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Supercomputer simulation of nanostructure complexes with account of nonlocal of transport processes


V.G. Maslov – D. Sc. (Phys.-Math.), National Research University of Information Technologies, Mechanics and Optics. Е-mail:
S.A. Chivilikhin – Ph. D. (Phys.-Math.), Senior Research Scientist, National Research University of Information Technologies, Mechanics and Optics. E-mail:
A.V. Boukhanovsky – Dr. Sc., professor, National Research University of Information Technologies, Mechanics and Optics. Е-mail:
A.I. Svitenkov – Graduate Student, Junior Research Scientist, National Research University of Information Technologies, Mechanics and Optics. E-mail:

The mechanical properties of nanostructural materials is often considerably different in comparison with properties of isotropic medium with similar mechanical parameters. This fact caused extensive studies of computational methods for modeling nanomaterials and nature of its integral properties formation. Even for particular case of rheological properties modeling there is a long list of such computational methods, as lattice-Boltzmann, dissipative particle dynamics, Langevin dynamics and some continual assumption. All of these methods are proposed for using in so called multiscale models with molecular mechanics (MM) computational methods, frequently molecular dynamics or Monte-Carlo molecular simulation. The subject of theoretical interest here is finding such general set of parameters measured with molecular mechanics methods and allowed more accurately estimation of integral properties of the material. This issue has not been resolved for today. Measurements of the same parameters for micro-scale and molecular-scale levels, as Young’s modulus and the like are quite obvious and often used way. This method is associated with so-called “representative volume element (RVE)” which unfortunately usually turns out too big for MM simulation. For example, for the polymer matrix with 100nm length nanotube inclusion RVE will be about 1μm3. In this research one new, more suitable and effective way of multiscale nanomaterials modeling is considered. In our model integral formulation of elasticity problem is used. It doesn’t contain any integral parameters of media, which all described by integral core functions. The last are solutions of Kelvin- Somilyany, can be both estimate analytically, and measured directly with molecular dynamics method. From the point of view of statistical mechanics, integral core functions are just space and time-dependent correlation function for values of local deformation and mass velocity. Reduced requirement for volume of MM simulation and statistical-vested method of MM measurements are main advantages of this molecular- to micro-scale bridge. We considered rheological properties of polymer nanocomposite material with inclusion of carbon nanotube. At micro-scale level, considered system was represented as continual polymer matrix with included nanotubes modeled as continual 1D objects. We also assume tube slipping relative to the polymer matrix. All necessary properties of medium were measured with MD simulation method. The main disadvantage of out model is a nonlocal character of interaction of particles and volume surface, therefore scalability of computational method is proportional to square of the volume. Starting from microscopic description the nonlocal mesoscale interactions concerned with nanoinclusions are investigated as well as its influence on parallel efficiency. As a result, it can be said that the nonlocal interaction is a fundamental feature of nanosystems.


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