(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.
[email protected]
Abstract— With advancement of computers and Internet, there has been an increasing trend in utilizing computers and Internet for teaching and Education. Advanced topics and High Tech experiments demand for lot of infrastructure. There are areas in living sciences and other subjects where the magnitude of information is so huge that it is more convenient to do the experiment by simulation using computers. The present work relates to development of computer based learning resource that can be used as an online teaching aid or an offline tool to study the Brownian motion in two dimensions. It is an interactive tool where the learner can change the parameters of interest to study the Brownian motion and actually see the effect by way of simulated graphics. Quantitative values of the parameters arising from the simulation study are also available to the learner. The Brownian motion is a phenomenon occurring at microscopic scale and thus actual study of the experiment requires real time monitoring of microscopic development and progress of the Brownian motion which is a tedious task and very difficult to implement in laboratory. To this effect, to carry out the experiment under different desired conditions, a computer based tool is developed that enables the learner to conduct experiment using simulation and see the results quantitatively. It is being uploaded on internet as an online e-learning material.
platform dependence, the cost of mailing materials, and identifying interested users. Instead of searching for people who would like to use a given CBT model, the Web allows the reader to find the material and review it at his own pace. Because Web pages can be updated at any point, it is possible to keep the CBT materials up to date without having to do anything except edit the HTML documents involved. It is also possible to keep channels of communication open between author and reader, even if the two have never met before or had any sort of contact. Finally, the use of server-side scripts and interactive forms make it possible for the reader to be tested on what he has learned without any need for supervision. Computer-based training (CBT) services are useful where a student learns by executing special training programs on a computer relating to their occupation. CBT is especially effective for training people to use computer applications because the CBT program can be integrated with the applications so that students can practice using the application as they learn. BROWNIAN MOTION
Keywords-Computer Simulation; CBT; Brownian Motion
The Brownian motion has been named in the honor of the Scottish botanist Robert Brown. He has presented the theory of Random movement of particles. The Brownian motion is the random movement of particles discovered by the Scottish botanist Robert Brown has made microscopically observations in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies, which can be found in the miscellaneous botanical works of Robert Brown, Volume 1. In his experiment he found that “the pollen particles appeared to move in a completely random fashion”.
INTRODUCTION The world is witnessing a change in every aspect of life since last 2 decades. The advance in Information Technology has opened up new vistas in the history of education also. Computer has become a useful teaching aid. It has infact became an integral part of learning E-LEARNING AND CBT The term E-Learning means electronic Learning and it is basically the online delivery of information, Communication, training and learning. E-Learning seems to have a multiplicity of definitions to each of its users and the term seems to mean something different. A very comprehensive definition has been given by the Cisco System, which defines ‘E-Learning is Internet-enabled learning. Components can include content delivery in multiple formats, management of the learning experience, and a networked community of learners, content developers and experts. E-Learning provides faster learning at reduced costs, increased access to learning, and clear accountability for all participants in the learning process.
The major contribution to the explanation, interpretation and application came from Albert Einstien in 1905and Marian Smoluchowski obtained that “If Kinetic theory of molecules was right, then the molecules in the water would move at random, the small particles to move in exactly the same way described by Brown.” This work of Einstien was further refined by Norbart Weiner a mathematician at MIT, in 1923, established the modern mathematical framework of Brownian motion. OUTLINE OF ACTUAL WORK
The World Wide Web now offers the possibility of conducting CBT on a global scale, without the usual restrictions of
The principles and logic of the Brownian motion is be derived from standard literature such as books and research journals.
