DMITRY NERUKH PUBLICATIONS  
[1] 
N. Atamas, V. Bardik, A. Bannikova, O. Grishina, E. Lugovskoi, S. Lavoryk,
Y. Makogonenko, V. Korolovych, and D. Nerukh,
The effect of water dynamics on conformation changes of albumin in predenaturation state: photon correlation spectroscopy and simulation, J. Mol. Liq., 235, 17  23 (2017), Physics of Liquid Matter: Modern Problems. PLMMP2016 Conference. [ DOI  at the journal's site  .pdf ] Water is essential for protein threedimensional structure, conformational dynamics, and activity. Human serum albumin (HSA) is one of major blood plasma proteins, and its functioning is fundamentally determined by the dynamics of surrounding water. The goal of this study is to link the conformational dynamics of albumin to the thermal motions in water taking place in the physiological temperature range. We report the results of photon correlation spectroscopy and molecular dynamics simulations of {HSA} in aqueous solution. The experimental data processing produced the temperature dependence of the {HSA} hydrodynamic radius and its zeta potential. Molecular dynamics reproduced the results of experiments and revealed changes in the secondary structure caused by the destruction of hydrogen bonds in the macromolecule's globule.

[2] 
Elvira Tarasova, Vladimir Farafonov, Reza Khayat, Noriaki Okimoto, Teruhisa S.
Komatsu, Makoto Taiji, and Dmitry Nerukh,
AllAtom Molecular Dynamics Simulations of Entire Virus Capsid Reveal the Role of Ion Distribution in Capsid's Stability, The Journal of Physical Chemistry Letters, 8 (4), 779784 (2017). [ DOI  at the journal's site  .pdf ] Present experimental methods do not have sufficient resolution to investigate all processes in virus particles at atomistic details. We report the results of molecular dynamics simulations and analyze the connection between the number of ions inside an empty capsid of PCV2 virus and its stability. We compare the crystallographic structures of the capsids with unresolved Ntermini and without them in realistic conditions (room temperature and aqueous solution) and show that the structure is preserved. We find that the chloride ions play a key role in the stability of the capsid. A low number of chloride ions results in loss of the native icosahedral symmetry, while an optimal number of chloride ions create a neutralizing layer next to the positively charged inner surface of the capsid. Understanding the dependence of the capsid stability on the distribution of the ions will help clarify the details of the viral life cycle that is ultimately connected to the role of packaged viral genome inside the capsid.

[3] 
Elvira Tarasova, Ivan Korotkin, Vladimir Farafonov, Sergey Karabasov, and
Dmitry Nerukh,
Complete virus capsid at allatom resolution: Simulations using molecular dynamics and hybrid molecular dynamics/hydrodynamics methods reveal semipermeable membrane function, Journal of Molecular Liquids, accepted (2017). [ DOI  at the journal's site ] Simulations of complete virus capsid at atomistic details have been performed using standard molecular dynamics as well as original hybrid molecular dynamics/hydrodynamics methodologies. The results show that the capsid is stable in water solution at room temperature and ions composition similar to physiological conditions. Detailed analysis of the flow of water molecules and ions through the capsid's wall is performed. It demonstrates that ions do not cross the capsid shell, while water exhibits substantial flows in both directions. This behaviour can be classified as a semipermeable membrane and may play a role in mechanical properties of the virus particle.

[4] 
Z. Zhuravlova, D. Nerukh, V. Reut, and N. Vaysfeld,
Investigation of idealized virus capsid model with the dynamic elasticity apparatus, Journal of Mathematical Sciences, in press (2017). [ at the journal's site  .pdf ] The 3dimentional (3D) elasticity dynamic theory is applied to investigate the mechanical properties of virus capsid. The idealized model of virus is based on the 3D mathematical physics boundary problem formulated in spherical coordinate system for the steadystate oscillation process. The virus is modeled as the hollow elastic sphere, which is situated and fullfilled with two different acoustic mediums. The stated boundary value problem is solved with the help of the integral transformation method and method of the discontinuous solutions. As a result, the exact solution of the problem is derived. The numerical calculations of the virus elastic characteristics are conducted.

[5] 
Z. Yu. Zhuravlova, D. A. Nerukh, V. V. Reut, D. G. Kozachkov, and N. D.
Vaysfeld,
On stress state of the PCV2 virus, Bulletin of Taras Shevchenko National University of Kyiv Series: Physics & Mathematics, in press (2017). [ at the journal's site  .pdf ] The virus capsid PCV2 is investigated by the construction of the idealized virus model. It is described by the 3D dynamical elasticity problem formulated in the spherical coordinate system for the steadystate oscillation process. The virus is modeled as the hollow elastic sphere, which is surrounded and fulfilled with the two different acoustic mediums. The integral Fourier and Legendre transformations were applied to the stated initialboundary value problem. With the help of the discontinuous solutions method the expressions for the displacements and acoustic potentials were derived in the exact form depending on the unknown jumps of the displacements and stresses. The conditions at the virus surfaces allowed to express the displacement and stress jumps via jumps of the acoustic potentials, which were obtained after solving of the two linear equations system. As a result, the exact solution of the problem is derived. The numerical calculations of the virus elastic characteristics are conducted. This problem is the first step in the virus simulation with the help of the elasticity equations. It was established that more complicated statement of the problem in the frame of the anisotropic elastic problem should be used for the more adequate virus modeling.

[6] 
Ivan Korotkin, Dmitry Nerukh, Elvira Tarasova, Vladimir Farafonov, and Sergey
Karabasov,
Twophase flow analogy as an effective boundary condition for modelling liquids at atomistic resolution, Journal of Computational Science, 17, Part 2, 446  456 (2016), Discrete Simulation of Fluid Dynamics 2015, Cited: 2 times. [ DOI  at the journal's site  .pdf ] A hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework based on the analogy with twophase hydrodynamics has been extended to dynamically tracking the feature of interest at allatom resolution. In the model, the hydrodynamics description is used as an effective boundary condition to close the molecular dynamics solution without resorting to standard periodic boundary conditions. The approach is implemented in a popular Molecular Dynamics package {GROMACS} and results for two biomolecular systems are reported. A small peptide dialanine and a complete capsid of a virus porcine circovirus 2 in water are considered and shown to reproduce the structural and dynamic properties compared to those obtained in theory, purely atomistic simulations, and experiment.

