Computer Simulation tool for Learning Brownian Motion

							                                                             (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                              Vol. 9, No. 1, January 2011

     Computer Simulation tool for Learning Brownian
                        Motion
                                           Dr Anwar Pasha Abdul Gafoor Deshmukh
            Lecturer, College of Computer and Information Technology, University of Tabuk , Tabuk., Saudi Arabia.
                                                  mdanwardmk@yahoo.com



Abstract— With advancement of computers and Internet, there               platform dependence, the cost of mailing materials, and
has been an increasing trend in utilizing computers and Internet          identifying interested users. Instead of searching for people
for teaching and Education. Advanced topics and High Tech                 who would like to use a given CBT model, the Web allows the
experiments demand for lot of infrastructure. There are areas in          reader to find the material and review it at his own pace.
living sciences and other subjects where the magnitude of
information is so huge that it is more convenient to do the
                                                                          Because Web pages can be updated at any point, it is possible
experiment by simulation using computers. The present work                to keep the CBT materials up to date without having to do
relates to development of computer based learning resource that           anything except edit the HTML documents involved. It is also
can be used as an online teaching aid or an offline tool to study         possible to keep channels of communication open between
the Brownian motion in two dimensions. It is an interactive tool          author and reader, even if the two have never met before or had
where the learner can change the parameters of interest to study          any sort of contact. Finally, the use of server-side scripts and
the Brownian motion and actually see the effect by way of                 interactive forms make it possible for the reader to be tested on
simulated graphics. Quantitative values of the parameters arising         what he has learned without any need for supervision.
from the simulation study are also available to the learner. The
Brownian motion is a phenomenon occurring at microscopic                  Computer-based training (CBT) services are useful where a
scale and thus actual study of the experiment requires real time          student learns by executing special training programs on a
monitoring of microscopic development and progress of the                 computer relating to their occupation. CBT is especially
Brownian motion which is a tedious task and very difficult to             effective for training people to use computer applications
implement in laboratory. To this effect, to carry out the
                                                                          because the CBT program can be integrated with the
experiment under different desired conditions, a computer based
tool is developed that enables the learner to conduct experiment
                                                                          applications so that students can practice using the application
using simulation and see the results quantitatively. It is being          as they learn.
uploaded on internet as an online e-learning material.                                          BROWNIAN MOTION
   Keywords-Computer Simulation; CBT; Brownian Motion                     The Brownian motion has been named in the honor of the
                        INTRODUCTION                                      Scottish botanist Robert Brown. He has presented the theory of
                                                                          Random movement of particles. The Brownian motion is the
The world is witnessing a change in every aspect of life since            random movement of particles discovered by the Scottish
last 2 decades. The advance in Information Technology has                 botanist Robert Brown has made microscopically observations
opened up new vistas in the history of education also.                    in the months of June, July and August, 1827, on the particles
Computer has become a useful teaching aid. It has infact                  contained in the pollen of plants; and on the general existence
became an integral part of learning                                       of active molecules in organic and inorganic bodies, which can
                    E-LEARNING AND CBT                                    be found in the miscellaneous botanical works of Robert
                                                                          Brown, Volume 1. In his experiment he found that “the pollen
The term E-Learning means electronic Learning and it is                   particles appeared to move in a completely random fashion”.
basically the online delivery of information, Communication,
training and learning. E-Learning seems to have a multiplicity            The major contribution to the explanation, interpretation and
of definitions to each of its users and the term seems to mean            application came from Albert Einstien in 1905and Marian
something different. A very comprehensive definition has been             Smoluchowski obtained that “If Kinetic theory of molecules
given by the Cisco System, which defines ‘E-Learning is                   was right, then the molecules in the water would move at
Internet-enabled learning. Components can include content                 random, the small particles to move in exactly the same way
delivery in multiple formats, management of the learning                  described by Brown.” This work of Einstien was further
experience, and a networked community of learners, content                refined by Norbart Weiner a mathematician at MIT, in 1923,
developers and experts. E-Learning provides faster learning at            established the modern mathematical framework of Brownian
reduced costs, increased access to learning, and clear                    motion.
accountability for all participants in the learning process.                               OUTLINE OF ACTUAL WORK
The World Wide Web now offers the possibility of conducting               The principles and logic of the Brownian motion is be derived
CBT on a global scale, without the usual restrictions of                  from standard literature such as books and research journals.