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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011
For the implementation of the CBT, necessary algorithms are designed and tested initially in C++ and later on implemented on a Windows based platform using Html java with strong graphics support for user friendly interactive input and output facility. This CBT tool is simulates the Brownian motion with the parameters provided by the user. As the Brownian motion precedes the random movement of the particle performing Brownian motion is displayed graphically. During its motion the path traced by the movement is also be displayed graphically. The basic concept involves the displacement of the particle performing the Brownian motion so the numerical values of the parameters of interest are separately recorded. At the end of the motion the variables of interest will be displayed and the user can go for a fresh experiment again or quit the program.
in pressure of gas results in an increase in the number of molecules present in a given volume of gas. By default the simulation window uses 100 molecules, an increase in value N corresponds to an increase in pressure (Figure-1(b)) and decrease in N correspond to decrease in pressure (Figure-1(a). Thus the simulation of the movement of the gas molecules can be studied under changing pressure conditions. Random zigzag motion of the molecules when collide with each other undergo deflection and the path is changed that can be clearly seen in the simulation. The effect of change in pressure can be visualized clearly from the simulation. In case if the particles collide with a particle with a different mass, the displacement of the particle will depend on the mass of the particle. To study the effect of the relative masses the 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 red molecule (M1) is 27 times greater than the rest of the molecules. This simulation allows for the study of the effect of M1/M2 on the distance moved by the particle in one collision or the mean free path when taken on an average basis. It can be clearly seen in the simulation that as the ratio of M1/M2 is large (Figure-1(c), the displacement of the particle is small and for smaller values of M1/M2, this distance moved in one 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)
TESTING AND PRESENTATION The opening page of the CBT is provided with active links to the resources within the CBT to make different features and information available. In addition to the links provided on the left giving information of related topics. The learner can visualize graphically and perceive the way the movement of the gas molecules behaves under changing conditions.
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 causes an increase in density of the gas molecules, an increase
Figure-1(d)Brownian motion with 25 mass(m2/m1)
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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011
successfully be demonstrated through the CBT as described above.
The zigzag random motion of the molecules also depends on the temperature of the gas, to study the effect of temperature of the gas on the nature of Brownian motion, the simulation window is provided with two buttons with + and – sign to vary the speed of motion of the gas molecules. This speed of the gas molecules is in fact due to the kinetic energy of the
KE =
CONCLUSIONS AND RESULTS The CBT developed under the present project work has been successfully designed, developed, implemented and thoroughly tested. We used this CBT in a small class of students and found it to be very effective. It is being uploaded on Web to study the Brownian motion. The CBT based on the study of Brownian motion was planned, designed and developed using techniques and tools described earlier. All the branching and links were carefully checked and tested for correctness.
1 mv 2 2 , where m is the mass and v is the
molecules velocity of the molecule. Thus increase in velocity of the gas molecules corresponds to increase in temperature and a decrease in velocity corresponds to a decrease in temperature of the gas. Thus With the help of the two buttons, the effect of change in temperature of the gas on the Brownian motion can be demonstrated. The learner can easily visualize the effect of the change in temperature on the Brownian motion and the effect of resulting collisions. The two options Trace and No Boundary allow to choose the display of the path of the particle to be enabled or disabled, when check the trace option, the path traced by the red molecule remains visible as a blue trace of zigzag line else the zigzag line will not appear (Figure-1(e)). No boundary option makes the walls of the container as penetrable as if the medium (gas) is continuous and particle crossing one boundary appears from the other side so that the total number of molecules in the container remains constant.(Figure-1(f))
REFERENCES [1] [2]
[3] [4] [5] [6]
Robert Brown, August 1827 “A brief account of microscopical observations” Volume 1. Stachel, John, 1998, “Einstein’s Miraculous Year: Five Papers that Changed the Face of Physics” Princeton: Princeton University Press, p173 Jerison, David and Daniel Stroock, Number 4 (1995) , “Norbert Weiner.” Notices of the AMS Volume 42, p432. Chetan Srivastava, “Fundamentals of Information Technology”, Kalyani Publishers, New Delhi. Rajaraman V, 1996. “Fundamentals of Computer”, (2nd Edition), New Delhi, Prentice Hall of India, , “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) E-Mail :
[email protected], Educational Qualification
Figure-1(e) Brownian motion without Trace the path
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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