10176

The Mathematics of Sand Piles: Eikonal Solution over an Elliptic Constraint

This Demonstration plots rectangular and elliptic solutions to the eikonal equation and a novelty known as a cross-figure solution together with their surface areas and volumes.

DETAILS

The eikonal equation is a nonlinear PDE that simulates the physical laws governing the piling of sand on a plate of a given shape held over a boundless chasm. With no loss of generality, the eikonal equation may be written as
.
The boundary conditions, being represented physically by the shaped plate, are dominated by a stretch factor that describes the elongation in a particular direction of the plane. Although the choice of direction along which applies is arbitrary, here are the conventions used in this Demonstration:
The three snapshots show different levels of elongation along the axis. With , the axis component is elongated and vice versa for . At , the stretches in each directions are equal and we recover a cone from the elliptic boundary condition solution and a pyramid from the rectangular boundary condition solution.
Some graphical errors may exist due to the large amount of information that must be processed at each slider setting. Users are welcome to reproduce true images by working off the supplied code. Additionally, due to the latency attributed to the number of computations being performed at each step, only image resizing is recommended.
Reference
[1] I. P. Stavroulakis and S. A. Tersian, Partial Differential Equations: An Introduction with Mathematica and Maple, Singapore: World Scientific, 2004.

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.