Laboratory for Computational Science & Engineering: High School Outreach Program

Program Goals:

• Introduce exposure to computational science in the high school curriculum.

• Target talented high school students with an interest in science and/or computing.

• Construct instructional materials that couple computationally intensive applications to graphical output through a point-and-click user interface accessible to students.

Program Leverage:

• Build on course materials developed for Woodward’s undergraduate-level course in computational methods for the physical sciences.

• Leverage computing and visualization expertise at the LCSE.

• Leverage LCSE’s close connection with SGI.

• Leverage location of LCSE in the midst of Minnesota’s major metro area.

The High School Teachers:

• Identify talented and motivated teachers.

• Bring teachers into the LCSE for 5 weeks each summer to introduce them to real scientific research environment and to cement personal relationships they can draw upon during the academic year.

• Involve the teachers in the choice of instructional software and the design of the user interfaces.

• Teachers test materials in their classes.

The High School Students:

• The high school teachers identify outstanding, talented, and motivated students to bring with them into the LCSE for 10 weeks during the summer.

• The students are involved in the design of the user interfaces to the instructional software.

• The students learn C programming so that they can modify/improve the user interfaces.

• The students help the teachers set up, maintain, and operate instructional labs.

The High Schools:

• The high schools are large, public high schools with diverse student bodies.

• The high schools are committed to the program, and therefore support the teachers with lab space and equipment.

• The high schools support the teachers by allowing them to develop new courses that grow out of their LCSE program experience.

• The high schools participate in other advanced math and science programs.

Program Components:

• Development of computer programs for instructional use.Leveraged from Woodward’s undergraduate course development work.

• Development of user interfaces to these programs.Performed by undergraduate student employees.

• Development of written instructional materials. LCSE postdoc part-time.

More Program Components:

• Guiding of work of teachers and high school students in the LCSE in the summer.LCSE postdocs, students, and staff.

• Assistance in high school lab set up and maintenance.LCSE system manager.

• LCSE lab tours for high school student groups.LCSE staff.

• Overall program management.Ms. Julia Sytine, LCSE Administrator.

Potential New Program Components:

• Summer programming course at LCSE for group of 20 high school students.Could potentially be taught by LCSE postdoc.

• Teacher training course at LCSE given for use of LCSE instructional materials.Could potentially be team taught by LCSE postdoc and high school teachers who helped develop these materials.

• A technology fair during the academic year for computer-related projects.Could be hosted at Arlington HS.

The Wave Table Program:

• Designed to duplicate a physically realizable experiment — a square table of shallow water with waves generated by moving one side back and forth.

• Objects of different shapes which change the water depth by different amounts may be introduced.

• A graph of the wave amplitude along a chosen horizontal line may be displayed dynamically.

The Science:

• Wave propagation in 2-D observed.

• Wave reflection.

• Wave diffraction.

• Wave refraction.

• Focusing of wave energy by lenses.

• Focusing of wave energy by curved mirrors.

• All can be directly observed; you can actually see the waves.

Student Actively Involved:

• This application is interactive. The student does not passively observe it; he or she designs the experiment, runs it, refines it, runs it again, . . .

• The result of the experiment can be saved and shown as a movie to another student, or to the instructor.

• The selected graphical output is quantitative, while the wave displays are more qualitative.

Computational Mathematics:

• This program represents the 2-D Laplacian operator in the wave equation

2a/t2 = c2 2aby an extremely simple 5-point difference formula. The designated objects alter the value of the local wave speed c and each of 2562 uniform grid points is updated on each time step by about 5 lines of Fortran code. The program runs in real time and gives graphic output as it executes.

Specific Example:

• Screen dumps saved from a run with a high frequency wave input, two completely reflecting rectangular objects, and a refracting, lens-shaped object are shown on the following slides.

• The first slide shows the problem set up.

• The dialog box at the upper left is shown defining the lens-shaped object.

• The graphical data will correspond to the horizontal dashed line.

The Heat Transfer Program:

• Designed to simulate a problem of real concern for Minnesotans — heat transfer in a house.

• A 2-D house floor plan is constructed by placing rectangular objects of selected materials onto a square region.

• An outside temperature on each side of the house is specified.

• Regions of constant temperature (heat registers, air conditioners) are specified

The Science:

• Heat transfer in 2-D is observed.

• Conduction front propagation and spreading.