[7] 
Ivan Korotkin, Sergey Karabasov, Dmitry Nerukh, Anton Markesteijn, Arturs
Scukins, Vladimir Farafonov, and Evgen Pavlov,
A Hybrid Molecular Dynamics/Fluctuating Hydrodynamics Method for Modelling Liquids at Multiple Scales in Space and Time, The Journal of Chemical Physics, 143, 014110 (2015), Cited: 4 times. [ DOI  at the journal's site  .pdf ] A new 3D implementation of a hybrid model based on the analogy with twophase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the LandauLifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoomin" userdefined function s that has the meaning of a partial concentration in the twophase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.

[8] 
Dmitry Nerukh,
Referee Report For: Molecular Dynamics Simulations of the Temperature Induced Unfolding of Crambin Follow the Arrhenius Equation. [version 1; referees: 1 approved, 1 approved with reservations], F1000Research, 4, 589 (2015). [ DOI  at the journal's site ] Open Peer Review on `Molecular Dynamics Simulations of the Temperature Induced Unfolding of Crambin Follow the Arrhenius Equation'

[9] 
Arturs Scukins, Vitaliy Bardik, Evgen Pavlov, and Dmitry Nerukh,
Molecular Dynamics implementation of BN2D or `Mercedes Benz' water model, Computer Physics Communications, 190, 129  138 (2015). [ DOI  at the journal's site  .pdf ] Twodimensional `Mercedes Benz' (MB) or BN2D water model (Naim, 1971) is implemented in Molecular Dynamics. It is known that the MB model can capture abnormal properties of real water (high heat capacity, minima of pressure and isothermal compressibility, negative thermal expansion coefficient) (Silverstein et al., 1998). In this work formulas for calculating the thermodynamic, structural and dynamic properties in microcanonical (NVE) and isothermalisobaric (NPT) ensembles for the model from Molecular Dynamics simulation are derived and verified against known Monte Carlo results. The convergence of the thermodynamic properties and the system's numerical stability are investigated. The results qualitatively reproduce the peculiarities of real water making the model a visually convenient tool that also requires less computational resources, thus allowing simulations of large (hydrodynamic scale) molecular systems. We provide the open source code written in C/C++ for the BN2D water model implementation using Molecular Dynamics.

[10] 
Arturs Scukins, Dmitry Nerukh, Evgen Pavlov, Sergey Karabasov, and Anton
Markesteijn,
Multiscale Molecular Dynamics/Hydrodynamics implementation of two dimensional `Mercedes Benz' water model, European Physical Journal E, 224 (12), 22172238 (2015), Cited: 1 time. [ DOI  at the journal's site  .pdf ] A multiscale Molecular Dynamics/Hydrodynamics implementation of the 2D Mercedes Benz (MB or BN2D) [1] water model is developed and investigated. The concept and the governing equations of multiscale coupling together with the results of the twoway coupling implementation are reported. The sensitivity of the multiscale model for obtaining macroscopic and microscopic parameters of the system, such as macroscopic density and velocity fluctuations, radial distribution and velocity autocorrelation functions of MB particles, is evaluated. Critical issues for extending the current model to large systems are discussed.

[11] 
Sergey Karabasov, Dmitry Nerukh, Alfons Hoekstra, Bastien Chopard, and Peter V.
Coveney,
Multiscale modelling: approaches and challenges, Phil. Trans. R. Soc., A 372, 20130390 (2014). [ DOI  at the journal's site  .pdf ] Introducation to a Theme Issue `Multiscale systems in fluids and soft matter: approaches, numerics and applications' of Phil. Trans. R. Soc. A.

[12] 
Anton Markesteijn, Sergey Karabasov, Arturs Scukins, Dmitry Nerukh, Vyacheslav
Glotov, and Vasily Goloviznin,
Concurrent multiscale modelling of atomistic and hydrodynamic processes in liquids, Phil. Trans. R. Soc., A 372 (2021), 20130379 (2014), Cited: 10 times. [ DOI  at the journal's site  .pdf ] Fluctuations of liquids at the scales where the hydrodynamic and atomistic descriptions overlap are considered. Importance of these fluctuations for atomistic motions is discussed and examples of their accurate modelling with a multispacetimescale Fluctuating Hydrodynamics scheme are provided. For resolving microscopic details of liquid systems, including bimolecular solutions, together with macroscopic fluctuations in spacetime, a novel hybrid atomistic/ Fluctuating Hydrodynamics approach is introduced. For smooth transition between the atomistic and continuum representations, an analogy with twophase hydrodynamics is used that leads to a strict preservation of macroscopic mass and momentum conservation laws. Examples of numerical implementation of the new hybrid approach for the multiscale simulation of liquid argon in equilibrium conditions are provided.

[13] 
Evgen Pavlov, Makoto Taiji, Arturs Scukins, Anton Markesteijn, Sergey
Karabasov, and Dmitry Nerukh,
Visualising and controlling the flows in biomolecular systems at and between multiple scales: from atoms to hydrodynamics at different locations in time and space, Faraday Discussions, 169 (1), 285302 (2014). [ at the journal's site  .pdf ] A novel framework for modelling biomolecular systems at multiple scales in space and time simultaneously is described. The atomistic molecular dynamics representation is smoothly connected with statistical continuum hydrodynamics description. The system behaves correctly at the limits of pure molecular dynamics (hydrodynamics) and at the intermediate regimes when the atoms move partly as atomistic particles, and at the same time follow the hydrodynamic flows. The corresponding contributions are controlled by a parameter, which is defined as an arbitrary function of space and time, thus, allowing an effective separation of the atomistic `core' and continuum `environment'. To fill the scale gap between the atomistic and the continuum representations our special purpose computer for molecular dynamics, MDGRAPE4, as well as GPUbased computing were used for developing the framework. These hardware developments also include interactive molecular dynamics simulations that allow to intervene the modelling through forcefeedback devices.

