Implementation of Monte Carlo and Numerical Integration Techniques within an Online Physics Laborato - PowerPoint PPT Presentation

1 / 38
About This Presentation
Title:

Implementation of Monte Carlo and Numerical Integration Techniques within an Online Physics Laborato

Description:

... students how to measure and analyze the decay of several radioactive sources. ... understanding radioactive decay based on observing the decay of multiple ... – PowerPoint PPT presentation

Number of Views:73
Avg rating:3.0/5.0
Slides: 39
Provided by: malachi3
Category:

less

Transcript and Presenter's Notes

Title: Implementation of Monte Carlo and Numerical Integration Techniques within an Online Physics Laborato


1
Implementation of Monte Carlo and Numerical
Integration Techniques within an Online Physics
Laboratory Environment
  • by Malachi Schram

2
Thesis Goals
  • Develop a robust and sophisticated online physics
    laboratory environment.
  • Compare the Flash 5 and Java development
    environments to determine which is best suited to
    develop the online physics laboratory environment.

3
Physical Modeling Techniques
  • Monte Carlo Techniques
  • Inverse Transformation Method
  • Rejection Method
  • Smearing Method
  • Numerical Integration Technique
  • Eulers Method

4
Monte Carlo Techniques
  • Monte Carlo techniques are statistical methods
    used to solve physical or mathematical problems.
  • These techniques use sequences of random numbers
    to perform simulations.
  • They are ideally suited to simulate random or
    probabilistic processes.

5
Inverse Transformation Method
  • Generates a random number from a probability
  • density function by solving the probability
    density
  • function's variable in terms of randomly
    generated
  • numbers. This is achieved as follows
  • We solve the inverse of the integral of our
    probability density function at an arbitrary
    point a F(a), in terms of a random number r.
  • We generate a unique random variable a, as
    follows
  • a F-1(r)

6
Rejection Method
  • Generates random numbers for a
  • distribution function f(x). This is achieved
  • as follows
  • Define a comparison function h(x) such that it
    encloses the desired function f(x).
  • Choose uniformly distributed random points under
    h(x).
  • If a point lies outside the area under f(x)
    reject it and choose another point.

7
Illustration of the Rejection Method
  • The following
  • is an illustration
  • of the rejection
  • method using
  • a square
  • function for the
  • comparison
  • function.

8
Generating points (xi, yi)
  • To generate a random number for xi, we can use a
    variant of the inverse transformation method.
  • To generate a random number for yi, we can
    multiply a random number between 0 and 1 with the
    value of h(xi). Therefore, we generate a number
    between 0 and h(xi).

9
Maxwell Speed Distribution
  • We generated the Maxwell speed distribution by
    using a square function for the comparison
    function h(x).
  • The simulated data closely represents the desired
    distribution function.

10
Smearing Method
  • Generates deterministic experimental results,
    including experimental uncertainties.
  • Assumes that the data being modeled has a
    Gaussian distribution.

11
Gaussian Distribution
  • The rejection method was used to generate the
    Gaussian distribution.
  • A square function was used as the comparison
    function h(x).
  • The simulated data closely represents the desired
    distribution function.

12
Eulers Method
  • Approximation technique commonly used to
  • solve the equations of motion. This is done
  • as follows
  • Approximate an infinitely small increment of time
    such that dt??t.
  • The velocity of a particle after a small
    increment of time with initial velocity v(t) is
    v(t?t)v(t)a?t.

