Computational Science Modules
Image Processing and Edge Detection: Student
Image Processing and Edge Detection: Instructor
Module Author: David Reed
Author Contact: dreed@capital.edu
Funded By: W. M. Keck Foundation
This module explores an area of image processing known as edge detection. As the name implies, the goal of edge detection is to process a two-dimensional image and computationally determine where there are edges or boundaries in the image. The module begins with asking students to use their intuition to find edges and progresses through a number of computational techniques to implement the edge detection code and then refine/improve the code they develop. The module is designed to be a standalone module that can be used anywhere in a scientific visualization course. A basic understanding of calculus is helpful to motivate the calculations for detecting edges, but knowledge of calculus is not necessary to implement the edge detection code. In this module, students will develop code to implement the various image processing techniques. It is recommended that students read about a technique and then implement it before reading and implementing the next technique (i.e., read a section, answer the questions, and implement the projects before reading the next section).
Diffusion Limited Aggregation
Diffusion Limited Aggregation: Zipped Files
Module Author: Robert Panoff
Author Contact: rpanoff@shodor.org
Funded By: W. M. Keck Foundation
This module presents the problem of growing aggregate structures one particle at a time through random processes. Such structures are seen throughout nature, through examples such as electrodeposition, dielectric breakdown, and snowflake formation. The main algorithm for modeling these aggregate structures is diffusion-limited aggregation (DLA). DLA models cover a wide range of phenomena and size sales, and variations range from lattice based models to models that allow free movement, models in multiple dimensions, and models that change how particles stick to the growing aggregate. One feature that many of the structures created by this process have in common is a filamentary nature over a range of size scales that resembles many fractal structures. Measures of the fractal dimension of these objects using box counting techniques shows DLA aggregates confined to a plane to have a non integer fractal dimension.
The 1-D Hydrogen Atom
The 1-D Hydrogen Atom: Zipped Files
Module Author: Robert Panoff
Author Contact: rpanoff@shodor.org
Funded By: W. M. Keck Foundation
This module presents the problem of determining the most likely position, or orbital, of an electron around a hydrogen atom. The mechanics of quantum particles are determined by a partial differential equation known as Schrödinger’s wave equation. This sets up an eigenvalue problem that limits the possible energies of the electron. The computational solution of Schrödinger’s equation for hydrogen is typically done via separation of variables, in which the radial solution is separated from the angular solution, in effect reducing the problem to 1 dimension and allowing for standard numerical integration techniques to be applied. The angular solution of Schrödinger’s equation for the hydrogen atom can be expressed in terms of the spherical harmonics. Once the solution is obtained, a variety of computational techniques can be used to visualize the orbitals for different energies. The importance of matching the types of boundary conditions to the problem will be demonstrated in the module, as well as limitations of the numerical techniques used.
Ablation, Aerobraking and Airbursting of a Hypersonic Projectile in Earth's Atmosphere
Module Authors: Paul J. Thomas, Marc Goulet, Andrew T. Phillips, Alex Smith
Author Contact: gouletmr@uwec.edu
Funded By: Battelle
In this module you will learn how to numerically integrate differential equations describing the hypersonic passage of a projectile through the Earth's atmosphere. The first set of differential equations describe the forces acting on the projectile: atmospheric drag, gravity and atmospheric lift. Atmospheric drag, as the name implies, acts to slows the projectile, while gravity will accelerate the projectile towards the center of the Earth. This latter effect will tend not only to increase the speed of the projectile but will also change its direction of motion towards a radius line from the center of the Earth. Finally, atmospheric lift will tend to change a projectile's direction of motion towards a more horizontal trajectory. This effect will be small for most of the objects that we consider here, but it can be important: the "Great Daylight 1972 Wyoming Fireball" was a meteor that generated suffcient lift during its 100 minute passage through the upper atmosphere that it "skipped" back into space [Rawclie et al., 1974; Ceplecha, 1994]. The second differential equation describes ablative heating. This effect is the extreme heating that a hypersonic projectile experiences as it passes through the atmosphere. The atmosphere in the vicinity of the projectile can reach temperatures hotter than the Sun's surface (6,000 C), which will cause the surface of the projectile to evaporate (ablate). Ablation in turn affects atmospheric drag, as the amount of drag is dependent on the cross-sectional area of the projectile, which is reduced by ablation. The third differential equation describes deformation of the projectile. This is caused by the extreme pressures due to the projectile's rapid motion through the atmosphere. The effect of deformation is to cause the projectile to assume a "pancake" shape, which can drastically increase atmospheric drag. In some cases, this process can cause an airburst explosion.
