Move size in hpmc.integrate

[Kaustav Chakraborty]

Dear HOOMD users,

I want to clear a confusion regarding hpmc with hard sphere. Let's say I have a single hard sphere inside a cubic box and running a monte carlo simulation. To run this I'm giving the following command (I use HOOMD-v2.3.4)-

mc = hoomd.hpmc.integrate.sphere(d=0.12,seed=193799, nselect=1)
mc.shape_param[type_id].set(diameter=diameter)

Does that mean the sphere will be displaced at every step (I'm giving nselect=1 to ensure that it is displaced only once at each mc step) from it's previous position by some  random value (taken from uniform distribution generated by some random number generator)  between 0 to 0.12?

Regards,

Kaustav Chakraborty

[Joshua Anderson]

Kaustav,

The documentation I wrote on this is very explicit: https://hoomd-blue.readthedocs.io/en/v3.9.0/module-hpmc-integrate.html#module-hoomd.hpmc.integrate

If there is a specific part of the documentation you don't find clear, please copy and paste that sentence and explain what clarification you need.

------

Joshua A. Anderson, Ph.D.

Research Area Specialist, Chemical Engineering, University of Michigan

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[Kaustav Chakraborty]

'default_d (float) – Default maximum size of displacement trial moves' 

 does that mean every trial move of each particle in the system is taken from uniformly distributed random numbers from 0 to this particular 'maximum size of displacement' ?

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[Kaustav chakraborty]

It seems that the random numbers for trial moves are sampled from exponential distribution starting from this 'Default maximum size of displacement trial moves', rather than from uniform distribution (And that perfectly makes sense if the target is to make moves closely to the value of maximum move size determined from practical conditions). Could you please  confirm this?

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[Eric Irrgang]

> On Mar 10, 2023, at 10:01 PM, Kaustav Chakraborty <kaustav.chakra...@gmail.com> wrote:
>
> 'default_d (float) – Default maximum size of displacement trial moves'
>
> does that mean every trial move of each particle in the system is taken from uniformly distributed random numbers from 0 to this particular 'maximum size of displacement' ?

No. The trial move is from [0, 0, 0] to [x, y, z], with x^2 + y^2 + z^2 <= d.

Per the documentation, the trial displacement move is generated with "a random vector uniformly distributed within the ball of radius 1", scaled by d (the maximum displacement).

It is not the magnitude of the vector (the displacement) that is uniformly distributed; it is the cartesian coordinate that is uniformly distributed.

Any symmetric probability density would be valid. This uniform density was found to be simple and effective in a large variety of systems.

[Kaustav Chakraborty]

Have you mistakenly written d, instead of d^2 at the end of the first sentence?

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[Joshua Anderson]

Kaustav,

I am attaching the relevant portions of the documentation so you can read them for yourself. 

Also see the implementation here: 

https://github.com/glotzerlab/hoomd-blue/blob/fbe46e9b1a321940b9b37bb016063747cdffcd58/hoomd/hpmc/IntegratorHPMCMono.h#L675-L739

https://github.com/glotzerlab/hoomd-blue/blob/fbe46e9b1a321940b9b37bb016063747cdffcd58/hoomd/hpmc/Moves.h#L42-L116

------

Joshua A. Anderson, Ph.D.

Research Area Specialist, Chemical Engineering, University of Michigan

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[Eric Irrgang]

Have you mistakenly written d, instead of d^2 at the end of the first sentence?

Yes. Sorry. 

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