.MCAD 304020000 1 74 3220674443 0
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 0 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=1
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 1.218750 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*
.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=2 family=Courier points=12 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.CMD COLORTAB_ENTRY 0 0 0
.CMD COLORTAB_ENTRY 128 0 0
.CMD COLORTAB_ENTRY 0 128 0
.CMD COLORTAB_ENTRY 128 128 0
.CMD COLORTAB_ENTRY 0 0 128
.CMD COLORTAB_ENTRY 128 0 128
.CMD COLORTAB_ENTRY 0 128 128
.CMD COLORTAB_ENTRY 128 128 128
.CMD COLORTAB_ENTRY 192 192 192
.CMD COLORTAB_ENTRY 255 0 0
.CMD COLORTAB_ENTRY 0 255 0
.CMD COLORTAB_ENTRY 255 255 0
.CMD COLORTAB_ENTRY 0 0 255
.CMD COLORTAB_ENTRY 255 0 255
.CMD COLORTAB_ENTRY 0 255 255
.CMD COLORTAB_ENTRY 255 255 255
.CMD COLORTAB_ENTRY 0 64 128
.TXT 3 19 -1074292929 0 0
Cg a74.000000,74.000000,53
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset0\fnil Arial;}}\plain\cf1\fs24 
\pard {\f1\fs36 Ideal Gas - Brownian Motion\par Einstein-Smoluchowsky Law}}
.TXT 6 0 -1074292930 0 0
Cg a72.000000,72.000000,20
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard Number of molecules:}
.EQN 0 31 -1074292918 0 0
{0:N}NAME:49
.EQN 3 0 -1074292919 0 0
{0:i}NAME:0;{0:N}NAME-1
.TXT 1 -31 -1074292932 0 0
Cg a72.000000,72.000000,22
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset0\fnil Arial;}}\plain\cf1\fs24 
\pard {\f1  }i --- particle index:}
.TXT 3 0 -1074292934 0 0
Cg a72.000000,72.000000,13
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs24 
\pard Time is j*{\f1 D}t:}
.EQN 0 31 -1074292921 0 0
{0:T}NAME:200
.EQN 3 0 -1074292920 0 0
{0:\Dt}NAME:0.01
.TXT 4 -31 -1074292937 0 0
Cg a74.000000,74.000000,19
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset0\fnil Arial;}}\plain\cf1\fs24 
\pard j --- time index: {\f1  }}
.EQN 0 31 -1074292922 0 0
{0:j}NAME:0;{0:T}NAME-1
.TXT 6 -49 -1074292884 0 0
Cg a74.000000,74.000000,85
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset0\fnil Arial;}}\plain\cf1\fs24 
\pard {\f1 Start with the N molecules from a random configuration 
inside a small square of size:}}
.EQN 4 28 -1074292883 0 0
{0:s}NAME:\({0:N}NAME)
.EQN 4 -14 9 0 0
({0:x}NAME)[({0:i}NAME,0):{0:rnd}NAME(1)*{0:s}NAME-({0:s}NAME)/(2)
.EQN 0 26 -1074292882 0 0
({0:y}NAME)[({0:i}NAME,0):{0:rnd}NAME(1)*{0:s}NAME-({0:s}NAME)/(2)
.TXT 5 -39 -1074292901 0 0
Cg a74.000000,74.000000,52
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset0\fnil Arial;}}\plain\cf1\fs24 
\pard {\f1 We set the limits of the box: |x| < lim, |y| < lim. }}
.EQN 3 14 -1074292964 0 0
{0:lim}NAME:40
.EQN 3 0 -1074292965 0 0
{0:limg}NAME:{0:lim}NAME+1
.EQN 3 -15 -1074293024 0 0
({0:u}NAME)[(1):({0:s}NAME)/(2)+.1
.EQN 1 14 -1074293023 0 0
({0:u}NAME)[(2):-(({0:s}NAME)/(2))+-.1
.EQN 0 16 -1074293022 0 0
({0:u}NAME)[(3):-(({0:s}NAME)/(2))+-.1
.EQN 0 12 -1074292877 0 0
({0:u}NAME)[(4):({0:s}NAME)/(2)+.1
.EQN 0 12 -1074292876 0 0
({0:u}NAME)[(0):({0:s}NAME)/(2)+.1
.EQN 3 11 -1074292864 0 0
{0:k}NAME:0;4
.EQN 4 -65 -1074293015 0 0
({0:t}NAME)[(1):({0:s}NAME)/(2)+.1
.EQN 0 13 -1074293014 0 0
({0:t}NAME)[(2):({0:s}NAME)/(2)+.1
.EQN 0 17 -1074293013 0 0
({0:t}NAME)[(3):-(({0:s}NAME)/(2)+.1)
.EQN 0 11 -1074292866 0 0
({0:t}NAME)[(4):-(({0:s}NAME)/(2)+.1)
.EQN 0 12 -1074292865 0 0
({0:t}NAME)[(0):-(({0:s}NAME)/(2)+.1)
.TXT 6 -51 -1074292888 0 0
Cg a71.000000,71.000000,29
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard The initial 
configuration is:}
.EQN 2 -2 -1074292889 0 0
{0:limg}NAME&-{0:limg}NAME&(-{0:lim}NAME&{0:lim}NAME)&({0:y}NAME)[({0:i}NAME,0),({0:t}NAME)[({0:k}NAME)@{0:limg}NAME&-{0:limg}NAME&(-{0:lim}NAME&{0:lim}NAME)&({0:x}NAME)[({0:i}NAME,0),({0:u}NAME)[({0:k}NAME)
0 0 0 0 0 2 1 1 1 
0 0 0 0 0 2 1 1 1 
0 0 0 0 1 1 NO-TRACE-STRING
0 3 1 5 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 65 26 10 0 3 
.TXT 35 -1 -1074292858 0 0
Cg a74.000000,74.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard COPYRIGHT MIRON 
KAUFMAN 1997}
.TXT 3 0 26 0 0
Cg a74.000000,74.000000,272
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Courier;}{\f1\fcharset0\fnil Arial;}{\f2
\fcharset2\fnil Symbol;}}\plain\cf1\fs24 \pard The new position of a 
molecule is{\f1  x}{\cf2\f1\dn new}{\f1  = x}{\cf2\f1\dn old}{\f1  + }{
\f2 D}x, y{\cf2\dn new} = y{\cf2\dn old} + {\f2 D}y, where {\f2 D}x=v{
\cf2\dn x}{\f2 D}t and {\f2 D}y=v{\cf2\dn y}{\f2 D}t. The velocities v{
\cf2\dn x} and v{\cf2\dn y }are random variables each normally 
distributed: v~{\b N(meanv,}{\f2\b s}{\b )}. The variance is  {\f2 s}{
\cf2\f2\up 2}{\f2  = }k{\cf2\dn B}T/m and in the absence of a driving 
force the mean of v is zero.}
.EQN 13 2 -1074292910 0 0
{0:meanvx}NAME:0
.EQN 0 25 -1074292902 0 0
{0:meanvy}NAME:0
.EQN 3 -25 -1074292911 0 0
{0:\sx}NAME:300
.EQN 1 25 -1074292903 0 0
{0:\sy}NAME:300
.EQN 3 -25 -1074292912 0 0
({0:vx}NAME)[({0:i}NAME,{0:j}NAME):({0:rnorm}NAME({0:N}NAME,{0:meanvx}NAME,{0:\sx}NAME))[({0:i}NAME)
.EQN 0 25 -1074292895 0 0
({0:vy}NAME)[({0:i}NAME,{0:j}NAME):({0:rnorm}NAME({0:N}NAME,{0:meanvy}NAME,{0:\sy}NAME))[({0:i}NAME)
.EQN 7 -25 -1074292913 0 0
({0:\Dx}NAME)[({0:i}NAME,{0:j}NAME):({0:vx}NAME)[({0:i}NAME,{0:j}NAME)*{0:\Dt}NAME
.EQN 0 25 -1074292905 0 0
({0:\Dy}NAME)[({0:i}NAME,{0:j}NAME):({0:vy}NAME)[({0:i}NAME,{0:j}NAME)*{0:\Dt}NAME
.TXT 5 -27 32 0 0
Cg a74.000000,74.000000,47
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset0\fnil Arial;}}\plain\cf1\fs24 
\pard {\f1  }{\f1 We }are using non-periodic boundary conditions.}
.EQN 8 0 33 0 0
({2,1}ö({0:y}NAME)[({0:i}NAME,{0:j}NAME+1)ö({0:x}NAME)[({0:i}NAME,{0:j}NAME+1)):({2,1}ö{0:if}NAME(({0:y}NAME)[({0:i}NAME,{0:j}NAME)+({0:\Dy}NAME)[({0:i}NAME,{0:j}NAME)>{0:lim}NAME,{0:lim}NAME,{0:if}NAME(({0:y}NAME)[({0:i}NAME,{0:j}NAME)+({0:\Dy}NAME)[(
{0:i}NAME,{0:j}NAME)<-{0:lim}NAME,-{0:lim}NAME,({0:y}NAME)[({0:i}NAME,{0:j}NAME)+({0:\Dy}NAME)[({0:i}NAME,{0:j}NAME)))ö{0:if}NAME(({0:x}NAME)[({0:i}NAME,{0:j}NAME)+({0:\Dx}NAME)[({0:i}NAME,{0:j}NAME)>{0:lim}NAME,{0:lim}NAME,{0:if}NAME(({0:x}NAME)[(
{0:i}NAME,{0:j}NAME)+({0:\Dx}NAME)[({0:i}NAME,{0:j}NAME)<-{0:lim}NAME,-{0:lim}NAME,({0:x}NAME)[({0:i}NAME,{0:j}NAME)+({0:\Dx}NAME)[({0:i}NAME,{0:j}NAME))))
.TXT 6 2 -1074292897 0 0
Cg a72.000000,72.000000,27
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard The final 
configuration is:}
.EQN 3 -1 -1074293101 0 0
{0:limg}NAME&-{0:limg}NAME&(-{0:lim}NAME&{0:lim}NAME)&({0:y}NAME)[({0:i}NAME,{0:T}NAME-1),({0:t}NAME)[({0:k}NAME)@{0:limg}NAME&-{0:limg}NAME&(-{0:lim}NAME&{0:lim}NAME)&({0:x}NAME)[({0:i}NAME,{0:T}NAME-1),({0:u}NAME)[({0:k}NAME)
0 0 1 0 0 2 1 1 1 
0 0 1 0 0 2 1 1 1 
5 0 0 0 1 1 NO-TRACE-STRING
