Igor P. Omelyan

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A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further(More)
  • I P Omelyan
  • 2006
A class of symplectic algorithms is introduced to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an advanced gradientlike decomposition approach. Its main advantage over the standard gradient scheme is the avoidance of time-consuming evaluations of force gradients by force extrapolation without any loss of(More)
A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This allows to resolve the rigidity problem rigorously using constraint forces. It is shown that the procedure for(More)
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(More)
A novel approach is developed to integrate the equations of motion in many-body systems of interacting rigid polyatomic molecules. It is based on an advanced gradient-like decomposition technique in the presence of translational and orientational degrees of freedom. As a result, a new class of reversible phase-space volume preserving fourth-order algorithms(More)
A methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the time step, all the conservation laws inherent in the description without breaking the time reversibility. As a result, an(More)
A new symplectic time-reversible algorithm for numerical integration of the equations of motion in magnetic liquids is proposed. It is tested and applied to molecular dynamics simulations of a Heisenberg spin fluid. We show that the algorithm exactly conserves spin lengths and can be used with much larger time steps than those inherent in standard(More)
An Enskog-Landau kinetic equation for a many-component system of charged hard spheres is proposed. It has been obtained from the Liouville equation with modified boundary conditions by the method of nonequilib-rium statistical operator. On the basis of this equation the normal solutions and transport coefficients such as bulk κ and shear η viscosities,(More)
We have developed several multiple time stepping techniques to overcome the limitations on efficiency of molecular dynamics simulations of complex fluids. They include the modified canonical and isokinetic schemes, as well as the extended isokinetic Nosé-Hoover chain approach. The latter generalizes the method of Minary, Tuckerman, and Martyna for(More)