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Re: [ESPResSo-users] unit of magnetization

From: Rudolf Weeber
Subject: Re: [ESPResSo-users] unit of magnetization
Date: Mon, 23 Jun 2014 14:22:58 +0200
User-agent: Mutt/1.5.21 (2010-09-15)

Hi Markus,
On Mon, Jun 23, 2014 at 01:53:52PM +0200, Markus Gusenbauer wrote:
> Hi all,
> I have a question regarding units in ESPResSo. I defined units for
> mass, time and displacement to work with microfluidics, forces and
> so on. What happens if I want to simulate magnetostatic
> interactions. What is the unit for the dipole moment of a particle?
> The unit of magnetic moment would be AmĀ², I have already defined m,
> but what about A? A=C/s won't help me either.
Typically, you use the thermal energy to express the magnetic moments.

For magnetostatic interactions between dipoles, one uses
lambda =mu_0 m^2 /(4 Pi sigma^3 k_B T)
mu_0: vacuum permittivity
m: magnetic moment of the particle
sigma: Diameter (Lennard Jones sigma)
k_B T: thermal energy

Lambda measures the interaction energy per particle of two touching dipolar 
particles in the head-to-tail configuration in units of the thermal energy.

In Espresso, the magnetic equivalent o the Bjerum length should be set to 1. 
inter magnetic 1 p3m ...

For an external magnetic field H, one uses the dimensionless parameter
alpha =mu_0 m H /(k_B T)

So the procedure would be to calculate alpha and lambda for your case and then 
set the dipole moment and field strength accordingly.

Hope that helps.

Regards, Rudolf

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