0 3 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 61 26 10 0 3 
.TXT 50 0 -1074292857 0 0
Cg b73.000000,73.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard COPYRIGHT MIRON 
KAUFMAN 1997}
.TXT 5 0 -1074292887 0 0
Cg a72.000000,72.000000,60
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard We look next at the 
motion of the center of mass of the gas.}
.EQN 7 1 -1074292886 0 0
({0:xcm}NAME)[({0:j}NAME):(1)/({0:N}NAME)*((0,{0:N}NAME-1,{0:i}NAME,({0:x}NAME)[({0:i}NAME,{0:j}NAME)){64})
.EQN 1 25 -1074292885 0 0
({0:ycm}NAME)[({0:j}NAME):(1)/({0:N}NAME)*((0,{0:N}NAME-1,{0:i}NAME,({0:y}NAME)[({0:i}NAME,{0:j}NAME)){64})
.EQN 4 -26 -1074292891 0 0
{0}31&-{0:limg}NAME&(-{0:lim}NAME&{0:lim}NAME)&({0:ycm}NAME)[({0:j}NAME),({0:t}NAME)[({0:k}NAME)@{0}31&-{0:limg}NAME&(-{0:lim}NAME&{0:lim}NAME)&({0:xcm}NAME)[({0:j}NAME),({0:u}NAME)[({0:k}NAME)
0 0 1 0 0 2 1 1 1 
0 0 1 0 0 2 1 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 3 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 63 26 10 0 3 
.TXT 39 0 -1074292861 0 0
Cg a70.000000,70.000000,119
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard Finally we compute the 
square of the distance between the initial position and the current 
position for each molecule: }
.EQN 6 3 -1074292862 0 0
({0:rsqr}NAME)[({0:i}NAME,{0:j}NAME):((({0:x}NAME)[({0:i}NAME,{0:j}NAME)-({0:x}NAME)[({0:i}NAME,0)))^(2)+((({0:y}NAME)[({0:i}NAME,{0:j}NAME)-({0:y}NAME)[({0:i}NAME,0)))^(2)
.TXT 3 -3 -1074292860 0 0
Cg a73.000000,73.000000,71
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard Then we calculate the 
mean of the squared distance for the N particles.}
.EQN 7 2 -1074292971 0 0
({0:meanrsqr}NAME)[({0:j}NAME):(1)/({0:N}NAME)*((0,{0:N}NAME-1,{0:i}NAME,({0:rsqr}NAME)[({0:i}NAME,{0:j}NAME)){64})
.EQN 4 -2 -1074292955 0 0
2000&&(_n_u_l_l_&({0:lim}NAME)^(2))&(({0:meanrsqr}NAME)[({0:j}NAME)),(({0:\sx}NAME)^(2)+({0:\sy}NAME)^(2))*{0:j}NAME*({0:\Dt}NAME)^(2)@200&&(_n_u_l_l_&_n_u_l_l_)&{0:j}NAME
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 1 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 57 18 10 0 3 
.TXT 28 0 -1074292856 0 0
Cg b73.000000,73.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard COPYRIGHT MIRON 
KAUFMAN 1997}
.TXT 5 0 -1074292854 0 0
Cg a73.000000,73.000000,613
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}
\plain\cf1\fs24 \pard Note that for short times:\par <r{\cf2\up 2}> = ({
\f1 s}x{\cf2\up 2}+{\f1 s}y{\cf2\up 2})*j*{\f1 D}t{\cf2\up 2 }= 2(k{
\cf2\dn B}T/m)*({\f1 D}t)*t{\b  = }4(k{\cf2\dn B}T/m)*{\f1 t}*t,\par 
where: {\f1 D}t = {\f1 2t} is average time between last and next 
collision. This{\b  }relation, in fact the 3d analog of this: \tab 
\tab \tab <r{\cf2\up 2}> = 6(k{\cf2\dn B}T/m)*{\f1 t}*t,{\b  }was 
discovered independently by Einstein (1905) and the Polish physicist 
Smoluchowski.  The diffusion constant is: D = (k{\cf2\dn B}T/m)*{\f1 t}
. At longer times the molecules reach the walls so that: <r{\cf2\up 2}
> < lim{\cf2\up 2}.{\b \par \par ASSIGNMENT}{\b 1}: Study the 
influence of the size of the box on the Smoluchowski-Einstein law.\par 
\par \pard {\b ASSIGNMENT}{\b 2}: Study the Smoluchowski-Einstein law 
by simulating the gas with periodic boundary conditions.}
.TXT 97 0 -1074292853 0 0
Cg b73.000000,73.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs24 \pard COPYRIGHT MIRON 
KAUFMAN 1997}