B. K. Clark and Richard F. Martin, Jr.
Illinois State University
Contributors:
E. Rosa
D. Holland
R. Balfanz
N. Jurasek
Q. Su
R. Grobe
N. Nutter
B. Vleck

2004 - 2006
Institution # of faculty publications % of faculty average grant % of faculty per faculty with publication amount with grant
Top 10 68 6.62 64 % $ 569 K 11 %
ISU Physics 12 4.83 83 % $ 92 K 17 %
Top 10 Physics departments
Cal Tech, Harvard, Cornell, JHU, UC
Berkeley, NYU, Michigan, Duke, Stanford,
UIUC
From:
“Chronicle of Higher Education” 1/12/2007 www.chronicle.com/stats/productivity

Nonlinear Dynamics
Nanoscience
Space Physics
Atomic, Molecular, and Optical Physics
Biophysics

Annual Average Number of
Graduates 2002-2004
United States Air Force Academy 24
Harvey Mudd College 22
U. of Wisconsin – La Crosse 22
Illinois State University 20
Source: American Institute of Physics
CPY: Computer physics
PTE: Physics
Teaching
PHY: Physics
ENG: 3/2 program
ISU Computer Physics Sequence
1998-2007
Total graduates 35
Graduates per year 4
Computation Research Mentors 9
Advanced Computational Physics
Modules 7 (3 per year)
Number of physics graduates from 1980 to present
30
25
20
15
10
5
0
198019811982198319841985 19861987198819891990 199119921993199419951996 19971998199920002001 200220032004200520062007
CPY
PTE
ENG
PHY

Frontiers in Physics
Physics for Scientists and Engineers I
Physics for Scientists and Engineers II
Physics for Scientists and Engineers III
Methods of Theoretical Physics
Mechanics I
Electricity and Magnetism I
Experimental Physics
Quantum Mechanics I
Thermal Physics
At least one from:
PHY 320 Mechanics II
PHY 340 Electricity and Magnetism II
PHY 384 Quantum Mechanics II
Elective Courses
One additional 300-level Physics course.
Recommended Electives
Nonlinear Science
Molecular Dynamics Simulations
Methods of Computational Science
Advanced Computational Physics
Computational Research in Physics
Computer Science Courses
Programming for Scientists
Hardware and Software Concepts

Techniques introduced in the core for both computer physics and physics majors
2D graphics: 6-8
Mathematica: 2-3
Function Evaluation: 2+
Data analysis/curve fitting: 3
ODE – Euler, 2
ODE – 2 nd Order Methods: 3
Monte Carlo (simple): 4
ODE – 4 th order Runge-Kutta: 3
Fourier: 4-5
Integration: 1+
Over relaxation: 1-2
Graphical analysis of transcendental equations: 1-2
Molecular Dynamics: 1-3
Phy 320, 340, 384
Complex Analysis: 1
Monte Carlo (variational): 1
Eigenvalues: 2
Molecular Dynamics:1-3
Other elective courses
Surface-of-section: 1
Ray Tracing: 1
Matrix methods: 1
Fractal Dimension: 1

Methods of Computational Science
ODE – Adaptive/High Order: 1-3
Computational efficiency: 1
Integral equations by matrix inversion: 1
Theory of ODE techniques:1
Advanced Computational Physics
Split operator: 1
Finite element: 1
Neural network: 1
Molecular Dynamics: 1-3
Monte Carlo: 1-4
Students see at least three of these
Computational Research in Physics
Mesh Method for Liouville eqn
Quadratic Programming and optimization
Matrix methods
Cellular Automata
Integral equations by matrix inversion
Neural network
Eigen analysis
Each student has seen one of these in the recent past
Number indicates the number of times a student is likely to encounter a skill or technique. Listings for advanced courses do not include all of the techniques a student has previously encountered.

Computational physics is on an equal footing with experimental and theoretical physics at ISU. This will probably be the norm in another generation.
When computational techniques were introduced across the program in the late 80’s and early 90’s, faculty teaching each course chose which techniques to include in their respective courses.
Some general discussion occurred in an attempt to make sure that students encountered a broad range of techniques and techniques deemed critical, in particular.
The computer physics sequence started in 1998. Methods of
Computational Science is designed to provide a theoretical framework for computational techniques. Computational Research in Physics evolved from an earlier course and provides students with a mixture of theoretical physics and related cutting edge computational techniques.
The program at ISU focuses on students writing their own computer code.
There are some exceptions. In a few instances a faculty member provides a working code and students must make some changes. The department also uses Mathematica.

