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Shodor > CSERD > Resources > Models

The Computational Science Education Reference Desk stores a variety of models. Each model includes one or more pieces of scientific software, clear instructions on how to use the software, and background theory describing the scientific application, the mathematical algorithm, and the computer architecture used in the model.

Physics: Mechanics  (...)
The Space Ship Pilot model is a model of motion under Newton's laws with and without resistive forces. The first environment puts the user in control of docking a space shuttle, and the second puts the user in control of docking a boat.

The Pendulum Motion Model lets users change the length, mass, initial displacement, initial velocity and acceleration due to gravity of a thin rigid pendulum capable of rotating a full 360 degrees. Different integration methods are provided.

The gravity calculator calculates the gravitational force between two masses. Also included is a visualization of the typical measurement of gravitational force (weight) in different environments (stationary and free fall).

Physics: Electricity and Magnetism  (...)
The blackbody calculator allows for visualization of the spectrum produced by objects of a given temperature. Users can see both a line graph of the spectrum and the spectrum as it would appear using a spectral grating, as well as the actual hot object.

The Electric Field Viewer allows for the visualization of electric fields caused by point charges.

Physics: Waves  (...)
The Superposition of Waves Calculators show the result of adding two or more waves of the form y = A * cos ( k * x + phi ) or y = A * cos ( k * x + phi - omega * t ). The calculation of wave packets is also included.

Physics: Solid State  (...)
The Diffusion Limited Aggregation (DLA) algorithm models the growth of an object one particle at a time sticking in random places. This calculator computes DLA on a square, hexagonal, or octagonal lattice, and allows for the computation of fractal dimension by a box counting method.

Physics: Modern Physics  (...)
This model numerically solves Schrodinger's equation for a particle trapped in a deep 1-D potential well.

This model solves the wave equation for a stretched string using a numerical model.

This calculator prints the closed form solution of the hydrogen wave function for given energy states. In addition, closed form expressions for the Associated Legendre Functions and Laguerre Polynomials (radial solution of hydrogen wave function) are included.

This model solves the radial component of Schrodinger's equation for the single electron Hydrogen atom.

Mathematics  (...)
This model presents a numerical solution of Legendre's equation subject to the conditions that it be well behaved on the range [-1,1].

The polar plot tool allows for the visualization of functions of an angle. The function r(theta) is plotted for a range of theta on an x-y plane. Users can choose to color the function by sign, or add an offset.

This tool allows the user to visualize functions of three variables as diffuse clouds. The "cloud" can be rotated and viewed from different angles. Also, slices of the x=0, y=0, and z=0 plans can be viewed. Plots can be viewed with different colormaps, including red-blue maps to indicate the sign of the function.

This tool allows the user to visualize functions as 3D contour plots that can be grabbed and rotated. Users can adjust resolution and choose filled versus wireframe renderings.

The purpose of this applet is to supply a 3D graphing utility that can plot both multivariable functions and sets of points.

The Newton's Method Calculator uses Newton's method to solve for the roots of a function of x.

The Newton-Raphson Method Calculator solves a system of equations of x, y, and z.

The Vector Component Calculator lets students look at components of vectors in 2 dimensions by dragging the tip of the vector within the xy plane

The Vector Addition Calculator lets students add vectors graphically in 2 dimensions by dragging the tips of the vectors. The results of a component method of addition for the same problem are also displayed.

This applet will let you visualize the result of a 2-D linear transformation to search out the real eigenvectors and eigenvalues of a matrix. The applet includes a calculation of eigenvalues as a ratio of vecotrs when eigenvectors are found and an autopilot feature that sweepes out the x-y plane.

The Numerical Derivative Calculator allows for the calculation of first and second derivatives of known functions or data.

The Ordinary Differential Equation Calculator solves coupled first order orindary differential equations of x, y, and z using either an Euler, Improved Euler, or 4th order Runge Kutta algorithm.

The traveling salesman problem is a classic optimization problem in which one seeks to minimize the path taken by a salesman in traveling between N cities, where the salesman stops at each city one and only one time, never retracing his/her route. This implementation is designed to run on UNIX systems with X-Windows, and includes parallelization using MPI.

Astronomy  (...)
LunaSee is a lunar phase viewer which allows the user to position the Moon relative to the Earth and Sun, and see the resulting phase. Views to study eclipses are also included.

The Astronomical Coordinates Calculator takes input in the form of right ascension, declination, and parallax and returns x, y, and z coordinates in parsecs.

The Dust in the Interstellar Medium model solves for the absorption and scattering of light from spherical particles assuming a Mie solution.

Earth Science  (...)
One of the most important measures of the health of the stream is the level of dissolved oxygen (DO) in the water. Oxygen (O2) dissolves in water through the mixing of the water surface with the atmosphere. The oxygen is used by fish and other animals in the water to "breath" through their gills or other respiratory systems and by plants. If the levels fall too low, many species of fish, macroinvertebrates, and plants cannot survive. At very low levels of oxygen, the stream becomes "septic" and smells rotten because low oxygen sulfur bacteria begin to dominate.

Biology  (...)
The Spotted Fish model attempts to track the trait change [spot size] of a population of spotted fish in a pond with ample food supply with a constant number of predators. The predators in the pond are attracted to the fishes spots, and the chance of a fish being spotted and eaten by a predator is proportional to it`s spot size squared.

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