[14] 
Alexander G. Nerukh and Dmitry A. Nerukh,
Timespatial drift of decelerating electromagnetic pulses, Opt. Express, 21 (14), 1736617371 (2013), Cited: 2 times. [ DOI  at the journal's site  .pdf ] A time dependent electromagnetic pulse generated by a current running laterally to the direction of the pulse propagation is considered in paraxial approximation. It is shown that the pulse envelope moves in the timespatial coordinates on the surface of a parabolic cylinder for the Airy pulse and a hyperbolic cylinder for the Gaussian. These pulses propagate in time with deceleration along the dominant propagation direction and drift uniformly in the lateral direction. The Airy pulse stops at infinity while the asymptotic velocity of the Gaussian is nonzero.

[15] 
Dmitry Nerukh and Sergey Karabasov,
WaterPeptide Dynamics during Conformational Transitions, The Journal of Physical Chemistry Letters, 4 (5), 815819 (2013), Cited: 9 times. [ DOI  at the journal's site  .pdf ] Transitions between metastable conformations of a dipeptide are investigated using classical molecular dynamics simulation with explicit water molecules. The distribution of the surrounding water at different moments before the transitions and the dynamical correlations of water with the peptide's configurational motions indicate that the water molecules represent an integral part of the molecular system during the conformational changes, in contrast with the metastable periods when water and peptide dynamics are essentially decoupled.

[16] 
Vitaliy Bardik, Vladimir Gotsulskii, Evgen Pavlov, Nikolai Malomuzh, Dmitry
Nerukh, Igor Yanchuk, and Serhiy Lavoryk,
Light scattering study of human serum albumin in predenaturation: Relation to dynamic transition in water at 42C, Journal of Molecular Liquids, 176 (0), 6064 (2012), (Special Issue Dynamics and Phase Transition: Selected Papers on Molecular Liquids presented at the EMLG/JMLG 2011 Annual Meeting 11  15 September 2011), Cited: 3 times. [ DOI  at the journal's site  .pdf ] Protein functional motions are ultimately connected to water dynamics. The goal of this study is to link the conformational dynamics of albumin to a dynamic transition taking place at 42C in water. We report the results of dynamic light scattering measurements of albumin aqueous solution in the temperature interval 2065C. The processing of the experimental data produced the temperature dependence of the macromolecular hydrodynamic radius. We demonstrate that the growth of the macromolecular size in this temperature range can be divided into two stages that are connected to the dynamical properties of water.

[17] 
V.Yu. Bardik, D. Nerukh, E.V. Pavlov, and M.S. Vlasyuk,
Free energy functional expansion as the generalized approach to the equation of state of dense fluids, Ukrainian Journal of Physics, 57 (6), 612618 (2012). [ .pdf ] A version of the thermodynamic perturbation theory based on scaling transformation of the partition function has been applied to the statistical foundation of the equation of state in the high pressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PVTdata on the isothermal compression for supercritical fluids of inert gases has been carried out.

[18] 
V.Yu. Bardik, D. Nerukh, E.V. Pavlov, M.S. Vlasyuk, and I.V. Zhyganiuk,
Equation of state for water in the small compressibility region, Ukrainian Journal of Physics, 57 (1), 4953 (2012). [ .pdf ] We derive the equation of state for supercritical fluids in the framework of the Sutherland and Katz potential models using the free energy perturbation expansion. The derived equation of state quantitatively agrees with experimental data on isothermal compression of water in the high pressure region. It establishes an explicit relationship between the thermodynamic experimental data and the parameters of the molecular potential. This can be used in calibration protocols for simulation forcefields for the high pressure regions.

[19] 
Dmitry Nerukh,
NonMarkov state model of peptide dynamics, Journal of Molecular Liquids, 176, 6570 (2012), (Special Issue Dynamics and Phase Transition: Selected Papers on Molecular Liquids presented at the EMLG/JMLG 2011 Annual Meeting 11  15 September 2011), Cited: 2 times. [ DOI  at the journal's site  .pdf ] A hidden Markov state model has been applied to classical molecular dynamics simulated small peptide in explicit water. The methodology allows increasing the time resolution of the model and describe the dynamics with the precision of 0.3ps (comparing to 6ps for the standard methodology). It also permits the investigation of the mechanisms of transitions between the conformational states of the peptide. The detailed description of one of such transitions for the studied molecule is presented.

[20] 
Dmitry Nerukh, Noriaki Okimoto, Atsushi Suenaga, and Makoto Taiji,
Ligand Diffusion on Protein Surface Observed in Molecular Dynamics Simulation, The Journal of Physical Chemistry Letters, 3 (23), 34763479 (2012), Cited: 5 times. [ DOI  at the journal's site  .pdf ] The process of binding of small ligands to dihydrofolate reductase protein has been investigated using allatom molecular dynamics simulations. The existence of a mechanism that facilitates the search of the binding site by the ligand is demonstrated. The mechanism consists of ligand diffusing on the protein's surface. It has been discussed in the literature before, but has not been explicitly confirmed for realistic molecular systems. The strength of this nonspecific binding is roughly estimated and found to be essential for the binding kinetics.

[21] 
Vladimir Ryabov and Dmitry Nerukh,
Statistical complexity of low and high dimensional systems, Journal of Atomic, Molecular, and Optical Physics, 2012, 589651 (2012). [ DOI  .pdf ] We suggest a new method for the analysis of experimental time series that can distinguish high dimensional dynamics from stochastic motion. It is based on the idea of statistical complexity, i.e. the Shannon entropy of the socalled emachine (a Markovtype model of the observed time series). This approach has been recently demonstrated to be efficient for making a distinction between a molecular trajectory in water and noise. In this paper we analyse the difference between chaos and noise using the ChirikovTaylor Standard map as an example in order to elucidate the basic mechanism that makes the value of complexity in deterministic systems high. In particular, we show that the value of statistical complexity is high for the case of chaos, and attains zero value for the case of stochastic noise. We further study the Markov property of the data generated by the Standard map to clarify the role of long time memory in differentiating the cases of deterministic systems and stochastic motion.

