Longitudinal wavevector- and frequency-dependent dielectric constant of the TIP4P water model

A computer adapted theory for self-consistent calculations of the wavevector- and frequency-dependent dielectric constant for interaction site models of polar systems is proposed. A longitudinal component of the dielectric constant is evaluated for the TIP4P water model in a very wide scale of wavenumbers and frequencies using molecular dynamics simulations. It is shown that values for the dielectric permittivity, calculated within the exact interaction site description, differ in a characteristic way from those obtained by the point dipole approximation which is usually used in computer experiment. It is also shown that the libration oscillations, existing in the shape of longitudinal time-dependent polarization fluctuations at small and intermediate wavevector values, vanish however for bigger wavenumbers. A comparison between the wavevector and frequency behaviour of the dielectric constant for the TIP4P water and the Stockmayer model is made. The static screening of external charges and damping of longitudinal electric excitations in water are considered as well. A special investigation is devoted to the time dependence of dielectric quantities in the free motion regime.Comment: 21 pages, 7 figure

Optimized Verlet-like algorithms for molecular dynamics simulations

New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the presence of a free parameter. The nonzero value for this parameter is obtained by reducing the influence of truncated terms to a minimum. As a result, the new algorithms appear to be more efficient than the original Verlet versions which correspond to a particular case when the introduced parameter is equal to zero. Like the original versions, the proposed counterparts are symplectic and time reversible, but lead to an improved accuracy in the generated solutions at the same overall computational costs. The advantages of the new algorithms are demonstrated in molecular dynamics simulations of a Lennard-Jones fluid.Comment: 5 pages, 2 figures; submitted to Phys. Rev.

Optimized Forest-Ruth- and Suzuki-like algorithms for integration of motion in many-body systems

An approach is proposed to improve the efficiency of fourth-order algorithms for numerical integration of the equations of motion in molecular dynamics simulations. The approach is based on an extension of the decomposition scheme by introducing extra evolution subpropagators. The extended set of parameters of the integration is then determined by reducing the norm of truncation terms to a minimum. In such a way, we derive new explicit symplectic Forest-Ruth- and Suzuki-like integrators and present them in time-reversible velocity and position forms. It is proven that these optimized integrators lead to the best accuracy in the calculations at the same computational cost among all possible algorithms of the fourth order from a given decomposition class. It is shown also that the Forest-Ruth-like algorithms, which are based on direct decomposition of exponential propagators, provide better optimization than their Suzuki-like counterparts which represent compositions of second-order schemes. In particular, using our optimized Forest-Ruth-like algorithms allows us to increase the efficiency of the computations more than in ten times with respect to that of the original integrator by Forest and Ruth, and approximately in five times with respect to Suzuki's approach. The theoretical predictions are confirmed in molecular dynamics simulations of a Lennard-Jones fluid. A special case of the optimization of the proposed Forest-Ruth-like algorithms to celestial mechanics simulations is considered as well.Comment: 12 pages, 3 figures; submitted to Computer Physics Communication

Symplectic integrators for classical spin systems

We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully utilized for other Hamiltonian systems, e. g. for molecular dynamics or non-linear wave equations. Our procedure rests on a decomposition of the spin Hamiltonian into a sum of two completely integrable Hamiltonians and on the corresponding Lie-Trotter decomposition of the time evolution operator. In order to make this method widely applicable we provide a large class of integrable spin systems whose time evolution consists of a sequence of rotations about fixed axes. We test the proposed symplectic integrator for small spin systems, including the model of a recently synthesized magnetic molecule, and compare the results for variants of different order

A consistent description of kinetics and hydrodynamics of systems of interacting particles by means of the nonequilibrium statistical operator method

A statistical approach to a self-consistent description of kinetic and hydrodynamic processes in systems of interacting particles is formulated on the basis of the nonequilibrium statistical operator method by D.N.Zubarev. It is shown how to obtain the kinetic equation of the revised Enskog theory for a hard sphere model, the kinetic equations for multistep potentials of interaction and the Enskog-Landau kinetic equation for a system of charged hard spheres. The BBGKY hierarchy is analyzed on the basis of modified group expansions. Generalized transport equations are obtained in view of a self-consistent description of kinetics and hydrodynamics. Time correlation functions, spectra of collective excitations and generalized transport coefficients are investigated in the case of weakly nonequilibrium systems of interacting particles.Comment: 64 LaTeX2e pages, 1 figure, special sty-files, additional font

Algorithm for numerical integration of the rigid-body equations of motion

A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in terms of either principal axes or quaternions. Due to specific features of the algorithm, orthonormality and unit norms of the orientational variables are integrals of motion, despite an approximate character of the produced trajectories. It is shown that the method presented appears to be the most efficient among all known algorithms of such a kind.Comment: 4 pages, 1 figur