Heat Flow on the Jovian Satellite Europa
Module Authors: Marc Goulet, Alex Smith, Andrew T. Phillips, Paul J. Thomas
Author Contact: gouletmr@uwec.edu
Funded By: W. M. Keck Foundation
The presence of a liquid ocean on Europa, one of the moons of Jupiter discovered by Galileo, is a topic of interest to many planetary scientists including physicist, chemists, geologists and biologists [Lucchita and Soderblom, 1982; Cassen et al., 1979]. This ocean is expected to lie beneath an icy crust of unknown thickness. D. Stevenson [2000], a prominent planetary scientist, says, "The possibility of water beneath this ice, perhaps as little as 10 km below the surface, has excited those interested in extraterrestrial environments for life and established a major role for Europa in NASA's plans for outer solar system missions." Data from the Galileo spacecraft indicates a magnetic field consistent with the presence of a near-surface saline liquid ocean [Kivelson et al., 2000]. The reason why this might be the case is due to the tidal heating of Europa in various ways [Ross and Schubert, 1987]. One way involves the heating of Europa's core due to the tugging from Jupiter's gravity. Another involves the exing of the ice sheet itself. One expects that over time, the freezing ice layer will have reached a steady state thickness that is determined by the amount of heat generated by the core and flexing ice shell. If this steady state thickness is less than 20 km, we might expect to find breaches in the ice due to impacts of asteroids and comets, or perhaps from thermal plumes from the tidally heated core [Thomson and Delaney, 2001]. For this reason, we might also be interested in estimating how long it might take such a breach to refreeze.
Computational Analysis of Orbital Motion in General Relativity and Newtonian Physics
Computational Analysis of Orbital Motion in General Relativity and Newtonian Physics: Supporting Documents
Module Authors: Marc Goulet, Alex Smith, Paul J. Thomas, Brandon Barrette
Author Contact: gouletmr@uwec.edu
Funded By: Battelle
The first comprehensive theory of gravitational orbits was developed by Newton. The orbits, or gravitational trajectories, are conic sections and arise as solutions to a second order linear differential equation. Newton assumed that time was absolute and the universe was described by Euclidean geometry. After Newton, Riemann developed the mathematics that describes the geometry of curved spaces [Spivak, 1979]. Einstein adapted this mathematics to describe gravity as the curvature of four-dimensional spacetime [Pais, 1982]. One early success was the application of this theory to explain the advance of the perihelion of Mercury. Soon afterwards, Schwarzschild found the first exact solution to Einstein's field equations. Subsequently this solution and others were interpreted as modeling the gravitational field surrounding a black hole.