[22] 
Maxim V. Fedorov, Jonathan M. Goodman, Dmitry Nerukh, and Stephan Schumm,
Selfassembly of trehalose molecules on a lysozyme surface: the broken glass hypothesis, Physical Chemistry Chemical Physics, 13, 22942299 (2011), (reproduced in Virtual Journal of Biological Physics Research, 21(3), (2011)), Cited: 18 times. [ DOI  at the journal's site  .pdf ] To help understand how sugar interactions with proteins stabilise biomolecular structures, we compare the three main hypotheses for the phenomenon with the results of long molecular dynamics simulations on lysozyme in aqueous trehalose solution (0.75 M). We show that the water replacement and water entrapment hypotheses need not be mutually exclusive, because the trehalose molecules assemble in distinctive clusters on the surface of the protein. The flexibility of the protein backbone is reduced under the sugar patches supporting earlier findings that link reduced flexibility of the protein with its higher stability. The results explain the apparent contradiction between different experimental and theoretical results for trehalose effects on proteins.

[23] 
Vladimir Ryabov and Dmitry Nerukh,
Computational mechanics of molecular systems: Quantifying highdimensional dynamics by distribution of Poincare recurrence times, Chaos: An Interdisciplinary Journal of Nonlinear Science, 21 (3), 037113 (2011), Cited: 3 times. [ DOI  at the journal's site  .pdf ] A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore it is shown that causal states, the constituent parts of the main construct of computational mechanics, the emachine, define areas of the phase space that are optimal in the sense of transferring information from the microvariables to the macroobservables. We have demonstrated that, based on the decay of their Poincare return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasiperiodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare theorem.

[24] 
Vladimir Ryabov and Dmitry Nerukh,
Quantifying long time memory in phase space trajectories of molecular liquids, Journal of Molecular Liquids, 159 (1), 99104 (2011), (Intermolecular Interactions and Liquid Structure, Selected Papers on Molecular Liquids presented at the EMLG/JMLG 2009 Annual Meeting 6  10 September 2009), Cited: 1 time. [ DOI  at the journal's site  .pdf ] A trajectory of liquid water simulated using classical molecular dynamics has been analysed in the framework of symbolic dynamics. The behaviour of symbolic subsequences (words) of nine symbols long has been studied at a very long time of 1us. Contrary to naive expectations, the molecular trajectory behaves very differently compared to both a random signal and a random surrogate with spectral properties identical to the molecular trajectory. The molecular system characteristics resemble those of a chaotic map, the Standard map. We conclude that the most probable reason for deviations from randomness in the molecular system is its deterministic dynamics, in particular, the stickiness of periodic islands in the bulk of chaotic motion.

[25] 
Dmitry Nerukh,
Why are MD simulated protein folding times wrong?, In Hamid R. Arabnia, editor, Advances in Computational Biology, volume 680 of Advances in Experimental Medicine and Biology. Springer (2010). [ at the journal's site  .pdf ] The question of significant deviations of protein folding times simulated using molecular dynamics from experimental values is investigated. It is shown that, in the framework of Markov State Model describing the conformational dynamics of peptides and proteins, the folding time is very sensitive to the simulation model parameters, such as forcefield and temperature. Using two peptides as examples we show that the deviations in the folding times can reach an order of magnitude for modest variations of the molecular model. We, therefore, conclude that the folding rate values obtained in molecular dynamics simulations have to be treated with care.

[26] 
Dmitry Nerukh,
On the question of calculating the free energies of biomolecular systems: how much of phase space is actually explored?, In Jelena Tsurko and Werner Kunz, editors, Thermodynamics of Amino Acid and Protein Solutions. Transworld Research Networks (2010). [ .pdf ] A novel statistical analysis of Molecular Dynamics generated trajectories is applied to various bulk liquids and a peptide in water. The analysis provides unique information on the full dimensional trajectory. In particular, it demonstrates that the phase space exploration is a very slow process that has the time scale of hundreds of nanoseconds even in bulk water and argon. Most importantly, the areas of the phase space visited at these times are different, in contrast to the commonly assumed uniform random search process. For a 21residue peptide in explicit water it has been found that the peptide exhibits nanoseconds long periods that significantly differ in the rates of the phase space exploration. During these periods the rates remain the same but different from other periods and from the phase space covering rate in water.

[27] 
Dmitry Nerukh, Christian H. Jensen, and Robert C. Glen,
Identifying and correcting nonMarkov states in peptide conformational dynamics, The Journal of Chemical Physics, 132 (8), 084104 (2010), Cited: 11 times. [ DOI  at the journal's site  .pdf ] Conformational transitions in proteins define their biological activity and can be investigated in detail using Markov State Model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analysing the transitions obtained directly from the dynamics of an MD simulated peptide VPAL (Valine  Proline  Alanine  Leucine) and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of 50ps and longer. However, at the time scale of 3040ps the dynamics looses its Markov property. Our methodology reveals the mechanism that leads to nonMarkov behaviour. It also provides a way of regrouping the conformations into new states that now posses the required Markov property of their dynamics.

[28] 
Dmitry Nerukh and Vladimir Ryabov,
Computational Mechanics of Molecular Systems, In Hans P. Berger, editor, Computational Mechanics Research Trends, Computer Science, Technology and Applications, pages 219247. Nova Science Publishers (2010). [ .pdf ] A framework that connects Computational Mechanics and molecular dynamics has been developed and described. As the key part of the framework the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore it is shown that causal states, the constituent parts of the main construct of Computational Mechanics, emachine, define areas of the phase space that are optimal in the sense of transferring information from the microvariables to the macroobservables. We have demonstrated that these areas of the phase space can be divided into two classes according to their Poincare return times. The first class is characterised by predominantly short time returns, typical to quasiperiodic trajectories of the dynamical system. This class includes a limited number of areas that are robust with respect to different total length of the molecular trajectory. The second class has a chaotic behaviour of the return times distributed exponentially in accordance with the Poincare theorem. In contrast to the first class, the number of such areas grows logarithmically with the length of the trajectory. We put forward and numerically illustrate a hypothesis that explains this behaviour by the presence of temporal nonstationarity in molecular trajectory.

