### Author Topic: Browian motion  (Read 106725 times)

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Browian motion
« on: May 16, 2005, 03:55:49 pm »
Qualitative evidence of the microscopic nature of gases is shown by an effect called Brownian motion.
All the particles are moving with different velocity and in random direction.
The only interaction between partciles is coiision.
There is one larger particles which will be collide by surrounding particles and the behavior is similar to a random walk pattern.
This simulation let you get a visual representation of Brownian motion.
-*-

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
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Here is a related youtube movie

#### noha khaled

• Newbie
• Posts: 1
##### topic178
« Reply #1 on: November 27, 2005, 05:47:34 am »
[b:d5f38f5fff]Good morning,

I read that one of einstein's three papers published in 1905 is about brownoian motion , it states that the perpendicular distance moved by a brownian particle is directly propotional as the square root of the time , for example in four seconds it moves 2 cm, in nine seconds it moves 3 cm and so on , so the body is slowing down , it is deccelarating , what is the reason for this deccelaration and what is the effect causing it , is it related to the soultion ??

Thanks [/b:d5f38f5fff]

• Newbie
• Posts: 3
##### can''t get
« Reply #2 on: March 25, 2006, 11:54:02 pm »
ie shows "no privilege"

#### pyragas

• Newbie
• Posts: 1
##### Brownian motion
« Reply #3 on: April 03, 2006, 12:16:04 am »
The new aplet for Brownian motion is very nice.
Can you send it to me for off line use?
Kestutis

#### rhipple

• Jr. Member
• Posts: 22
• Relativity, Electromagnetism, Open Source Physics
##### Offline use
« Reply #4 on: April 03, 2006, 08:15:48 am »
If you register with an email address, they will be emailed to you automatically

• Newbie
• Posts: 3
##### the reason
« Reply #5 on: April 04, 2006, 07:57:15 pm »
i have find the :?:
i have the ZoomAlarm firewall
when i turn off it
all OK
the ejs is so great,it help me a lot
thanks Prof. Fu-Kwun Hwang and National Taiwan Normal University
you have done great work :!: :!: :!: ...

#### sarig

• physics student
• Newbie
• Posts: 1
##### topic178
« Reply #6 on: July 24, 2006, 11:19:27 pm »
The applet is great. thank you

#### Yves

• Newbie
• Posts: 8
##### Re: Browian motion
« Reply #7 on: September 21, 2007, 12:06:00 pm »
Dear Professor and All,

Thanks.

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Re: Browian motion
« Reply #8 on: September 21, 2007, 05:40:12 pm »
Sorry! It should work now. Please try it again!

#### Yves

• Newbie
• Posts: 8
##### Re: Browian motion
« Reply #9 on: September 21, 2007, 10:11:04 pm »
Thanks, Prof. Much appreciated.

This is a great site to learn about Brownian motion!

#### lookang

• Hero Member
• Posts: 1772
• http://weelookang.blogspot.com
##### Ejs Open source Best Brownian motion java applet
« Reply #10 on: March 19, 2010, 02:44:15 pm »
This is the best particles collision java applet i have ever seen.
800 particles and still not lag! it is incredible.
will study it carefully and add it here http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1455.msg5505#msg5505
Well done! credits to Francisco Esquembre and Fu-Kwun Hwang for this Best Brownian motion java applet
« Last Edit: March 19, 2010, 02:51:45 pm by lookang »

#### lookang

• Hero Member
• Posts: 1772
• http://weelookang.blogspot.com
##### Ejs Open source Brownian Motion Applet
« Reply #11 on: March 19, 2010, 04:29:05 pm »
Dear Prof,

Is it normal is terms of the computation that there is a small total kinetic energy (TKE) and total momentum (TMOM) lost in this model?

I hope i coded the TKE and TMOM correct.

Whichever solver Euler, Euler-Richardson, ......, QSS 3 etc there seems to be a small loss.

it that true? can i verify this model's has computation carried over error ?

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Re: Browian motion
« Reply #12 on: March 19, 2010, 05:43:15 pm »
Euler's method is only good for constant motion (velocity is constant).
Euler-Richardson or midpoint method is good for constant acceleration.

Normally, I use Runge-Kutta 4th order method, it is rough 100 times better resolution than midpoint error. This is good for most cases.
Sometime, I used Runge-Kutta Fehlberg adjustable time step method for interaction for like 1/r2 (when r is small , the error become larger).
However, you need to asjust time step carefully.
Smaller time will give you smaller run time error until run-offer error become major problem (10-6 for float, 10-13 for double).
If the particle size is very small , or there are many particels. the error will accumuate.

You need to study numerical method to understand what is the best way to used for different cases.

I would suggest you use Runge-Kutta 4th order method for most of the cases.
The error could be due to numerical method. However, it could be due to the coding.

You can calculate error if you know the theoretical value in advance.
Otherwise, it will depend on how much you know about the system to have a better guess.

#### lookang

• Hero Member
• Posts: 1772
• http://weelookang.blogspot.com
##### Re: Browian motion
« Reply #13 on: March 23, 2010, 11:40:43 pm »
I would suggest you use Runge-Kutta 4th order method for most of the cases.
The error could be due to numerical method. However, it could be due to the coding.

i was analyzing the codes and realized
public double getA (int i,double[] v) {
if(i==0)return 0; // b*v[0]; i removed the b*v[0]; because original used a speed decay constant b = -.25 i think
else return 0;
}

after i change it to return 0, the TKE is constant now!
cool! so it was the coding.