                                                                    156                              http://sites.google.com/site/ijcsis/
                                                                                                     ISSN 1947-5500
                                                             (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                              Vol. 9, No. 1, January 2011
For the implementation of the CBT, necessary algorithms are               in pressure of gas results in an increase in the number of
designed and tested initially in C++ and later on implemented             molecules present in a given volume of gas. By default the
on a Windows based platform using Html java with strong                   simulation window uses 100 molecules, an increase in value N
graphics support for user friendly interactive input and output           corresponds to an increase in pressure (Figure-1(b)) and
facility. This CBT tool is simulates the Brownian motion with             decrease in N correspond to decrease in pressure (Figure-1(a).
the parameters provided by the user. As the Brownian motion               Thus the simulation of the movement of the gas molecules can
precedes the random movement of the particle performing                   be studied under changing pressure conditions. Random zigzag
Brownian motion is displayed graphically. During its motion               motion of the molecules when collide with each other undergo
the path traced by the movement is also be displayed                      deflection and the path is changed that can be clearly seen in
graphically. The basic concept involves the displacement of the           the simulation. The effect of change in pressure can be
particle performing the Brownian motion so the numerical                  visualized clearly from the simulation.
values of the parameters of interest are separately recorded. At
                                                                          In case if the particles collide with a particle with a different
the end of the motion the variables of interest will be displayed
                                                                          mass, the displacement of the particle will depend on the mass
and the user can go for a fresh experiment again or quit the
                                                                          of the particle. To study the effect of the relative masses the
program.
                                                                          ratio of M1: M2 can be changed; the value of M1/M2 is
                                                                          assigned a value of 27 by default This means the mass of the
                 TESTING AND PRESENTATION                                 red molecule (M1) is 27 times greater than the rest of the
                                                                          molecules. This simulation allows for the study of the effect of
The opening page of the CBT is provided with active links to
                                                                          M1/M2 on the distance moved by the particle in one collision
the resources within the CBT to make different features and
                                                                          or the mean free path when taken on an average basis. It can be
information available. In addition to the links provided on the
                                                                          clearly seen in the simulation that as the ratio of M1/M2 is
left giving information of related topics. The learner can
                                                                          large (Figure-1(c), the displacement of the particle is small and
visualize graphically and perceive the way the movement of the
                                                                          for smaller values of M1/M2, this distance moved in one
gas molecules behaves under changing conditions.
                                                                          collision is large. Thus the process of Brownian motion can be
                                                                          clearly studied, perceived and understood by a learner which is
                                                                          not that easy in actual laboratory. This also demonstrates the
                                                                          concept of momentum transfer as the larger mass undergoes
                                                                          smaller displacement and vice versa. (Figure-1(d)




          Figure-1(a) Brownian motion of 50 gas molecules’


                                                                                Figure-1(c)Brownian motion with 50 mass(m2/m1)




        Figure-1(b) Brownian motion of 200 gas molecules’

To study the effect of pressure, one has to change the number
of particles present in the container. As an increase in pressure                 Figure-1(d)Brownian motion with 25 mass(m2/m1)
causes an increase in density of the gas molecules, an increase



