To create your network, start off by choosing "Add Boundary Node" from the drop-down menu and then click anywhere on the screen, creating boundary nodes. The order with which you enter nodes is very important. Always enter boundary nodes first in some sort of circular order. Then choose "Add Interior Node" from the drop-down menu and place them where you like. Boundary nodes are blue and interior nodes are green. To make a connection, choose "Set Conductance" from the menu, enter the desired conductance in the box in the upper right hand corner, and then click on 2 separate nodes. Continue entering conductances in the box and clicking on 2 nodes until you have made all desired connections. You can display information such as node ordering and the conductivites of the current network by clicking on the appropriate checkbox. Press the button "Restart" if you wish to start all over again. You can construct a rectangular lattice network by choosing the appropriate choice from the drop-down menu and then entering the number of rows and columns you desire. The maximum dimensions are 13x12. Who would want one any bigger anyway??
The Dirichlet problem is as follows: given boundary voltages of an electrical network, we wish to find the interior voltages. The solution exists and is unique. Start off by allowing node numbering by clicking the "Show Node Ordering" box at the bottom of the applet. Now choose "Enter Boundary Voltages" from the drop-down menu. A pop-up box will come up. Highlight the text entry box with your mouse. It should say "Node 0". Now, enter the appropriate voltages for each node and press return, noticing the node number in the box that correlates to the node in your network. After all have been entered, allow for the display of node voltages by clicking on the appropriate box on the bottom of the screen. Now press the "Dirichlet" button. The interior voltages that were calculated by solving a linear system of equations and the boundary voltages that you entered will be displayed. You can modify conductivities and boundary voltages of your current network by choosing the appropriate drop-down menu item. Then just click "Dirichlet" again and you will see the changes. Cool, huh!
1. Determining if the graph is critical or not
2. Constructing an equivalent critical network given a non-critical network using Y-delta transformations
3. Calculation of the lambda matrix
4. Representation of current flow using arrows and color
If you have comments/questions/ideas please e-mail me:
Mark Hoefer