[29] 
Svitlana Ruzhytska, Martin Nilsson Jacobi, Christian H. Jensen, and Dmitry
Nerukh,
Identification of metastable states in peptide's dynamics, The Journal of Chemical Physics, 133 (16), 164102 (2010), (reproduced in Virtual Journal of Biological Physics Research, 20(9), (2010)), Cited: 3 times. [ DOI  at the journal's site  .pdf ] A recently developed spectral method for identifying metastable states in Markov chains is used to analyse the conformational dynamics of a four residue peptide ValineProlineAlanineLeucine. We compare our results to empirically defined conformational states and show that the found metastable states correctly reproduce the conformational dynamics of the system.

[30] 
Dmitry Nerukh,
Dynamical frustration of protein's environment at the nanoseconds time scale, Journal of Molecular Liquids, 145 (3), 139144 (2009), (Special Issue of contributions to the International Conference: Modern Physical Chemistry for Advanced Materials), Cited: 1 time. [ DOI  at the journal's site  .pdf ] A 21residue peptide in explicit water has been simulated using classical molecular dynamics. The system's trajectory has been analysed with a novel approach that quantifies the process of how atom's environment trajectories are explored. The approach is based on the measure of Statistical Complexity that extracts complete dynamical information from the signal. The introduced characteristic quantifies the system's dynamics at the nanoseconds time scale. It has been found that the peptide exhibits nanoseconds long periods that significantly differ in the rates of the exploration of the dynamically allowed configurations of the environment. During these periods the rates remain the same but different from other periods and from the rate for water. Periods of dynamical frustration are detected when only limited routes in the space of possible trajectories of the surrounding atoms are realised.

[31] 
Dmitry Nerukh, Vladimir Ryabov, and Makoto Taiji,
Molecular phase space transport in water: Nonstationary random walk model, Physica A: Statistical Mechanics and its Applications, 388 (22), 47194726 (2009), Cited: 3 times. [ DOI  at the journal's site  .pdf ] Molecular transport in phase space is crucial for chemical reactions because it defines how prereactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a nonrandom character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of nonstationarity in the transition probabilities of the segments of molecular trajectories can account for the observed nonuniform filling of the phase space. Surprisingly, the characteristic periods in the model nonstationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

[32] 
Dmitry Nerukh and Makoto Taiji,
21residue peptide's dynamics at and between elementary structural transitions, Journal of Molecular Liquids, 147 (12), 124127 (2009), (Molecular Approaches to Complex Liquid Systems, Selected Papers on Molecular Liquids presented at the Joint Conference of JMLG/EMLG Meeting 2007 and 30th Symposium on Solution Chemistry of Japan). [ DOI  at the journal's site  .pdf ] Elementary conformational changes of the backbone of a 21residue peptide A5(A3RA)3A are studied using molecular dynamics simulations in explicit water. The processes of the conformational transitions and the regimes of stationary fluctuations between them are investigated using minimal perturbations of the system. The perturbations consist of a few degrees rotation of the velocity of one of the systems' atoms and keep the system on the same energy surface. It is found that (i) the system dynamics is insignificantly changed by the perturbations in the regimes between the transitions; (ii) it is very sensitive to the perturbations just before the transitions that prevents the peptide from making the transitions; and (iii) the perturbation of any atom of the system, including distant water molecules is equally effective in preventing the transition. The latter implies strongly collective dynamics of the peptide and water during the transitions.

[33] 
V.A. Buts, A.G. Nerukh, N.N. Ruzhytska, and D.A. Nerukh,
Wave chaotic behaviour generated by linear systems, Optical and Quantum Electronics, 40 (8), 587601 (2008), Cited: 4 times. [ DOI  at the journal's site  .pdf ] It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying halfspace. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time.

[34] 
Christian H. Jensen, Dmitry Nerukh, and Robert C. Glen,
Controlling protein molecular dynamics: How to accelerate folding while preserving the native state, The Journal of Chemical Physics, 129 (22), 225102 (2008), (reproduced in Virtual Journal of Biological Physics Research, 16(12), (2008)), Cited: 3 times. [ DOI  at the journal's site  .pdf ] The dynamics of peptides and proteins generated by classical MD is described using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1us. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide VPAL (Valine  Proline  Alanine  Leucine) in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.

[35] 
Christian H. Jensen, Dmitry Nerukh, and Robert C. Glen,
Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory, The Journal of Chemical Physics, 128 (11), 115107 (2008), (reproduced in Virtual Journal of Biological Physics Research, 15(7), (2008)), Cited: 10 times. [ DOI  at the journal's site  .pdf ] We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500ns molecular dynamics trajectory of the peptide valineprolinealanineleucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

[36] 
Dmitry Nerukh,
Computational mechanics reveals nanosecond time correlations in molecular dynamics of liquid systems, Chemical Physics Letters, 457 (46), 439  443 (2008), Erratum to [Chem. Phys. Lett. 457 (2008) 439]: Chem. Phys. Lett., 459(16), 203 (2008), Cited: 4 times. [ DOI  at the journal's site  .pdf ] Statistical complexity, a measure introduced in computational mechanics has been applied to MD simulated liquid water and other molecular systems. It has been found that statistical complexity does not converge in these systems but grows logarithmically without a limit. The coefficient of the growth has been introduced as a new molecular parameter which is invariant for a given liquid system. Using this new parameter extremely long time correlations in the system undetectable by traditional methods are elucidated. The existence of hundreds of picosecond and even nanosecond long correlations in bulk water has been demonstrated.

[37] 
Dmitry Nerukh, Vladimir Ryabov, and Robert C. Glen,
Complex temporal patterns in molecular dynamics: A direct measure of the phasespace exploration by the trajectory at macroscopic time scales, Phys. Rev. E, 77, 036225 (2008), (reproduced in Virtual Journal of Biological Physics Research, 15(7), (2008)), Cited: 10 times. [ DOI  at the journal's site  .pdf ] Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the shorttime correlations corresponding to the velocity autocorrelation decay times (<0.1ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longertime correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced.

