Christopher G Jesudason

arXiv2007

Effective conservation of energy and momentum algorithm using switching potentials suitable for molecular dynamics simulation of thermodynamical systems

During a crossover via a switching mechanism from one 2-body potential to another as might be applied in modeling (chemical) reactions in the vicinity of bond formation, energy violations would occur due to finite step size which determines the trajectory of the particles relative to the potential interactions of the unbonded state by numerical (e.g. Verlet) integration. This problem is overcome by an algorithm which preserves the coordinates of the system for each move, but corrects for energy discrepancies by ensuring both energy and momentum conservation in the dynamics. The algorithm is tested for a hysteresis loop reaction model with an without the implementation of the algorithm. The tests involve checking the rate of energy flow out of the MD simulation box; in the equilibrium state, no net rate of flows within experimental error should be observed. The temperature and pressure of the box should also be invariant within the range of fluctuation of these quantities. It is demonstrated that the algorithm satisfies these criteria.

physics.comp-ph↗

arXiv2004

Linear algebra of reduced units and discussion of temperature parameter

A formal linear vector field representation for scientific equations is developed to rationalize the intuitive methods that are constantly employed. It is shown that unlike mechanical units that appear in the basis of the space, the reduced temperature and Boltzmann parameter cannot be described by the basis set individually and can only be described as a product. Further, the definition and determination of temperature is dependent on theory and not on standard mechanical units. It is shown that there is no reason to reduce the number of degrees of freedom in temperature determination via equipartition since stochastic variables are involved, and this observation is significant in that the temperature variable reported in simulation studies would have a discrepancy to the extent of using the decreased number of freedom, which is most cases is not large nor significant. The standard assignments used in reduced units do not lead to errors because operationally the resulting reduced temperature parameter represents the reduced product of the temperature and Boltzmann parameters. The non-independence of these quantities explains why entropy and other associated functions cannot be calculated directly, but are always scaled in dimensionless increments of the Boltzmann parameter.

physics.gen-ph↗