Most faculty actively contribute to the integration of computer physics into the curriculum. Some have been encouraged to boost the level of computer physics in core courses.
In informal discussion with 3 rd semester physics students, teacher education students generally prefer less computer physics integration, computer physics students really like it, and traditional physics students fall somewhere in between. By graduation, each student has selected the course of study most appealing to him or her, and each program is responsible for about a quarter of our graduates.
Computer physics and traditional physics students generally agree that computational physics has helped them to more clearly understand equations and systems.
The Computer physics sequence at ISU thrives in part because 75% of faculty classify themselves as computational (at least in part), providing a strong base. All faculty support the program. Computational physics is more financially accessible to under-funded state schools than experimental physics.

Neural networks
Comparison of classical and quantum physics
Bio-optical physics
Finite element analysis
Computational study of synchronization of coupled non-linear oscillator systems
Gerrymandering and fractal dimensions of congressional districts
Cellular automaton investigation of the transition from non-flocking to flocking behavior
Central current sheet ion distribution functions

Interdisciplinary field active since 1940’s
Used regularly in science and engineering for prediction, optimization, data mining, etc.
Pedagogical goals: students will
Understand neural models
Build intuition for selecting net parameters
Reinforce basic timeseries analysis (e.g. power spectrum & autocorrelation function)
Understand when to train with causal inputs
(physics example) vs. self-prediction (financial example)
Write ANN code to do self-prediction with Dow Jones index
See at least one associative or self-organizing network model

Scientific ANN example: the Auroral Electrojet (AE) Index
Fast decorrelation time so use causal inputs
Train with several different sets of input data to determine which sets allow best prediction
Example: Single hidden layer net, using backpropagation
[Gleisner & Lundstedt. 1997]
Go over network design choices
Results consistent with years of data analysis

ANN Topics
Biological NNs, learning theory
Neuron models, training, limitations
Learning rules: Hebb, Delta, Backpropagation
Net design: theorems, rules of thumb, testing
Predictability of timeseries
Backpropagation for timeseries (AE and financial)
Hopfield nets: character recognition Predict Dow Jones
Train with 200 months
Predict for 300 months
Written Assignments
Basic neuron models
Linear separability
Programs
Single neuron for NOR
Delta rule for XOR
Backpropagation for time series, DJIA

(based on research program of R. Grobe and Q. Su)
Classical and quantum physics are employed to describe many phenomena. Understanding their range of applicability is important in developing students physics intuition
Pedagogical goals: students will
Simulate non-interacting classical ensembles with a Monte Carlo technique
Use non-uniformly distributed random numbers, Box-Muller algorithm, rejection method, and Fast Fourier transformation
Use Split-operator techniques
Create an NCAR graphics animation inputs (physics example) vs. self-prediction (financial example)

Students calculate spreading of a classical ensemble of particles and wave function that describes the equivalent quantum mechanical picture. The particles experience a constant (linear) force.
Classical results: particle distribution in phase space at three times
Quantum results: wave function at three times

Topics in Classical and Quantum Topics
Distribution functions, average values, higher moments
The Liouville equation, multi-particle simulations
The Schrödinger equation, exploiting linearity, decomposition into advantageous states
Free-time evolution using FFT
Second and Third order split-operator scheme with error estimates
Written Assignments
Calculate moments of a swarm of bees
Liouville equation and the conservation of the norm of r
Programs
Evolution of a classical distribution of particles
Evolution of a quantum mechanical wave packet

(based on research program of Q. Su and R. Grobe)
One of the youngest fields and expected to play a significant role in the “century of life sciences”
Non-invasive optical diagnostic techniques are expected to have great impact on the economics of medicine and help provide early detection of cancers
Pedagogical goals: students will
Understand the physics of x-ray and IR imaging
Understand the micro- and macroscopic pictures of light/matter interactions
Apply the Boltzmann equation to light scattering using Monte
Carlo techniques
Model the propagation of light through a turbid medium

Transmission and reflection of modulated beam
Beam spread for constant intensity Beam spread for modulated intensity

Topics in bio-optical physics
Introduction to bio-optical physics
A matrix model of X-ray image reconstruction
Micro- and macro-scopic views of light-tissue interactions
The Boltzmann equation (BE) for light
The scattering phase functions
A bi-directional model of light scattering
A Monte-Carlo algorithm to solve the BE
The photon density waves
The diffusion approximation
Imaging with mirrors
Written Assignments
X-ray shadow gram absorption coefficients
1-D diffusion equation
Programs
1-D Boltzmann equation via a Monte-Carlo algorithm
Photon density waves with constant and periodic time dependence

Powerful numerical method for solving problems in physics and engineering such as: fluid flow, heat transport, structural mechanics (torsion, elasticity, etc.)
Frequently used in engineering for modeling problems such as the structural framework of automobiles and aircraft, groundwater flow, and heat flow.
Easily generalized to handle 1D, 2D and 3D problems with complicated boundaries, sources, sinks, and multiple materials.

