The EJS Classical Helium Model is an example of a three-body problem that is similar to the gravitational three-body problem of a heavy sun and two light planets. The important difference is that the helium atom's two electrons repel one another, unlike the planetary case where the intraplanetary interaction is attractive.
The Colliding Galaxies Model is an implementation of Alar and Juri Toomres' 1972 super computer model showing the formation of galactic bridges and tails under the assumption that galactic cores are point masses and that one galactic core is surrounded by 2D concentric rings of orbiting stars. The model assumes is that the stars (test particles) orbiting the galactic cores are non-interacting. When the two galaxies pass one another, tidal forces deform the star distribution into classic tidal features. Our EJS model reproduces this result showing that there is a long curving tail and that only the outermost ring of stars is affected by its companion galaxy. A thin bridge is also formed and some of the stars are captured by the companion galactic core.
Data Tool is a data analysis tool for plotting and fitting data from laboratory experiments, simulations, video analysis, or any other data set organized into columns. A click of a checkbox in Data Tool allows the user to change the appearance of plots, see standard statistics for the data set or apply built-in linear, quadratic or cubic fits to the data set. Data Tool also includes a number of standard mathematical functions that can be applied to the data set, allowing for further analysis and extending the range of potential fits to the data.
Easy Java Simulations (EJS) is a Java program that enables both programmers and novices to quickly and easily prototype, test, and distribute packages of Java simulations. Version 4.1 adds grouping and affine transformations to 2D drawing Elements.
The EJS Energizer model explores the relationship between kinetic, potential, and total energy. Users create a potential energy curve and observe the resulting motion.
A Galton board is a vertical board with n rows of pegs onto which a ball is dropped. Each time a ball hits a peg, it has a probability p of bouncing to the left and a probability of 1-p of bouncing to the right. The simulation's histogram shows the distribution of x-coordinates as the balls leave the board and are collected into bins. The simulation gives rise to the binomial distribution if the probabilities of left and right bounces are equal. At first there does not seem to be any pattern but after many trials the familiar "bell curve" shape begins to emerge.
This course is designed to acquaint students with topics in mechanics and classical electricity and magnetism. The materials are assembled from UC College preparatory courses and covers two semesters. The first semester is devoted to Newtonian mechanics including: kinematics, laws of motion, work and energy, systems of particles, momentum, circular motion, oscillations, and gravitation. The second semester discusses the topics of electricity and magnetism. The course emphasizes problem solving including calculus, and there are numerous interactive examples throughout. Students will also gain laboratory experience through interactive lab simulations and wet labs.
The Linear Congruent Number Generator Model The method generates a sequence of integers xi over the interval [0, m-1] by the recurrence relation x[i+1] = (ax[i]+c) mod m Where the modulus m is greater than zero, the multiplier a is greater than zero and less than m, and the increment c is greater than zero and less than m. All numbers are integers and all arithmetic is integer arithmetic. The initial value x0 is known as the seed.
Subject:
Mathematics and Statistics, Science and Technology
The butterfly-like Lorenz attractor is a simplified model of two-dimensional convective fluid flow and is one of the best known images of chaos. Embedded in this attractor are unstable periodic orbits described by Viswanath and this model computes a number of these orbits. Each periodic orbit is classified by the number of times the trajectory orbits the A and B fixed points before it repeats. Note that because the attractor is chaotic and because of numerical errors and the finite precision of the initial conditions, errors accumulate and the trajectory leaves the vicinity of a periodic orbit after a half dozen cycles.
Subject:
Mathematics and Statistics, Science and Technology
This Java archive contains a collection of simple Easy Java Simulations (EJS) programs for the teaching of computer-based modeling. The materials and text of this resource appeared in an article of the same name in The Physics Teacher [Phys. Teach. 76, No. 45, pp. 474-480 (2007)].
Modeling a Changing World written by mathematics professor Tim Chartier and his student Nick Dovidio presents curricular material in an OSP Launcher package to motivate the need for numerically solving ordinary differential equations. The package discusses such applications as a mass-spring system and its connection to computer simulation for movies. An interactive model that simulates a two-body gravitational model of the moon and earth allows for exploring the topic of numerical error. Other models explore topics that include slope fields, numerical integration and numerical solvers for ordinary differential equations.
The EJS Roller Coaster model explores the relationship between kinetic, potential, and total energy as a cart travels along a roller coaster. Users can create their own roller coaster curve and observe the resulting motion.
The STP Eclipse Workspace contains a ready to use Eclipse worksapce with source code for Statistical and Thermal Physics (STP) programs by Jan Tobochnik and Harvey Gould. Unzip this workspace and open it from within Eclipse to compile and run these programs.
The Scalar Field Gradient Model displays the gradient of a scalar field using a numerical approximation to the partial derivatives. This simple teaching model also shows how to display and model scalar and vector fields using EJS.
Subject:
Mathematics and Statistics, Science and Technology
The Two-Color Multiple Slit Diffraction Model allows users to explore multiple slit diffraction by manipulating characteristics of the aperture and incident light to observe the resulting intensity. An exploration of resolving power in spectroscopy is included in the model.
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