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- I P Omelyan, I M Mryglod, R Folk
- Physical review. E, Statistical, nonlinear, and…
- 2002

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
- Physical review. E, Statistical, nonlinear, and…
- 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)

- Igor P. Omelyan
- 1998

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)

- I P Omelyan, I M Mryglod, R Folk
- Physical review. E, Statistical, nonlinear, and…
- 2001

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)

- I P Omelyan, I M Mryglod, R Folk
- Physical review letters
- 2001

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)

- Igor P Omelyan
- The Journal of chemical physics
- 2007

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)

- Igor P. OMELYAN
- 1996

It is rigorously shown that the fluctuation formula, which is used in simulations to calculate the dielectric constant of interaction site models, corresponds to the reaction field with an individual site cutoff rather than with the usual molecular center of mass truncation. Within the molecular cutoff scheme, a modified reaction field is proposed. An… (More)

- I P Omelyan, I M Mryglod, R Folk
- Physical review. E, Statistical, nonlinear, and…
- 2002

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)

- Igor P Omelyan, Andriy Kovalenko
- The Journal of chemical physics
- 2011

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)

- I R Yukhnovskii, M V Tokarchuk, +5 authors O L Ivankiv
- 2007

The main forms of nuclear fuel remaining inside the \Shelter" object and the main interrelated factors of nuclear and ecological danger are considered. Processes of interaction of fuel containing masses with water are analysed on the basis of experimental data. A statistical model for the description of radioactive elements is proposed. The pair structure… (More)