                                                                    157                              http://sites.google.com/site/ijcsis/
                                                                                                     ISSN 1947-5500
                                                             (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                              Vol. 9, No. 1, January 2011
The zigzag random motion of the molecules also depends on                 successfully be demonstrated through the CBT as described
the temperature of the gas, to study the effect of temperature of         above.
the gas on the nature of Brownian motion, the simulation
window is provided with two buttons with + and – sign to vary                                  CONCLUSIONS AND RESULTS
the speed of motion of the gas molecules. This speed of the gas
                                                                          The CBT developed under the present project work has been
molecules is in fact due to the kinetic energy of the
                                                                          successfully designed, developed, implemented and thoroughly
                  1
          KE =      mv 2                                                  tested. We used this CBT in a small class of students and found
molecules         2      , where m is the mass and v is the               it to be very effective. It is being uploaded on Web to study the
velocity of the molecule. Thus increase in velocity of the gas            Brownian motion.
molecules corresponds to increase in temperature and a                    The CBT based on the study of Brownian motion was planned,
decrease in velocity corresponds to a decrease in temperature             designed and developed using techniques and tools described
of the gas. Thus With the help of the two buttons, the effect of          earlier. All the branching and links were carefully checked and
change in temperature of the gas on the Brownian motion can               tested for correctness.
be demonstrated. The learner can easily visualize the effect of
the change in temperature on the Brownian motion and the                                                 REFERENCES
effect of resulting collisions.
The two options Trace and No Boundary allow to choose the                      [1]   Robert Brown, August 1827 “A brief account of microscopical
display of the path of the particle to be enabled or disabled,                       observations” Volume 1.
                                                                               [2]   Stachel, John, 1998, “Einstein’s Miraculous Year: Five Papers that
when check the trace option, the path traced by the red                              Changed the Face of Physics” Princeton: Princeton University
molecule remains visible as a blue trace of zigzag line else the                     Press, p173
zigzag line will not appear (Figure-1(e)). No boundary option                  [3]   Jerison, David and Daniel Stroock, Number 4 (1995) , “Norbert
makes the walls of the container as penetrable as if the medium                      Weiner.” Notices of the AMS Volume 42, p432.
                                                                               [4]   Chetan Srivastava, “Fundamentals of Information Technology”,
(gas) is continuous and particle crossing one boundary appears                       Kalyani Publishers, New Delhi.
from the other side so that the total number of molecules in the               [5]   Rajaraman V, 1996. “Fundamentals of Computer”, (2nd Edition),
container remains constant.(Figure-1(f))                                             New Delhi, Prentice Hall of India, ,
                                                                               [6]   “Electronic learning - Wikipedia, the free encyclopedia” Computer
                                                                                     Based Learning, sometimes abbreviated CBL, refers to the use of
                                                                                     ... reuse of electronically-based teaching materials and in particul
                                                                                     creating en.wikipedia.org/wiki/E-learning


                                                                                                     AUTHORS PROFILE
                                                                          Personal Detail
                                                                          Name                   : Deshmukh Anwar Pasha
                                                                          Father Name            : Deshmukh Abdul Gafoor
                                                                          Date of Birth          : 25-1-1977
                                                                          Marital Status         : Married
                                                                          Languages Known : English, Marathi, Hindi, Urdu
                                                                          Permanent Address : Near Aman Masjid, Motiwala Nager, New Baigipura,
                                                                          Indira Nager, Gali No 21, Aurangabad, Phone No. +966-544354254(KSU),
                                                                          +91-9326966582(India)
     Figure-1(e) Brownian motion without Trace the path                   E-Mail                 : mdanwardmk@yahoo.com,
                                                                          Educational Qualification
                                                                          Doctor of Philosophy (Computer Science)
                                                                          July-2010 Magadh University, Bodhgaya, India.
                                                                          Master of Philosophy (Information Technology)
                                                                          August-2008 Yashvantrao Chavan Maharashtra Open University, Nasik,
                                                                          India.
                                                                          Master of Science (Information Technology)
                                                                          June 2003 Dr. Babasaheb Ambedkar Marathwada University, Aurangabad,
                                                                          India.




    Figure-1(f) Brownian motion without Trace and
                    With Non boundary

  Thus the role of the main parameters, gas pressure,
temperature and the relative mass of molecules can



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                                                                                                           ISSN 1947-5500