Pedagogical goals: students will
Understand the theoretical basis for the finite element method, i.e. minimization of a functional on a grid. (Calculus of Variations.)
Understand how to set up the element grid in 1 and 2 dimensions.
Write a 1-D finite element code for calculating the temperature in a fin with various boundary conditions (e.g. insulated/non insulated) and with varying materials.
Topics in Finite Element Analysis
Fundamental concepts
Nodes, elements, shape functions
Calculus of variations
Functionals
Heat transfer
Embedding equations

Written Assignments
Calculate various shape functions
Determine single element equation matrices
Determine embedding equations
Programs
Solve 1-D heat transfer along a fin (circular rod)
Example results for a 1-D uninsulated rod of radius 1cm and length 10 cm. The ambient air temperature is 30

C and the thermal conductivity of the material is
75 W/cm-

C. There is a continuous heat input of 450
W/cm 2 on the left end of the rod. Calculation in done using 10 elements.

(a component of E. Rosa research program)
Student: Brian Vlcek Advisor: E. Rosa
Chua Circuit and Chaotic
Attractors dx/dt = (G(x
2
-x
1
)-y(x
1
))/C
1 dy/dt = (G(x
1
-x
2
)-x
3
)/C
2 dz/dt = -x
2
/L
G = 1/R
Phase difference: Δ j
12
= j
1
j
2

ε
12
= ε
13
= 0.0
fast medium slow
ε
12
= 0.055 ε
13
= 0.010

Hodgkin-Huxley Neural Spiking Model
ε
12
= ε
13
= 0.0
ε
12
= ε
13
= 0.01

Student: Nicholas Jurasek Advisors: B. Clark, D. Holland
Written in C++
Uses SDL image library for image manipulations
It has a very easy to use point and click interface.
Very fast, can calculate the fractal dimension in seconds.
Chicago Congressional Districts

The program loads in a BMP image, then displays it on the screen.
The user then clicks on the boarder Color.
A district color is then selected.
The program then breaks the image into boxes and looks in each box to see if it contains both the border color and the district color.
If a box meets both conditions it is on the perimeter of the district, and it is counted.
The number of boxes is then plotted against the box dimension.
The boxes are then decreased in size by a factor of 2 and the process is repeated.
After several iterations the slope of the emerging line is calculated and this becomes the fractal dimension.

Ln(S)
0
.693147
1.38629
2.07944
2.77259
Ln(N)
0
0
1.38629
2.19722
3.17805
3.5
3
2.5
2
1.5
1
0.5
0
0
Von Koch Snowflake y = 1.2925x - 0.4338
1
Ln(S)
2 3

Student: Ryan Balfanz Advisors: D. Holland, B. Clark
Flocking can be simulated from a few simple “microscopic” rules (Reynolds)
W
1
W
2
, Flock Centering: head to the center of the other boids
, Collision Avoidance: don’t fly into other boids
W
3
, Velocity Matching: approach the average velocity of the other boids
By applying the rules to each boid, a macroscopic behavior emerges
What causes the transition between non-flocking and flocking motion?

W
1
0
1
10
10
10
W
2
0
1
100
100
100
W
3
-1
1
0
0
1
Observed Behavior
No Organization
Bird Flocking
Vortex
Fish
Swarm v final v initial v
1
* w
1 v
3
* w
3 v
2
* w
2
No Organization Bird Flocking

Vortex Fish
Swarm v final v initial v
1
* w
1 v
3
* w
3 v
2
* w
2

(a component of D. Holland research program)
Student: Nathan Nutter Advisor: D. Holland
Ions interacting with the magnetotail have complicated trajectories resulting in a relative redistribution of particles as compared to their incident distribution.
Transient Orbit
-50.0
-40.0
-30.0
-20.0
x
-10.0
0.0
10.0
6.0
-1.0
0.0
1.0
4.0
2.0
3.0
4.0
5.0
-6.0
-8.0
6.0
y
2.0
0.0
-2.0
z
-4.0
Integrable Orbit
-0.2
0.0
0.2
0.4
0.6
x 0.8
1.0
1.2
-1.0
-0.5
0.0
y
0.5
1.5
1.0
0.5
0.0
z
-0.5
-1.0
-1.5
1.0
Chaotic Orbit
-50.0
-40.0
-30.0
-20.0
-10.0
x 0.0
10.0
6.0
4.0
2.0
-3.0
-2.0
-1.0
0.0
1.0
y
2.0
3.0
-6.0
-8.0
4.0
0.0
-2.0
z
-4.0

Use a test particle code to push a distribution of particles through a model magnetic field.
Each particle should contribute equal phase space “weight” in the uniform magnetic field region.
Create single particle distribution by putting the particle in its proper energy/pitch angle/z-position bin at each time step. f i
(H,

,z)
Divide the single particle distribution by the total number of “counts” in the top grid cell so that each particle contributes unit density to the total distribution.
Sum the single particle distributions to get an overall distribution.
f tot
( H ,

, z )
 i
N 

1 f i
( H ,

, z )

Since individual particles are non-interacting, this is an ideal problem for parallel processing.
(xgrid)