Parameter Definitions for pythag

• BC: This determines how the string is terminated (the Boundary Condition).
  • ``Fixed'' (the initial default) corresponds to holding the position Y of the string fixed at that position.
  • ``Free'' corresponds to letting the string flap (no force applied from the boundary).
  • ``Refless'' produces reflectionless boundary conditions: a viscous damping force
    F_boundary = - gamma dY/dt = sqrt(mu tau) dY/dt
    and a mass for the endpoint of half that in the middle segments (only half a segment of the string is there!) leads to perfect termination.
• Forcing: This determines the wave pulses coming in from the sides.
  • ``Pulse'' (the initial default on the left) produces a Gaussian pulse with time duration full-width half maximum FWHM and amplitude Amplitude (discussed below under Configure).
  • ``Wave'' produces a sine wave input of frequency Omega (under Configure) and amplitude Amplitude, but tapered on by a Gaussian of full width half maximum FWHM (to avoid numerical problems).
  • ``Packet'' produces a sine wave times a Gaussian, which models a wave packet of frequency Omega and length FWHM.
  • ``NegPulse'' produces a pulse minus that of ``Pulse'', to study the interference of two pulses.
  • ``None'' (the initial default on the right)

• Versus X: Shows one of a variety of animations of the string motion as a function of X, varying with time. The menu just below the graph and to the right allows one to choose to plot
  • ``Y'', the height of the string, in meters (initial default)
  • ``Y DOT'', the chunk velocity dY/dt, or more specifically the vertical velocity of a small piece of string at the point x
  • ``PE'', the potential energy density, 1/2 tau (dy/dx)^2
  • ``KE'', the kinetic energy density 1/2 mu(x) (dy/dt)^2
  • ``u'', the total energy density KE + PE
  • ``Power'', the net energy flow to the right, -tau (dy/dx)(dy/dt)
  The Copy Graph button to the right of the graph selection menu allows you to capture a plot; you can then combine plots, print plots, save trajectories, ...
• Versus T: Shows one of a variety of plots of one point on the string (denoted in the Versus X plot by a dark rectangle) as a function of X, varying with time. The menu to the right of the graph allows one to choose from the same list as for the Versus X plot above. The Copy Graph button also works the same way, but for this graph.

  The ``Versus T'' plot gets longer and longer as you run. At some point, this begins to slow down the rest of the program: replotting thousands of points each time step can get slow. To avoid this, the plot is automatically pruned to no more than NMAX points (currently 1000): this is substantially larger than the resolution of the plot, but can cause noticable roughness under zooming or after long runs.

  See the help for graphs.

• Initialize: Starts the system over at time t=0.
• Stop (Run): Starts and stops the simulation. The simulation by default begins by running and will halt automatically after a time given by the value input as ``Time to Run'' (below). Stop followed by Run will restart where it left off. This can cause confusing results if the forcing from the boundaries is changed without re-initializing.
• Your Name: Type your name in here, so your graphs will be labelled correctly.
• Time: Displays the current time (also found as the final point on the vs. T plot). The current time affects the forcing at the boundaries.
• Time to Run: While the simulation is off, it gives the net time the simulation will run if the Run button is pushed (and left going). This is useful to measure velocities for example: run for one second, and find out how far you got... When the simulation is running, it displays the future time the simulation will run if it isn't interrupted.
• presets: Starts up one of various preset configurations, for various sections of the lab and/or for homework problems. You can save the current configuration of the system using ``save...'', and search for other presets (e.g., ones you stored in other directories) using ``load...''
• Configure: Allows one to reset most of the parameters in the simulation. (Details on a separate page.)
• Work and Help: Hypertext help and discussion of the assignments and lab.
• Quit: Exit the program.

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).