arXiv subjects

Igor Omelyan

Publications and source records attributed to Igor Omelyan.

7 recordsLinked to original sources

arXiv2020

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles placed in $\mathbb{R}^d (d \geq 1)$. The particles perform random jumps with pair wise repulsion, in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The derivation of the algorithm is based on the use of space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, adjustable system-size schemes, etc. The algorithm is then applied to the one-dimensional version of the equation with various initial conditions. It is shown that for special choices of the model parameters, the solutions may have unexpectable time behaviour. A numerical error analysis of the obtained results is also carried out.

math.DS↗

arXiv2019

Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids

We propose an enhanced approach to the extrapolation of mean potential forces acting on atoms of solute macromolecules due to their interactions with solvent atoms in complex biochemical liquids. It improves and extends previous extrapolation schemes by including additionally new techniques such as an exponential scaling transformation of coordinate space with weights complemented by a dynamically adjusted balancing between the least square minimization of force deviations and the norm of expansion coefficients in the approximation. The expensive mean potential forces are treated in terms of the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model with the Kovalenko-Hirata closure). During the dynamics they are calculated only after every long enough (outer) time interval, i.e., quite rarely to reduce the computational costs. At much shorter (inner) time steps, these forces are extrapolated on the basis of their outer values. The equations of motion are then solved using a multiple time step integration within an optimized isokinetic Nosé-Hoover chain thermostat. The new approach is applied to molecular dynamics simulations of various systems consisting of solvated organic and biomolecules of different complexity. Namely, we consider hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y and protein G in aqueous solution. It is shown that in all these cases, the enhanced extrapolation provides much better accuracy of the solvation force approximation than the existing approaches. As a result, it can be used with much larger outer time steps, leading to a significant speedup of the simulations.

physics.chem-ph↗

arXiv2019

Spatial population dynamics: beyond the Kirkwood superposition approximation by advancing to the Fisher-Kopeliovich ansatz

The superior Fisher-Kopeliovich closure is applied to the hierarchy of master equations for spatial moments of population dynamics for the first time. As a consequence, the population density, pair and triplet distribution functions are calculated within this closure for a birth-death model with nonlocal dispersal and competition in continuous space. The new results are compared with those obtained by ``exact'' individual-based simulations as well as by the inferior mean-field and Kirkwood superposition approximations. It is shown that the Fisher-Kopeliovich approach significantly improves the quality of the description in a wide range of varying parameters of the model.

physics.comp-ph↗

arXiv2018

Spatially inhomogeneous population dynamics: beyond the mean field approximation

We propose a novel method for numerical modeling of spatially inhomogeneous moment dynamics of populations with nonlocal dispersal and competition in continuous space. It is based on analytically solvable decompositions of the time evolution operator for a coupled set of master equations. This has allowed us -- for the first time in the literature -- to perform moment dynamics simulations of spatially inhomogeneous systems beyond the mean-field approach and to calculate the inhomogeneous pair correlation function using the Kirkwood superposition ansatz. As a result, we revealed a number of new subtle effects, possible in real populations. Namely, for systems with short-range dispersal and mid-range competition, strong clustering of entities at small distances followed by their deep disaggregation at larger separations are observed in the wavefront of density propagation. For populations in which the competition range is much shorter than that of dispersal, the pair correlation function exhibits a long-tail behavior. Remarkably, the latter effect takes place only due to the spatial inhomogeneity and thus was completely unknown before. Moreover, both effects get stronger in the direction of propagation. All these types of behavior are interpreted as a trade-off between the dispersal and competition in the coexistence of reproductive pair correlations and the inhomogeneity of the density of the system.

q-bio.PE↗

arXiv2001

On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems

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 collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.

cond-mat.stat-mech↗

arXiv2001

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.

cond-mat.stat-mech↗

arXiv2001

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.

cond-mat.stat-mech↗