in	O
real-time	O
,	O
e.g.	O
,	O
in	O
training	B-Application
simulations	I-Application
.	O
</s>
<s>
Furthermore	O
,	O
simulation	O
results	O
are	O
often	O
aggregated	O
into	O
static	O
images	O
using	O
various	O
ways	O
of	O
scientific	B-Application
visualization	I-Application
.	O
</s>
<s>
This	O
technique	O
can	O
also	O
detect	O
buffer	B-General_Concept
overflow	I-General_Concept
and	O
similar	O
"	O
hard	O
to	O
detect	O
"	O
errors	O
as	O
well	O
as	O
produce	O
performance	O
information	O
and	O
tuning	B-Device
data	O
.	O
</s>
<s>
Although	O
sometimes	O
ignored	O
in	O
computer	B-Application
simulations	I-Application
,	O
it	O
is	O
very	O
important	O
to	O
perform	O
a	O
sensitivity	O
analysis	O
to	O
ensure	O
that	O
the	O
accuracy	O
of	O
the	O
results	O
is	O
properly	O
understood	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
probabilistic	O
risk	O
analysis	O
of	O
factors	O
determining	O
the	O
success	O
of	O
an	O
oilfield	O
exploration	O
program	O
involves	O
combining	O
samples	O
from	O
a	O
variety	O
of	O
statistical	O
distributions	O
using	O
the	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
.	O
</s>