Electric Potential Due to Continuous Charge Distribution
Electric Potential: Ancillary Documents 1
Electric Potential: Ancillary Documents 2
Electric Potential: Ancillary Documents 3
Electric Potential: Ancillary Documents 4
Electric Potential: Ancillary Documents 5
Electric Potential: Ancillary Documents 6
Electric Potential: Ancillary Documents 7
Electric Potential: Ancillary Documents 8
Electric Potential: Ancillary Documents 9
Electric Potential: Ancillary Documents 10
Module Author: Ignatios Vakalis
Author Contact: ivakalis@csc.calpoly.edu
Funded By: National Science Foundation (9952806)
This module is comprised of three parts. It models the electric potential due to a continuous charge distribution for the following cases:
- 1-D Finite Length Wire
- 1-D Infinite Length Wire
- 2-D Finite Plate
Enzyme Kinetics
Enzyme Kinetics: Ancillary Documents 1
Enzyme Kinetics: Ancillary Documents 2
Enzyme Kinetics: Ancillary Documents 3
Enzyme Kinetics: Ancillary Documents 4
Enzyme Kinetics: Ancillary Documents 5
Enzyme Kinetics: Ancillary Documents 6
Enzyme Kinetics: Ancillary Documents 7
Enzyme Kinetics: Ancillary Documents 8
Enzyme Kinetics: Ancillary Documents 9
Enzyme Kinetics: Ancillary Documents 10
Module Author: Ignatios Vakalis
Author Contact: ivakalis@csc.calpoly.edu
Funded By: National Science Foundation (9952806)
This module is comprised of three parts:
- Rates of Chemical Reactions
- Enzyme Kinetics: No inhibition
- Enzyme Kinetics: With inhibition
Cost of a Financial Portfolio
Module Author: Ignatios Vakalis
Author Contact: ivakalis@csc.calpoly.edu
Funded By: National Science Foundation (9952806)
Portfolios in the context of financial markets are defined as a collection of financial securities (e.g., stocks, bonds). It is necessary to estimate a priori the cost of a financial portfolio according to existing and projected data. In this module you learn two techniques (replication, stochastic discount factors) for pricing portfolios on simple markets given a specific cash flow. The model, even though very simple, is extremely powerful and provides the foundation for solid intuitive understanding of the complexity of the illusive real-world case.
Spread of Infectious Disease
Spread of Infectious Disease: Ancillary Documents 1
Spread of Infectious Disease: Ancillary Documents 2
Spread of Infectious Disease: Ancillary Documents 3
Spread of Infectious Disease: Ancillary Documents 4
Spread of Infectious Disease: Ancillary Documents 5
Spread of Infectious Disease: Ancillary Documents 6
Spread of Infectious Disease: Ancillary Documents 7
Spread of Infectious Disease: Ancillary Documents 8
Spread of Infectious Disease: Ancillary Documents 9
Spread of Infectious Disease: Ancillary Documents 10
Module Author: Ignatios Vakalis
Author Contact: ivakalis@csc.calpoly.edu
Funded By: National Science Foundation (9952806)
The spread of epidemic diseases is one of the major problems in the medical sciences. For example, AIDS is increasing in many countries and many other diseases such as malaria, measles, and cholera take a substantial toll on human life. Epidemiology is the scientific study of the occurrence, transmission, and control of a disease. In such a field, mathematical models are important for quantifying and analyzing patterns of the spread of the disease and understanding the process of transmission. Such models of the dynamics of a communicable disease can have direct bearing on the choice of an immunization program, the optional allocation of resources, or the best combination of control or eradication techniques. In this module you learn how to construct, solve, and analyze the results of a model that describes the spread of a disease in a large population. The model is constructed as an extension of single models, which are presented in the background section of the model. Only deterministic models (models expressed by ordinary differential equations) are considered in this module. The assessment section briefly presents a statistic model, and compares it with the deterministic model.
Satellite Surveillance
Module Author: Ignatios Vakalis
Author Contact:ivakalis@csc.calpoly.edu
Funded By: National Science Foundation (9952806)
A large number of satellites have been launched in the last few years. These include navigational, meteorological, communication and spy satellites. Among the very complex technology on board, a spy satellite carries a wide-angle high-resolution camera returning to earth a picture of every point on earth in direct “line of sight” from the satellite. In this module you learn how to construct, solve, and analyze a simple model in computing the area on earth that a spy satellite sees at a particular time instance. Calculating the total area under the satellite’s surveillance in one complete revolution around the earth will be given as a project in this module.