New Editor's Choice Applications

Flow Dynamics in Connected Liquid Tanks

Maplesoft — Mon, 09 Jan 2012 05:00:00 Z

This models investigates the flow dynamics between three liquid tanks connected by two pipes (the first pipe connecting Tank 1 and 2, and the second pipe connecting Tank 2 and 3).

The liquid level in each tank oscillates due to the flow inertia in each pipe. Flow inertia is damped by pipe friction, and eventually the liquid height in each tank reaches an equilibrium.

A Maple worksheet that models the system from a first-principle momentum balance is also attached (see Project > Attachments > Documents > OscillatingTanks.mw). In the Maple worksheet, differential equations that describe a momentum balance and the dynamic change in liquid height in each tank are solved numerically.

The results of the MapleSim model and Maple worksheet agree.

Water Hammer

Maplesoft — Mon, 09 Jan 2012 05:00:00 Z

When a valve at the end of a pipeline suddenly closes, a pressure surge hits the valve and travels along the pipeline. This process is modeled by two PDEs. The PDEs can be discretized along the spatial dimension to give a set of ODEs. This application, for a given set of parameters, solves the resulting ODEs numerically and plots the pressure dynamics at the valve.

Linear Algebra Example Generator

Jeff Knisley — Thu, 05 Jan 2012 05:00:00 Z

One of the challenges in Linear Algebra is in developing problems, projects, and exercises that are both larger dimensional and student-accessible. Indeed, round-off error, computational complexity, difficulty factoring characteristic polynomials of degree 3 or higher, and similar aspects often mean that any problems or applications of rank 3 or higher are approached solely via technology.

However, that same technology can be used to create student-accessible problems and applications of ranks 4 or 5 or even higher, even allowing the creation -- if desired -- of a technology-free course featuring only hand-calculable problems. In this presentation, we present a freely downloadable Maple worksheet that produces these types of problems. Moreover, it can be used to create hand-calculable applications of arbitrarily large rank involving stochastic matrices, eigenvalues and eigenvectors, Leslie matrix models, the simplex method, and several others.

Two files are included. The first is LinearAlgebraExamples and includes all the example generators. The second is LinearAlgebraExamplesApp and is stripped to only the main component interface of the first.

Street-fighting Math

Dr. Robert Israel — Thu, 29 Dec 2011 05:00:00 Z

This interactive Maple document contains a simple street-fighting game and performs a mathematical analysis of it, involving probability and game theory. The document is suitable for presentation in an undergraduate course on operations research, probability or linear programming. No knowledge of Maple is required.

Car Talk Puzzler

Dr. Robert Lopez — Thu, 15 Dec 2011 05:00:00 Z

National Public Radio in the USA carries Car Talk, a humorous phone-in program in which Tom and Ray Magliozzi (Click and Clack, the Tappet Brothers) diagnose and offer solutions for mysterious auto-related maladies. One of the program's segments is a weekly Puzzler, a logic (or other) mental puzzle begging for a solution. On May 21, 2011, their Puzzler caught my attention. Here’s the synopsis:

A six-digit odometer shows a palindromic number. The car it's in is driven no more than an hour, and again the odometer shows a palindromic number. How far was the car driven?

Intrigued, I decided to use Maple to solve the problem. I also wrote a blog post describing how I solved it.

Simple Harmonic Motion

Ali Abu Oam — Fri, 09 Dec 2011 05:00:00 Z

The aim of this topic is to visualize the motion of a simple pendulum which consist of a small mass m suspended by a light inextensible cord of length L from a fixed support.

Coriolis Effect

Pascal Thériault Lauzier — Fri, 09 Dec 2011 05:00:00 Z

The Coriolis effect is a force that modifies the trajectory of falling object on Earth. It is due to the rotation of the referential and, thereby, it is not a real force. The mathematical expression of this effect is obtained from the crossproduct of Earth's angular velocity (omega) with the object's linear velocity (v). The exact equation is F = 2m(v x omega). This worksheet demonstrates the action of the Coriolis effect on a projectile launched from our planet. It includes a graphic of the projectile's path as well as a procedure that determines how far the projectile will travel.

Lead Acid Battery

Maplesoft — Thu, 10 Nov 2011 05:00:00 Z

A model of a lead-acid battery powers a configurable reactive load. This equivalent-circuit battery model is implemented directly from governing equations. The model incorporates both electrical and thermal elements. In the model, the power from a lead-acid battery is used to drive a DC motor. The current sources are used to change the circuit switch from the battery driving the motor to the current sources driving the motor at the 6 hour mark. Then, the current sources drive the motor and recharge the battery at the 10 hour mark.

Quadski Turning and Activation

Maplesoft — Wed, 09 Nov 2011 05:00:00 Z

A quadski actuation model, double wishbone front suspension and steering linkages for a small off-road vehicle are simulated. Suspension and steering are actuated to determine practical parameters, such as turning radius and bump steer. These multibody models can easily be incorporated into a larger system that includes powertrain, tires, and other elements.

Great Expectations

Dr. Robert Israel — Thu, 27 Oct 2011 04:00:00 Z

An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.

This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.

Syrup: Circuit Analysis Package

Joseph Riel — Sun, 23 Oct 2011 04:00:00 Z

This is an update to the old Syrup package for analyzing electric circuits with Maple. The new version now runs on Maple 15 and is easily installable (it uses a Maple installer). New features include an export to Modelica, so it can be used with MapleSim.

Hollywood Math

Maplesoft — Fri, 23 Sep 2011 04:00:00 Z

Over its storied and intriguing history, Hollywood has entertained us with many mathematical moments in film. John Nash in “A Beautiful Mind,” the brilliant janitor in “Good Will Hunting,” the number theory genius in “Pi,” and even Abbott and Costello are just a few of the Hollywood “mathematicians” that come to mind. This document highlights just a few examples of mathematics in film, and how Maple can work with them.

Why I Needed Maple to Make Cream Cheese Frosting

Dr. Jason Schattman — Tue, 23 Aug 2011 04:00:00 Z

A recipe for cream cheese frosting I was making called for 8 oz. (about 240 grams) of cream cheese. Unfortunately, I didn't have a kitchen scale, and the product I bought came in a 400 gram tub in the shape of a truncated cone, which has a rather cumbersome volume formula.
Given the geometry of this tub, how deep into the tub should I scoop to get 240 grams? The mathematics is trickier than you might think but lots of fun! And the final, tasty result is worth the effort!

Importing Earthquake Data from the Internet

Maplesoft — Wed, 13 Apr 2011 04:00:00 Z

This application plots the location of all earthquakes of magnitude M1 or greater in the US over the last 7 days. It uses worldwide earthquake data downloaded from http://earthquake.usgs.gov/earthquakes/catalogs/

Financial Modeling in Maple