Publications and research interests

Publications

  • A. Kirshtein, and C. Liu, Energetic variational approach to phase-field models
    of mixtures with polymeric fluids
    ,
    //(in preparation)

  • A. Kirshtein, and C. Liu, Energetic variational approach to phase-field models
    of mixtures with viscoelastic fluids
    ,
    //(in preparation)

  • J. Brannick, A. Kirshtein, and C. Liu, Analysis of the energy in thermodynamically
    consistent multi-component phase-field models,

    //(in preparation)

  • J. Brannick, A. Kirshtein, and C. Liu, Multigrid methods for degenerate
    multi-component phase-field systems
    ,
    //(in preparation)

  • Q. Yang, A. Kirstein, Y. Ji, C. Liu, J. Shen, L.-Q. Chen, A thermodynamically
    consistent Phase-Field-Navier-Stokes model for viscous sintering
    ,
    //(in preparation)

  • Q. Yang, A. Kirstein, Y. Ji, C. Liu, J. Shen, L.-Q. Chen, A thermodynamically
    consistent Phase-Field-Navier-Stokes model for solid-state sintering
    ,
    //(in preparation)

  • M.-H. Giga, A. Kirshtein, and C. Liu,  Variational Modeling and Complex Fluids,
    //In Y. Giga and A. Novotny (eds). Handbook of Mathematical Analysis in Mechanics
    of Viscous Fluids, pp. 1–41. Springer International Publishing, Cham, 2017. 
    (url) (PDF)

  • J. Brannick, A. Kirshtein, and C. Liu,  Dynamics of multi-component flows: 
    diffusive interface methods with energetic variational approaches,
    //In: Hashmi, S and Buggy, M. (eds). Reference Module in Materials Science
    and Materials Engineering, pp 1 -- 7. Elsevier, Oxford, 2016. 
    (url) (PDF)

  • M. Tournus, A. Kirshtein, L. V. Berlyand, and I. S. Aranson,  Flexibility of bacterial
    flagella in external shear results in complex swimming trajectories
    //Journal of The Royal Society Interface, 2015, 12; Published 5 November 2014. 
    (url)

  • P.P.Matus, A. A.Kirshtein, U. A. Irkhin,  Exact difference schemes for the system
    of acoustic equations and analysis of Riemann problem
    //Journal of Numerical and Applied Mathematics, No. 2, 2011, pp.83-97

Current research direction

Calculus of variations and numerical methods for complex fluids

Research interests

PDE analysis and computations, complex fluids, hyperbolic systems of conservation laws, mathematical modelling in biology, fluid dynamics, finite difference schemes, applications of exact difference schemes.