[38] 
A.V. Luzanov and Dmitry Nerukh,
Simple Oneelectron Invariants of Molecular Chirality, Journal of Mathematical Chemistry, 41 (4), 417435 (2007), Cited: 3 times. [ DOI  at the journal's site  .pdf ] Pseudoscalar measures of electronic chirality for molecular systems are derived using the spectral moment theory applied to the frequencydependent rotational susceptibility. In this scheme a oneelectron chirality operator k naturally emerges as a quantum counterpart of the triple scalar product, involving velocity, acceleration and second acceleration. Averaging k over an electronic state vector gives rise to an additive chirality invariant (kindex), considered as a quantitative measure of chirality. A simple computational technique for quick calculation of the kindex is developed and various structural classes (cyclic hydrocarbons, cageshaped systems, etc.) are studied. Reasonable behaviour of the chirality index is demonstrated. The chirality changes during the betaturn formation in LeuEnkephalin is presented as a useful example of the chirality analysis for conformational transitions.

[39] 
Dmitry Nerukh, George Karvounis, and Robert C. Glen,
Dynamic Complexity of Chaotic Transitions in HighDimensional Classical Dynamics: LeuEnkephalin Folding, In Michael R. Berthold, Robert C. Glen, and Ingrid Fischer, editors, Computational Life Sciences II, volume 4216 of Lecture Notes in Computer Science, pages 129140. Springer Berlin Heidelberg (2006), Cited: 1 time. [ DOI  at the journal's site  .pdf ] LeuEnkephalin in explicit water is simulated using classical molecular dynamics. A betaturn transition is investigated by calculating the topological complexity (in the ?computational mechanics? framework [J. P. Crutchfield and K. Young, Phys. Rev. Lett., 63, 105 (1989)]) of the dynamics of both the peptide and the neighbouring water molecules. The complexity of the atomic trajectories of the (relatively short) simulations used in this study reflect the degree of phase space mixing in the system. It is demonstrated that the dynamic complexity of the hydrogen atoms of the peptide and almost all of the hydrogens of the neighbouring waters exhibit a minimum precisely at the moment of the betaturn transition. This indicates the appearance of simplified periodic patterns in the atomic motion, which could correspond to highdimensional tori in the phase space. It is hypothesized that this behaviour is the manifestation of the effect described in the approach to molecular transitions by Komatsuzaki and Berry [T. Komatsuzaki and R.S. Berry, Adv. Chem. Phys., 123, 79 (2002)], where a ?quasiregular? dynamics at the transition is suggested. Therefore, for the first time, the less chaotic character of the folding transition in a realistic molecular system is demonstrated.

[40] 
Y. C. Chesnokov, D. Nerukh, and R. C. Glen,
Individually adaptable automatic QT detector, In 2006 Computers in Cardiology, pages 337340 (2006), ISSN 02766574, Cited: 5 times. [ at the journal's site  .pdf ] ters in Cardiology challenge presents the clinically important problem of developing and testing fully automated methods for measurement of the QT interval with clinically acceptable accuracy. For this purpose a fully automated method was developed using timefrequency methods of continuous (CWT) and fast wavelet transforms (FWT). It consists of QRS detection and P, T wave boundaries identification which is implemented using consecutive ECG data filtering with CWT and FWT transforms. The frequency of the CWT transform can be adjusted for more precise identification of the T wave boundaries for an individual patient. A representative beat with a T wave is selected from an automatically annotated signal if it is not annotated as ectopic, noise or artefact. The final score is the highest one in division three and second place in division two.

[41] 
A.V. Luzanov and D. Nerukh,
Complexity and chirality indices for molecular informatics: differential geometry approach, Functional materials, 12 (1), 5564 (2005). [ at the journal's site  .pdf ] Novel molecular complexity measures are designed based on the quantum molecular kinematics previously suggested in [A.V.Luzanov, E.N.Babich, J. Mol. Stucture (Theochem), 333, 279 (1995)]. The Hamiltonian matrix constructed in a quasitopological approximation describes the temporal evolution of the modelled electronic system and determines the time derivatives for the dynamic quantities. This allows to define the average kinematic characteristics closely related to the curvatures of the electron paths. A special attention has been given to the computational scheme for this chirality measure. The calculations on realistic molecular systems demonstrate reasonable behaviour of the proposed molecular complexity indices.

[42] 
George Karvounis, Dmitry Nerukh, and Robert C. Glen,
Water network dynamics at the critical moment of a peptide's betaturn formation: A molecular dynamics study, The Journal of Chemical Physics, 121 (10), 49254935 (2004), Cited: 12 times. [ DOI  at the journal's site  .pdf ] Allatom molecular dynamics simulations for a single molecule of LeuEnkephalin in aqueous solution have been used to study the role of the water network during the formation of betaturns. We give a detailed account of the intramolecular hydrogen bonding, the waterpeptide hydrogen bonding, and the orientation and residence times of water molecules focusing on the short critical periods of transition to the stable betaturns. These studies suggest that, when intramolecular hydrogen bonding between the first and fourth residue of the betaturn is not present, the disruption of the water network and the establishment of water bridges constitute decisive factors in the formation and stability of the betaturn. Finally, we provide possible explanations and mechanisms for the formations of different kinds of betaturns.

