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Topics of study

New mathematical and computer methods are developed based on natural science models, which are actively being studied in the world science. These models present great opportunities for the development of high technologies.

Themes of scientific research carried out at the laboratory in 2016

  • study of generalized virial theorem for the gas of massless electrons in Dirac materials,
  • study of the deformation influence on origination of a pseudomagnetic field, and study of the effects arising in the pseudomagnetic field of graphene under the action  of periodic deformations,
  • study of the optical properties of hyperbolic metasurfaces,
  • study of clusterization in Erdoes-Renyi random graphs with different parameters of distribution over the degrees of connection, study of clusterization in a model of network with vertices of two types and a fixed degree of connection (two-color network), study of networks with vertices of n types (many-colored network), study of the influence of the distribution over the degrees of connection,
  • artificial construction of networks of a given topology: bimodal distribution, multimodal distribution.
  • study of models of dipole systems of virus and molecule capsids,
  • study of the Rayleigh-type equation arising in the problem of flow past a surface with small imperfections, construction of uniformly bounded families of weak  asymptotic solutions to the Navier-Stokes equations in the compressible case, construction of stable difference schemes for the Navier-Stokes equation in the compressible case.

Themes of scientific research carried out at the laboratory in 2015

  • models of biaxial nematic liquid crystals (BNC),  which are actual in condensed-matter physics,
  • models of quantum many-particle effects exhibited in graphene characteristics, which are important both from the standpoint of fundamental studies of behavior of massless electrons and from the standpoint of specific applications of graphene in nanoelectronics,
  • models of nanotraps for solitary electrons whose characteristics permit implementation of quantum computations,   
  • models of the autoemission process on a nanocathode with a curvilinear surface, which is actual for designing effective devices in nanoelectronics,
  • models of hydrodynamic systems with vortex flows and boundary layer structures of multideck type,
  • hierarchically organized web structures actual in condensed-matter physics, biophysics, general theory of complex systems,
  • atomistic multiscale models of physical media and development of appropriate optimal strategies for using the supercomputer resources

 

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