# [lammps-users] the definition of energies in DPD simulation

Dear all

I have two questions with respect to the definition of energy in DPD
simulation.

1. I think the definition of the kinetic energy for N particle system is
defined as
\sum_{i=1}^N \frac{m}{2}(v_i^x*v_i^x+v_i^y*v_i^y+v_i^z*v_i^z).
But I wonder the data obtained by lammps is not so.
It may be devided by N.
Is it true?
I obtain the data by adding the following line:

thermo_style custom step ke

2. I cannot find the definition of the potential energy in lammps Manual.
Obviously the value of potential energy is dependent on the zero point.
What is the definition of the zero point in DPD simulation?
In other words, what is the definition of the DPD-potential?
I obtain the data by adding the following line:

thermo_style custom step pe

or

thermo style custom step evdwl

Thank you.
Best regards.

The thermo output can be normalized by N. See the
doc page for thermo_style and thermo_modify for details.

Re: PE for DPD - in pair_dpd.cpp you'll see this line:

evdwl = a0[itype][jtype] * r * (1.0 - 0.5*r/cut[itype][jtype]);

Steve

Dear Steve Plimpton.

I have a question for your ansering.

Is the sign of the potential true?

I think evdwl be given by
evdwl = - a0[itype][jtype]*r*(1.0-0.5*r/cut[itype][jtype])
because the DPD force is repulsive.

Is this bug?
Or do I misunderstand it?

Thank you.
Best regards.

The formula I gave (w/out the minus sign) is positive
for r < cutoff. Isn't that what it should be
for a repulsive force (e.g. compressing a spring) ?

Steve

2008/6/9 Takenobu Nakamura <[email protected]>:

Dear Steve Plimpton.

The formula I gave (w/out the minus sign) is positive
for r < cutoff.

Yes.

But, the value for the potential energy itself
is irrelevant to whether the force is repulsive or not.
You can shift its value by adding constant term.

Isn't that what it should be
for a repulsive force (e.g. compressing a spring) ?

The potential energy for a repulsive force takes
maximum value when two particles overlap(r=0) each other.
For DPD-potential, such a situation is realized when r=0.
On the other hand, potential energy takes lowest value
when two particles "contact" each other (r=cutoff).

But the formula you gave (without the minus sign) is not so.
evdwl = 0 for r=0.
evdwl = 0.5*a0 cutoff^2 for r=cutoff

i.e. evdwl(r=0)<evdwl(r=cutoff).

Therefore particles "feel happier" when they overlap each other
than they contact.
It is not repulsive force.

Thank you.
Best regards.

Dear Steve Plimpton

I have not got the answer for the following mail.

The derivative of the potentail is not force.
The derivative of the potentaial with minus sing is force.

f(x)= - U'(x).

This was a sign error bug in the DPD pairwise energy. Just posted
a patch - 25 Jun 08.

Thanks,
Steve

2008/6/13 Takenobu Nakamura <[email protected]>: