Re: [ESPResSo-users] Fwd: Active matter

[Pierre de Buyl]

Hi,

The rotational component of the motion is defined with quaternions as follows:

1. The position of the particles relative to the rigid body center of mass
position, in the laboratory reference frame, is

r = q r_B q*

Where r_B is the body frame position (fixed in time by definition) and q depends
on time.

2. There is a equation of motion for q:

dq / dt = 1/2 omega q

where omega is the angular velocity.

You can look the algorithm up in Martys and Mountain
doi:10.1103/PhysRevE.59.3733 that is the reference used by ESPResSo (see
src/core/rotation.cpp).

The force for the swim mechanism comes relies on the orientation of the swimmer
that is defined by the quaternion (hence the explanation above).

For more information, look for "swimming" in the user guide.

Regards,

Pierre

On Fri, Feb 24, 2017 at 12:31:47PM +0530, Nairhita Samanta wrote:
> Dear Joost,
> 
> Thank you for your reply. I have seen this paper earlier. However, I still
> exactly dont understand the mechanism used in Espresso for the swimming
> feature, that how this orientation (*u*) is updated. Does it follow a
> separate equation of motion like a Langevin equation for rotation, which
> gets updated at each step along with position and then the force (F) is
> applied in that direction? Otherwise it is difficult for Espresso to find
> the orientation of a symmetric single particle. I am trying to understand
> for a system without any Hydrodynamic interaction.
> 
> Regards,
> Nairhita
> 
> On Thu, Feb 23, 2017 at 9:47 PM, Joost de Graaf <address@hidden>
> wrote:
> 
> > Dear Samantha,
> >
> > Perhaps reading the 2016 J. Chem. Phys. by De Graaf et al. (144, 134106)
> > on anisotropic swimmers will be helpful.
> >
> > Best Wishes,
> >
> > Joost
> >
> > On Thu, 23 Feb 2017 at 12:31, Nairhita Samanta <address@hidden>
> > wrote:
> >
> >> Hi all!
> >>
> >> I am using the v_swim/f_swim feature of ESPResSo. But I really want to
> >> understand the more clearly. So, can you please guide me to find the
> >> algorithm, or at least the articles which is followed for the equation of
> >> motion of the quaternions.
> >>
> >> Thanking you.
> >>
> >> With regards,
> >> Nairhita
> >>
> >>
> >>

-- 
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Pierre de Buyl
KU Leuven - Institute for Theoretical Physics
T +32 16 3 27355
W http://pdebuyl.be/
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