<s>
In	O
statistical	O
mechanics	O
,	O
the	O
mean	B-General_Concept
squared	I-General_Concept
displacement	I-General_Concept
(	O
MSD	O
,	O
also	O
mean	B-General_Concept
square	I-General_Concept
displacement	I-General_Concept
,	O
average	O
squared	O
displacement	O
,	O
or	O
mean	O
square	O
fluctuation	O
)	O
is	O
a	O
measure	O
of	O
the	O
deviation	B-General_Concept
of	O
the	O
position	O
of	O
a	O
particle	O
with	O
respect	O
to	O
a	O
reference	O
position	O
over	O
time	O
.	O
</s>
<s>
In	O
the	O
realm	O
of	O
biophysics	O
and	O
environmental	O
engineering	O
,	O
the	O
Mean	B-General_Concept
Squared	I-General_Concept
Displacement	I-General_Concept
is	O
measured	O
over	O
time	O
to	O
determine	O
if	O
a	O
particle	O
is	O
spreading	O
slowly	O
due	O
to	O
diffusion	O
,	O
or	O
if	O
an	O
advective	O
force	O
is	O
also	O
contributing	O
.	O
</s>
<s>
The	O
MSD	O
at	O
time	O
is	O
defined	O
as	O
an	O
ensemble	B-General_Concept
average	I-General_Concept
:	O
</s>
<s>
Since	O
all	O
the	O
coordinates	O
are	O
independent	O
,	O
their	O
deviation	B-General_Concept
from	O
the	O
reference	O
position	O
is	O
also	O
independent	O
.	O
</s>
<s>
Hence	O
,	O
the	O
final	O
result	O
of	O
mean	B-General_Concept
squared	I-General_Concept
displacement	I-General_Concept
in	O
n-dimensional	O
Brownian	O
motion	O
is	O
:	O
</s>