[43] 
Dmitry Nerukh and Trevor R. Griffiths,
Real and imaginary parts of the vibrational relaxation of acetonitrile in its electrolyte solutions: new results for the dynamics of solvent molecules, Journal of Molecular Liquids, 109 (2), 8397 (2004), <ce:title>Sixth Liblice Conference on the Statistical Mechanics of Liquids</ce:title>, Cited: 2 times. [ DOI  at the journal's site  .pdf ] Isotropic scattering Raman spectra of liquid acetonitrile (AN) solutions of LiBF4 and NaI at various temperatures and concentrations have been investigated. For the first time imaginary as well as real parts of the solvent vibrational correlation functions have been extracted from the spectra. Such imaginary parts are currently an important component of modern theories of vibrational relaxation in liquids. This investigation thus provides the first experimental data on imaginary parts of a correlation function in {AN} solutions. Using the fitting algorithm we recently developed, statistically confident models for the Raman spectra were deduced. The parameters of the band shapes, with an additional correction, of the nu(2) {AN} vibration (CN stretching), together with their confidence intervals are also reported for the first time. It is shown that three distinct species, with lifetimes greater than 10e13 s, of the {AN} molecules can be detected in solutions containing Li+ and Na+. These species are attributed to {AN} molecules directly solvating cations; the single oriented and polarised molecules interleaving the cation and anion of a Solvent Shared Ion Pair (SShIP); and molecules solvating anions. These last are considered to be equivalent to the next layer of solvent molecules, because the {CN} end of the molecule is distant from the anion and thus less affected by the ionic charge compared with the anion situation. Calculations showed that at the concentrations employed, 1 and 0.3 M, there were essentially no other solvent molecules remaining that could be considered as bulk solvent. Calculations also showed that the internuclear distance in these solutions supported the proposal that the ionic entity dominating in solution was the SShIP, and other evidence was adduced that confirmed the absence of Contact Ion Pairs at these concentrations. The parameters of the shape of the vibrational correlation functions of all three species are reported. The parameters of intramolecular anharmonic coupling between the potential surfaces in {AN} and the dynamics of the intermolecular environment fluctuations and intermolecular energy transfer are presented. These results will assist investigations made at higher and lower concentrations, when additional species and interactions with {AN} molecules will be present.

[44] 
Dmitry Nerukh, George Karvounis, and Robert Glen,
Quantifying the complexity of chaos in multibasin multidimensional dynamics of molecular systems, Complexity, 10 (2), 4046 (2004), Cited: 4 times. [ DOI  at the journal's site  .pdf ] The simulated classical dynamics of a small molecule exhibiting selforganizing behavior via a fast transition between two states is analyzed by calculation of the statistical complexity of the system. It is shown that the complexity of molecular descriptors such as atom coordinates and dihedral angles have different values before and after the transition. This provides a new tool to identify metastable states during molecular selforganization. The highly concerted collective motion of the molecule is revealed. Lowdimensional subspaces dynamics is found sensitive to the processes in the whole, highdimensional phase space of the system.

[45] 
Natalia N. Ruzhitskaya, Alexander G.G. Nerukh, and Dmitry Nerukh,
Accurate modelling of pulse transformation by adjustableintime medium parameters, Optical and Quantum Electronics, 35 (45), 347364 (2003), Cited: 9 times. [ DOI  at the journal's site  .pdf ] A possibility of a strong change of an electromagnetic signal by a short sequence of time cycles of pulses that modulate the medium parameters is shown. The backward wave is demonstrated to be an inevitable result of the medium time change. Dependence of the relation between backward and forward waves on the parameters of the medium modulation is investigated. The finite statistical complexity of the electromagnetic signal transformed by a finite sequence of modulating cycles is calculated. Increase of the complexity with the number of cycles is shown.

[46] 
Dmitry Nerukh, George Karvounis, and Robert C. Glen,
Complexity of classical dynamics of molecular systems. I. Methodology, The Journal of Chemical Physics, 117 (21), 96119617 (2002), Cited: 18 times. [ DOI  at the journal's site  .pdf ] Methods for the calculation of complexity have been investigated as a possible alternative for the analysis of the dynamics of molecular systems. "Computational mechanics" is the approach chosen to describe emergent behavior in molecular systems that evolve in time. A novel algorithm has been developed for symbolization of a continuous physical trajectory of a dynamic system. A method for calculating statistical complexity has been implemented and tested on representative systems. It is shown that the computational mechanics approach is suitable for analyzing the dynamic complexity of molecular systems and offers new insight into the process.

[47] 
Dmitry Nerukh, George Karvounis, and Robert C. Glen,
Complexity of classical dynamics of molecular systems. II. Finite statistical complexity of a waterNa+ system, The Journal of Chemical Physics, 117 (21), 96189622 (2002), Cited: 7 times. [ DOI  at the journal's site  .pdf ] The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated waterNa+ system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis.

[48] 
Dmitry Nerukh and Trevor R. Griffiths,
Complex vibrational correlation functions extracted from the resolved nu(2) band of liquid acetonitrile, Phys. Chem. Chem. Phys., 3, 17991805 (2001), Cited: 1 time. [ DOI  at the journal's site  .pdf ] The development of a sophisticated model is presented for fitting the experimental Raman spectra of liquid acetonitrile. A new approach for extracting all possible band shape details of highly overlapping spectral bands is derived and implemented. A unique, statistically justified resolution is obtained of the [small nu] vibrational band into its components at 25, 50 and 75[degree]C. The parameters of both the real and imaginary parts of the vibrational correlation functions are reported for the first time together with their confidence intervals. The quantitative characteristics obtained of the nu mode dynamics can be considered as experimental data and used for testing theoretical models of vibrational relaxation.

[49] 
Dmitry Nerukh and John H. Frederick,
Multidimensional quantum dynamics with trajectories: a novel numerical implementation of Bohmian mechanics, Chemical Physics Letters, 332 (12), 145153 (2000), Cited: 44 times. [ DOI  at the journal's site  .pdf ] A novel implementation of the de BroglieBohm mechanics is presented. The method employs the use of ndimensional Delaunay tesselation for the purpose of computing the quantum potential term and is fully generalizable for the multidimensional case. We simulate the scattering of a Gaussian wavepacket from an Eckart barrier in two and threedimensions and compare our results against the dynamics obtained using a numerically exact propagation scheme.

[50] 
Trevor R. Griffiths, Dmitry A. Nerukh, and Sergey A. Eremenko,
The application of theoretical models of complex shape to the fitting of experimental spectra having closely overlapping bands, Phys. Chem. Chem. Phys., 1, 31993208 (1999), Cited: 11 times. [ DOI  at the journal's site  .pdf ] The problem of the uniqueness of parameters obtained during fitting of experimental spectra containing closely overlapping bands has been evaluated, since conventional methods of fitting do not produce reliable results. It is here shown that, despite the difficulties inherent in both the formal mathematical problem and its numerical solutions, typical and representative spectra can be resolved unambiguously within a reasonably chosen theoretical model. Reliable values of the parameters of the model, including parameters of band shape, can also be obtained. A random search method of global minimisation of a function with a significant number of arguments is derived. A program and algorithm to implement this method for spectra decomposition have been developed. The program allows the microdynamics of liquids to be obtained directly upon performing numerical Fourier transformations on a model (theoretical) time correlation function together with using model spectra obtained thereby in each fitting step. A model spectrum for any desired accuracy and frequency range can hence be generated without the unavoidable errors inherent in conventional methods. The apparatus function of the spectrophotometer is also now readily incorporated. Using the algorithm, the parameters of the microdynamics of acetonitrile molecules are obtainable for the first time upon decomposition of its nu Raman vibration, and a value of 0.069 was obtained for the dimensionless modulation speed in liquid acetonitrile. This method has also enabled for the first time the detection of molecules in the second solvation shell around Li in acetonitrile, from within its Raman spectrum.

