Re: [Phys-L] simulation of "bonding"

[Bernard Cleyet <bernardcleyet@redshift.com>]

> On 2016, Mar 06, , at 07:08, Jeff Spirko <spirko@gmail.com> wrote:
>
> I think John Denker's interpretation of the dependence on the initial
> temperature is correct.  The reaction energy depends on the binding energy
> and the energy required to get to/from STP.
>
> On the trend toward higher total energy, does the time step affect this?
> Change Ndisp and the delay at the same time as dt.  I'm on my way out the
> door or I would fiddle with it.

I‘ve found if there’s dissipation, reducing the time step does not improve the accuracy, more correctly worsens it.  i’ve obviously not studied this simulation, so I presume there is no dissipation.  

I haven’t completed my study of various ODE solutions. [1] I’m using both oscillators with linear dissipation so I can fit to the analytic solution and a falling body with drag (quadratic dissipation with constant coefficient), which also has an analytic solution (the skydiver).  

> It looks like the numerical technique is good.  It's the "symplectic Euler"
> method, aka Euler-Cromer method that Bruce Sherwood said they kind of
> stumbled across.  In each time step, velocities (here, momenta) are first
> calculated based off the old coordinates.  Then all coordinates are updated
> using the new velocities.
>
> In the integrator, the effect of the electric force is ignored if the
> electrons bounce.  I wonder if this introduces error in the energies.

Is this not various potentials (Morse - Leonard Jones) leading to van der Waals, etc???? 

Intuitively I suspect “hard” balls won’t change the result, but them I’ve not read the simulation.

> If you ever expand to particles of different masses, the transform from lab
> to C.M. frame must be adjusted.
 

[1]  Velocity Verlet, two of the Cromer’s (last step and half step) those due to Sandvik and Peter Young.  I suppose I should give up and learn 4th R-K..  though I‘ve read for some ODEs, it’s flawed.