Add "docs in progress"

Author: rklancer

docs-in-progress.txt

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+Issues with temperature control and velocity rescaling
+
+  First, note that [erfectly elastic reflective collisions with walls impart linear and angular momentum to the system
+  every time a particle bounces off the wall.
+
+  Here are some options for dealing with translation and rotation:
+
+  1. Not adjusting for translation or rotation at all.
+
+    This leads to rather distracting problems with condensed clusters:
+
+    - If you form a cluster, and it bumps a wall or otherwise gets significant translation or rotation when it's
+      relatively cold, and then you increase the temperature, the translation and rotation get scaled up so the thing
+      bounces around between the walls and/or spins like crazy.
+
+      Although, considered from a macro scale, this translation and rotation of the whole cluster could legitimately be
+      considered thermal energy--if the cluster had real surfaces to interact with, the energy would be quickly
+      repartitioned--it still presents a pretty non-representative picture of thermal energy. It also is especially
+      unrepresentative of how thermal energy would be added in a real experiment.
+
+
+    - If you leave a non-moving, cold cluster alone, eventually it will accelerate spontaneously due to the way velocity
+      rescaling works. Basically, rescaling periodically multiplies all velocities by a factor that is proportional to
+      sqrt(1/T) where T is the temperature at that instant. But T fluctuates as molecules vibrate, and the time average
+      of sqrt(1/T) is greater than sqrt(1/(the time average of T)) to the extent that T fluctuates. This results in a
+      "pump" that slowly takes energy out of vibrational modes and puts it into translation and/or rotation (this
+      causes T to fluctuate less). This transfer isn't obvious at first, but once the acceleration starts it quickly
+      becomes very obvious.
+
+
+  2. Removing translation of the center of mass and rotation around the center of mass before scaling velocities, and
+     adding them back after scaling velocities. (This is what is currently done.)
+
+    This has some advantages relative to case (1) above:
+
+    - Now, once a cluster has begun to spin or translate, increasing the temperature doesn't make the whole cluster
+      spin or bounce around quite so wildly. However, if there are two or more clusters, they may move and spin relative
+      to each other, and the non-equipartitioned nature of the thermal energy is again obvious, just not as blatant as
+      or long-lived as in case (1) above.
+
+    - In addition, velocity rescaling should no longer cause the whole cluster to accelerate as it does in case (1)
+      above. That said, individual particles that escape a cluster can appear to accelerate by themselves for the same
+      reason as described above for the whole cluster. However, they are much smaller and their independence from the
+      cluster is usually short lived, so again this effect is not as blatant as in case (1) above.
+
+    However, there are some side effects of this choice.
+
+    - First, if the system is in a "gaseous" phase so that molecules bounce off the walls, then dropping the temperature
+      quickly stops the relative motion of the particles but makes the whole system appear to drift and/or spin. This
+      can be discocerting.
+
+    - Second, the kinetic energy of the system is no longer perfectly related to the thermal energy, since the overall
+      translation and rotation is not considered part of the system's thermal energy. This might lead to some confusion
+      if not managed carefully (for example, by making it explicit that there are translational, rotational, and
+      thermal contributions to the kinetic energy, and making it possible to visualize these.)
+
+
+  3. Using periodic boundary conditions.
+
+    A different take on how to deal with distracting effects caused by the combination of velocity rescaling and
+    motions caused by collisions with hard walls is to remove the hard wall boundary conditions entirely, and instead to
+    use a scheme commonly employed in research simulations, "periodic" boundary conditions.
+
+    In this case, particles "wrap around" the left edge to re-appear at the right edge, and vice versa, and similarly
+    for the bottom and top. This is a bit like the old-school video game "Asteroids". When calculating the interaction
+    between two particles, the simulation considers whether which "wrapped around" image of the second particle is
+    closer, and that closest image is used for subequent calculations.
+
+    This has the advantage of simulating the essential properties of a fluid in the tiny volume that is practical to
+    simulate, without incurring effects that are caused by having a large proportion of the particles being so near the
+    edge -- there effectively is no "edge".
+
+    On the other hand, for our purposes this may not be ideal, because "wrap around" behavior isn't visually realistic
+    and students (or other naive observers) are almost certain to be confused by it. Molecular Workbench does use
+    periodic boundary conditions in some cases, although the wrap-around behavior is apparently hidden by only
+    revealing the center of the simulated area, not the edges where the wrap-around happens.
+
+    For the "Simple Atoms" demo, one might be concerned that if we used this solution, then a cluster of atoms might
+    wander off the edge of the screen, but actually the solution might be workable. The large cluster would not wander
+    off the edge of the screen because the system doesn't get constant "kicks" from the wall.
+
+
+  - Because the system doesn't get "kicks" from the wall, any velocity of the center of mass is due to numerical error
+    and can be safely subtracted out and, correspondingly, increasing the temperature won't simply scale up translation
+    and rotation. Relative motion of two condensed clusters, of course, will scale up when temperature is scaled up, as
+    in case (2) above.
+
+  - However, unlike in case (2) above, because of the lack of "kicks" from collision with the wall, the condensed
+    clusters may not move relative to each other at all, and it may be hard to get them to condense with each other.
+    Bounces off the wall in case (1) and (2) provide mixing.
+
+  - Spontaneous acceleration of particles may be reduced relative to case (2) because the center of mass isn't being
+    subject to "kicks". I haven't experimented with this yet, however.
+
+
+  4. Removing translation of the center of mass and rotation around the center of mass at every frame (while
+     distributing the translational and rotational energy removed back into the thermal motion of the particles)
+
+     In some ways, this is the most aggressively "artificial" treatment of the center of mass in that it involves the
+     most blatant adjustment of the laws of motion. It leads to artifacts because it's not obvious to observers that,
+     in effect, the "camera" is moving and rotating to compensate when particles move relative to each other.
+
+     That said, the micro behavior is still reasonable, and this may be the best approximation to the periodic boundary
+     condition case that still allows particles to bounce off the walls.
+
+
+
+* Potential speedups
+
+* Running md outside the browser using Node