[51] 
A.A. Avdeenko, V.V. Eremenko, N.I. Gorbenko, P.V. Zinovev, D.A. Nerukh, A.T.
Pugachev, N.B. Silaeva, Yu.A. Tiunov, and N.P. Churakova,
Luminescence of thin films of C60 at low temperatures, Sverkhtverdyye materialy (Superhard materials), 3, 5460 (1997), (in Russian). [ .pdf ] Исследованы люминесценция и структура тонких пленок (10 нм) фуллерита С60, полученных осаждением в вакууме на скол монокристалла NaCl. По данным электроннооптических исследований, пленки С60 были сплошными, достаточно однородными, имели ГЦКрешетку, ориентированную таким образом, что плоскость (111) была параллельна плоскости (001) монокристалла NaCl. Проведены измерения спектров фотолюминесценции пленок фуллерита С60, на NaCl и в свободном состоянии при температуре 5К. Экспериментальные спектры с плохо выраженной структурой разделены на составляющие полосы гауссовой формы. Отмечено влияние подложки и длины волны возбуждения на спектры люминесценции. Обсуждаются механизмы формирования спектров люминесценции.

[52] 
S.A. Eremenko, D.A. Nerukh, and O.N. Kalugin,
Dynamic parameters of acetonitrile molecule from the analysis of band shape of its Raman spectrum, Proc. Kharkov Univ., Chemistry, 1, 3443 (1997), (in Russian). [ .pdf ] 
[53] 
Alexander G. Nerukh, Igor V. Scherbatko, and Dmitriy A. Nerukh,
Using evolutionary recursion to solve an electromagnetic problem with timevarying parameters, Microwave and Optical Technology Letters, 14 (1), 3136 (1997), Cited: 9 times. [ DOI  at the journal's site  .pdf ] The method for handling a transient electromagnetic problem with arbitrary time dependence of a medium parameter is proposed. The method is based on the evolutionary approach, which reduces the problem to a Volterra integral equation. A parameter's arbitrary time variation is approximated by a stepped function. The problem is exactly solved at each step by virtue of the same resolvent. Various parameter time dependences are considered. ?© 1997 John Wiley & Sons, Inc.

[54] 
O. N. Kalugin, D. A. Nerukh, S. A. Eremenko, A. V. Vankevich, and A. G. Nerukh,
Molecular Dynamics of Acetonitrile in Its Electrolyte Solutions by Raman Spectroscopy, Russian Journal of Inorganic Chemistry, 41 (2), 249 (1996), Cited: 1 time. [ at the journal's site  .pdf ] The region of the 2(a1) (CN) and 4(a1) (CC) stretching vibrations of isotropic and anisotropic Raman spectra of acetonitrile and 1 M NaI, NaBPh4 , and Bu4NI solutions in acetonitrile at ca. 22°C were stud ied. The spectra were decomposed into components assuming that the lineshape of a separate band is described by integrated convolution of the Lorentzian and Gaussian functions. The spectra of Na+containing solutions were found to exhibit a new band in the region of the 2 and 4 vibrations, which corresponds to the solvent molecules incorporated in the first solvation shell of Na+. Vibrational and rotational relaxation times of aceto nitrile molecules were calculated by the suggested method. Molecular relaxation was found to slow down on going from the neat solvent to electrolyte solutions and, in the latter, with an increase in the electrostatic influ ence of ions. Autocorrelation functions of the corresponding relaxation processes in neat acetonitrile and, espe cially, in electrolyte solutions considerably deviate from a pure exponential form.

[55] 
Oleg N. Kalugin, Dmitry A. Nerukh, Ivan N. Vyunnik, Elena G. Otlejkina,
Yurij N. Surov, and Nikolaj S. Pivnenko,
IR and NMR studies of hydrogen bonding in hexan1oltetrabutylammonium iodide solutions in the temperature range 28145 [degree]C and in tetrachloromethane, J. Chem. Soc., Faraday Trans., 90, 297303 (1994), Cited: 2 times. [ DOI  at the journal's site  .pdf ] IR spectra of (BuNI)hexan1ol solutions at 25, 55, 85, 115 and 145 [degree]C in the OH stretching region have been investigated. The OH stretching spectra and the H NMR chemical shifts of the hexanol OHgroup were obtained from BuNIhexanolCCl solutions in the alcohol concentration range 3 [times] 107.8 mol dm . The relationship between absorbance and wavenumber is represented as the product of a Lorentzian and a Gaussian curve. Using this dependence deconvolution of the OHband was carried out by the Simplex method. From these data, it was established that BuNI is a structurebreaker at moderate temperatures and/or low concentrations of CCl. At higher temperatures or in very dilute solutions of BuNIhexanol in CCl, BuNI is observed to be a structuremaker.

[56] 
S.M. Gubsky, I.N. Vyunnik, and D.A. Nerukh,
Temperature dependence of equilibrium and transport properties of 11 electrolytes in 1propanol. I. Limiting molar conductivities and association constants, Zhurn. Fiz. Khimii (Russ. J. Phys. Chem.), 65 (1), 114119 (1991), Cited: 3 times. [ .pdf ] На основе выбранной модели равновесии, уравнения концентрационной зависимости молярной электрической проводимости из кондуктометричесних данных рассчитаны предельные молярные электрические проводимости и константы ассоциации 11электролитов в 1пропаноле в интервале 200368 К. Обнаружены минимумы на политермах констант ассоциации.

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