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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)

- 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)

- Igor P. Omelyan
- 1999

The method of molecular dynamics (MD) plays a prominent role in studying molecular liquids. All existing techniques appropriate to simulate such systems can be categorized in dependence on what type of parameters are chosen to represent the rotational degrees of freedom and what kind of numerical algorithm is applied to integrate the corresponding equations… (More)

- Igor Omelyan, Andriy Kovalenko
- The Journal of chemical physics
- 2013

We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata… (More)

- Igor P. Omelyan
- 1999

A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are integrated within the Verlet framework in velocity form. It is shown that, contrary to previous methods, in the approach… (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)

- 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
- 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 cut-off rather than with the usual molecular center of mass truncation. Within the molecular cut-off scheme, a modified reaction field is proposed. An… (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 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)