13
Technical Environments
  • Flash 5
  • Scripting Language
  • Cross-Platform
  • Short Learning Curve
  • Ease in Creating Graphical Objects
  • Minimal Programming Required
  • Poor Simulation Performance
  • Java
  • Interpreted Language
  • Cross-Platform
  • Long Learning Curve
  • Lengthy in Creating Graphical Objects
  • Extensive Programming Required
  • Strong Simulation Performance

14
Nuclear Decay Laboratory
Note...
This nuclear decay laboratory was created using
Flash 5.
15
Explanation of the Stationary States
Note...
This animation was created using Flash 5.
16
Java Laboratory (JLab)
  • Designed to be an expandable online
  • software package used to simulate physics
  • experiments.
  • Development Considerations
  • Ease in developing new online experiments
  • Ease in adding new functionality to existing JLabs

17
Graphical User Interface Structure
Note...
Two components laboratory GUI option panel and
HTML Viewer.
18
Laboratory GUI Option Panel
Note...
Provides the ability to manipulate the
experimental parameters.
19
HTML Viewer
Note...
Presents the theory and experimental procedures
to the student.
20
How does a JLab work?
  • A student logs on to the desired JLab.
  • The JApplet is initialized.
  • The student reads the theory and experimental
    procedures.
  • The student manipulates the experimental
    parameters as instructed.
  • The student clicks on the run button.
  • The JApplet calls the necessary methods and
    returns an output to the student.
  • The student analyzes the data using his/her
    preferred analysis tool.

21
Nuclear Decay JLab
22
Educational Goals
  • Teach students how to measure and analyze the
    decay of several radioactive sources.
  • Guide students in understanding radioactive decay
    based on observing the decay of multiple sources.
  • Instruct students on how to determine the decay
    properties of an unknown decay source and then
    identify the source.

23
Advantages of a Nuclear Decay JLab
  • Broader Target Audience
  • Flexibility in choosing a radioactive
    gamma-emitter source
  • Flexibility in choosing the experimental
    parameters
  • Teaching Flexibility

24
Java Implementation
  • Simulate particle decay
  • Simulate background noise
  • Account for source location in respect to
    detector location

25
Nuclear Decay Distribution
  • We generated the nuclear decay events by using
    the inverse transformation method.
  • The simulated data closely represents the desired
    distribution function.

26
Background Decay Distribution
  • We generated the background decay events by using
    the smearing method.
  • The simulated data closely represents the desired
    distribution function.

27
Accounting for the Source Location
  • Divide the total number of generated decay events
    by the location of the source in respect to the
    detector.

28
Nuclear Decay JLab GUI
29
Stern-Gerlach JLab
30
Educational Goals
  • Teach students how to measure and analyze the
    distribution of the deflection for various beam
    sources.
  • Guide students in understanding the quantization
    of angular momentum and the Maxwell distribution
    by observing the distribution of deflection for
    multiple beam sources.

31
Advantages of a Stern-Gerlach JLab
  • Broader Target Audience
  • Flexibility in choosing a molecular beam source
  • Flexibility in choosing the experimental
    parameters
  • Teaching Flexibility

32
Java Implementation
  • Simulate the distribution of the quantized
    magnetic substates of the atom.
  • Simulate the velocity distribution of the
    emerging molecular beam.
  • Simulate the transport system of the atom.

33
Substates of the Atom
  • Atom object was created to store crucial physical
    properties of each atom.
  • The getSpin() method assigns the atoms spin
    state.

34
Velocity Distribution of Atoms
  • The MolecularBeam class was developed to assign a
    velocity to the atoms in the beam.
  • We generated the velocity by using the rejection
    method.
  • The simulated data closely represents the desired
    distribution function.

35
Distribution of the Beam Deflection
  • The deflection was generated using the rejection
    and Eulers method.
  • The simulated data closely represents the desired
    distribution function.

36
Stern-Gerlach GUI Option Panel
37
Summary
  • We developed
  • Online Virtual Nuclear Decay Laboratory
  • Online Virtual Stern-Gerlach Laboratory
  • Java Physics Library

38
Future Possibilities
  • Major Enhancements
  • Combining Flash 5 and Java
  • Icon-Oriented Modeling System
  • Professor GUI Interface
  • Analysis Visualization
  • Minor Enhancements
  • Implement XML MathML
  • Develop new numerical integration techniques
Write a Comment
User Comments (0)
About PowerShow.com