Davit(David) Harutyunyan


Research Assistant Professor

University of Utah
Department of Mathematics

Office: JWB 125
email: davith(at)math(dot)utah(dot)edu
Phone: 801-585-5793

Research Interests
  • My research is in Applied Analysis, including but not limited to:
  • Analysis of Partial Differential Equations
  • Calculus of Variations (Optimization)
  • Homogenization of PDEs, Systems of PDEs and Integrals, Asymptotic (multiscale) Analysis
  • Geometric and Analytic Inequlities
  • Continuum Mechanics (Elasticity)
  • Composite Materials, Metamaterials
  • Micromagnetics

  • I am a research assistant professor working with distinguished professor Graeme W. Milton . I obtained my Ph.D. in applied mathematics in June 2012 from the Hausdorff Center for Mathematics (University of Bonn, Germany) under the supervision of professor Stefan Mueller .

    CV

    Awards

    Publications and preprints

    19. D. Harutyunyan. A new formula for the differtence of arithmetic and geometric means: Optimal estimates. submitted, 2016. arxiv
    18. G.W.Milton, D. Harutyunyan and M. Briane . Towards a complete characterization of effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase. submitted, 2016. arxiv
    17. G.W.Milton, M. Briane and D. Harutyunyan. On the possible effective elasticity tensors of 2-dimensinal and 3-dimensional printed materials. submitted, 2016. arxiv
    16. D. Harutyunyan. Quantitative anisotropic isoperimetric and Brunn-Minkowski inequalities for convex sets with improved defect estimates. submitted, 2016. arxiv
    15. D. Harutyunyan. Gaussian curvature as an identifier of shell rigidity. submitted, 2016. arxiv
    14. Y.Grabovsky and D. Harutyunyan. Korn inequalities for shells with zero Gaussian curvature. submitted, 2016. arxiv
    13. D. Harutyunyan, G.W.Milton and R.V.Craster . High frequency homogenization for travelling waves in periodic media, Proceedings of the Royal Society A, 2016, online , arxiv
    12. D. Harutyunyan. Sharp weighted Korn and Korn-like inequalities and an application to washers. Journal of Elascitiy, accepted, 2016. arxiv
    11. D. Harutyunyan and G.W.Milton . Towards characterization of all 3\times 3 extremal quasiconevex quadratic forms, submitted, 2016. arxiv
    10. D. Harutyunyan, G.W.Milton, T.J. Dick and J.Boyer. On ideal dynamic climbing ropes, Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 2016. online
    9. D. Harutyunyan and G.W.Milton . On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials, Archive for Rational Mechanics and Analysis, 2016. online, arxiv
    8. Y.Grabovsky and D. Harutyunyan. Scaling intability in buckling of axially compressed cylindrical shells. Journal of Nonlinear Science, Vol. 26, Iss. 1, pp. 83-119, Feb. 2016. online, arxiv
    7. D. Harutyunyan. On the existence and stability of minimizers in ferromagnetic nanowires. Journal of Mathematical Analysis and Applications, 2015. Vol. 434, Iss. 2, pp. 1719-1739. 15 Feb. 2016. online, arxiv
    6. D. Harutyunyan and G.W.Milton . Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex. Calculus of Variations and Partial Differential Equations, October 2015, Volume 54, Issue 2, pp. 1575-1589. online , arxiv
    5. Y.Grabovsky and D. Harutyunyan. Rigurous derivation of the formula for the buckling load in axially compressed circular cylindrical shells. Journal of Elasticity, 120(2), pp. 249-276, 2015. .online, arxiv
    4. D. Harutyunyan. New asymptotically sharp Korn and Korn-like inequalities in thin domains. Journal of Elasticity, 117(1), pp. 95-109, 2014. online , arxiv
    3. Y.Grabovsky and D. Harutyunyan. Exact scaling exponents in Korn and Korn-type inequalities for cylindrical shells. SIAM Journal on Mathematical Analysis. 46(5), pp. 3277-3295, 2014 .online, arxiv.
    2. D. Harutyunyan. Scaling laws and the rate of convergence in magnetic thin films. Journal of Mathematical Analysis and Applications, 420(2), pp. 1744-1761, 2014.online, arxiv
    1. D. Harutyunyan. On the number of arrangements of n-ary brackets , Lomonosov 2002 proceedings, Moscow State University, 2002.
  • [Ph.D. Thesis] D. Harutyunyan. On the G-convergence of the energies and the convergence of almost minimizers in infinite magnetic cylinders, Dissertation: Universitaets und Landesbibliothek Bonn, 2012, online

    In preparation

  • D. Harutyunyan. The stability of the Urisohn inequality.
  • D. Harutyunyan and G.W.Milton . A note on the fundamental solutions of second order differential equations and systems.
  • D. Harutyunyan. A direct approach to sharp geometric rigidity estimates in 2 dimensions.
  • D. Harutyunyan. Buckling of washers under in-pane pressure.
  • G.W.Milton , R.V.Craster and D. Harutyunyan. The slanted coordinate approach in high frequency homogenization.


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