• Approach to asymptotic steady temperature distribution.

• Behavior of materials with different thermal conductivities.

• Variation of thermal insulation with material layer thickness. Windows versus walls. Brick versus wood.

Student Actively Involved:

• This application is interactive. The student does not passively observe it; he or she designs the experiment, runs it, refines it, runs it again, . . .

• The result of the experiment can be saved and shown as a movie to another student, or to the instructor.

• This application is computationally intensive. Runs are expensive and are therefore must be planned thoughtfully.

Computational Mathematics:

• This program represents the 2-D Laplacian operator in the heat equation

T/t = 2Tby an extremely simple 5-point difference formula. The designated objects alter the value of the local conductivity , and each of 5122 uniform grid points is updated on each time step by about 5 lines of Fortran code. The program runs in the background, generating image files for subsequent movie animation.

Specific Example:

• Images saved from a run for a fairly elaborate 2-D house are shown on the following slides.

• The first slide shows the material dialog box used for problem set up.

• The second slide shows the blank house layout area with outside temperature selectors.

• The fifth slide shows the finished house, then the heat transfer movie follows.

The Vibrating String Program:

• Designed to simulate a physical system that can be realized in the lab — a vibrating string (a slinky will also do).

• A set of points along the string are selected with mouse clicks and dragged up or down to pluck the string.

• Sliders allow the string tension, mass per unit length, and transverse velocity to be specified at each selected point.

• Intermediate values are interpolated.

The Science:

• Wave propagation in 1-D is observed.

• Initial velocities allow modes travelling purely in one direction to be set up.

• String tension and density determine local wave propagation speed.

• Wave transmission and reflection at changes in string density and tension.

• Impedance matching to minimize wave reflection, via gradual changes rather than sudden ones in density or tension.

Student Actively Involved:

• This application is interactive. The student does not passively observe it; he or she designs the experiment, runs it, refines it, runs it again, . . .

• The result of the experiment can be saved and shown as a movie to another student, or to the instructor.

• The default number of 2000 mass points connected by 1999 springs can be reduced, and convergence to continuous string behavior can be observed.

Computational Mathematics:

• This program represents the string by a discrete mechanical model consisting of N mass points interconnected by N-1 springs. No calculus is needed, and the equations of motion are trivial (but many). Only Hooke’s law relating the force linearly to spring extension is needed, and of course F=ma. A trivial leap-frog numerical scheme is imple-mented, with numerical noise damping. The Fortran code is very simple, but time steps cannot exceed Courant limit.

Specific Example:

• Images saved from a run for plucking the string at 9 points are shown on the following slides.

• The initial transverse velocities are 0, so each triangular disturbance launches 2 identical half-amplitude signals traveling in opposite directions.

• These waves all pass through each other, since the equations are linear because the transverse displacements are assum-ed small (and exaggerated in plots).

The Planetary System Program:

• Designed to simulate a physical system that cannot be realized in the lab — a solar system with 3 planets, named Venus, Earth, and Mars.

• The default is the actual 3 planets, begun at points on their actual orbits.

• The mass of each planet can be modified by any positive factor.

• Either the planetary positions or the orbit traces are displayed dynamically.

The Science:

• The actual orbits of these 3 planets may be observed, but this is boring.

• One planet, say Earth, can be made more massive, in which case it will disrupt the other orbits, temporarily capturing other planets as satellites and/or ejecting them from the system.

• The sensitivity of this dynamical system, when one planet is massive, to the initial conditions (the big planet’s mass) has to be seen to be believed.

Student Actively Involved:

• This application is interactive. The student does not passively observe it; he or she designs the experiment, runs it, refines it, runs it again, . . .

• The result of the experiment can be saved and shown as a movie to another student, or to the instructor.

• The program can be instructed to use different numerical integration techniques, and their relative (and very different) effectiveness can be studied.

Computational Mathematics:

• The program uses predictor-corrector methods to advance the planets’ positions. The forces come from Newton’s law of gravitation and F=ma. The new position is first guessed using the present position, velocity, and acceleration only. This “prediction” is then “corrected” by incorporating the knowledge of the force at the newly guessed position. Without this correction step, the numerical scheme is unstable. This scheme is really simple.

Specific Example:

• Planet positions for the default orbits appear in the first set of slides.

• Planetary orbits are traced in the second set of slides for a more interesting case.