New Langevin and gradient thermostats for rigid body dynamics

Area of Science:

• Computational physics
• Molecular dynamics
• Numerical analysis

Background:

• Rigid body dynamics simulations require accurate thermostatting methods.
• Quaternion representation is effective for describing rotations.

Purpose of the Study:

• Introduce novel Langevin and gradient thermostats for rigid body dynamics.
• Develop and analyze geometric numerical integrators for these thermostats.
• Compare the performance and accuracy of different integrators.

Main Methods:

• Formulated rotation using quaternion representation.
• Developed geometric numerical integrators preserving quaternion unit length and tangent space.
• Implemented and compared Langevin and gradient thermostats in rigid body simulations.

Main Results:

• Both thermostats preserve quaternion unit length; Langevin thermostat maintains angular momenta in tangent space.
• Developed integrators automatically preserve quaternion properties.
• Langevin integrators (weak order two) are more computationally efficient and accurate than the gradient integrator (weak order one) for TIP4P water simulations.

Conclusions:

• The developed geometric integrators accurately reflect thermostat properties.
• Langevin integrators are recommended for rigid body dynamics simulations due to superior efficiency and accuracy.
• The study provides guidance on selecting appropriate integrators for specific simulation needs.