Homepage of Andrii Khrabustovskyi, Ph.D.
assistant professor at the Department of Physics, Faculty of Science, University of Hradec Králové

Office address: Hradecká 1285 (Room: 72180, 2. floor), 500 03 Hradec Králové, Czechia
Office tel.: +420 493332762
E-mail: andrii.khrabustovskyi[at]uhk.cz
Official webpage: link


Research

Research interests

Publications

Submitted

  1. Construction of self-adjoint differential operators with prescribed spectral properties
    Jussi Behrndt, Andrii Khrabustovskyi
    arXiv:1911.04781 [math.SP]
    preprint

Articles in peer-reviewed journals

  1. Periodic quantum graphs with predefined spectral gaps
    Andrii Khrabustovskyi
    Journal of Physics A: Mathematical and Theoretical 53(40) (2020), 405202
    preprint, article (open access)
  2. Towards more general constitutive relations for metamaterials: A checklist for consistent formulations
    Fatima Z. Goffi, Karim Mnasri, Michael Plum, Carsten Rockstuhl, Andrii Khrabustovskyi
    Physical Review B 101(29) (2020), 195411
    preprint, article
  3. The inverse problem of two-state quantum systems with non-adiabatic static linear coupling
    Andrii Khrabustovskyi, Imen Rassas, Eric Soccorsi
    Communications in Contemporary Mathematics (2020), doi: 10.1142/S0219199720500029
    preprint, article
  4. δ-interaction as a limit of a thin Neumann waveguide with transversal window,
    Giuseppe Cardone, Andrii Khrabustovskyi
    Journal of Mathematical Analysis and Applications 473(2) (2019), 1320-1342
    preprint, article
  5. Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations
    Karim Mnasri, Andrii Khrabustovskyi, Michael Plum, Carsten Rockstuhl
    Physical Review B 99 (3) (2019), 035442
    preprint, article
  6. Spectral estimates for Dirichlet Laplacian on tubes with exploding twisting velocity
    Diana Barseghyan, Andrii Khrabustovskyi
    Operators and Matrices 13 (1) (2019), 311-322
    preprint, article
  7. Operator estimates for the crushed ice problem
    Andrii Khrabustovskyi, Olaf Post
    Asymptotic Analysis 110(3-4) (2018),137-161
    preprint, article
  8. Gap control by singular Schrödinger operators in a periodically structured metamaterial
    Pavel Exner, Andrii Khrabustovskyi
    Journal of Mathematical Physics, Analysis, Geometry 14(3) (2018), 270-285
    preprint, article
  9. Surface Plasmon Polaritons Sustained at the Interface of a Nonlocal Metamaterial
    Joshua Feis, Karim Mnasri, Andrii Khrabustovskyi, Christian Stohrer, Michael Plum, Carsten Rockstuhl
    Physical Review B 98 (11) (2018), 115409
    preprint, article
  10. Beyond local effective material properties for metamaterials
    Karim Mnasri, Andrii Khrabustovskyi, Christian Stohrer, Michael Plum, Carsten Rockstuhl
    Physical Review B, 97 (2018), 075439
    preprint. part 1, preprint. part 2, article
  11. Spectrum of a singularly perturbed periodic thin waveguide
    Giuseppe Cardone, Andrii Khrabustovskyi
    Journal of Mathematical Analysis and Applications 454(2) (2017), 673-694
    preprint, article
  12. Example of a periodic Neumann waveguide with a gap in its spectrum
    Giuseppe Cardone, Andrii Khrabustovskyi
    In: J. Dittrich, H. Kovarik, A. Laptev (Eds.), Functional Analysis and Operator Theory for Quantum Physics. The Pavel Exner Anniversary Volume, Europ. Math. Soc. Publ. House, 2017, pp.177-187
    preprint, article
  13. Spectral properties of elliptic operator with double-contrast coefficients near a hyperplane
    Andrii Khrabustovskyi, Michael Plum
    Asymptotic Analysis, 98 (1-2) (2016), 91-130.
    preprint, article
  14. Spectral analysis of a class of Schrödinger operators exhibiting a parameter-dependent spectral transition
    Diana Barseghyan, Pavel Exner, Andrii Khrabustovskyi, Milos Tater
    Journal of Physics A: Mathematical and Theoretical, 49 (16) (2016), 165302
    preprint, article
  15. On the spectrum of narrow Neumann waveguide with periodically distributed δ' traps
    Pavel Exner, Andrii Khrabustovskyi
    Journal of Physics A: Mathematical and Theoretical, 48 (31) (2015), 315301
    preprint, article
  16. Neumann spectral problem in a domain with very corrugated boundary
    Giuseppe Cardone, Andrii Khrabustovskyi
    Journal of Differential Equations, 259(6) (2015), 2333-2367
    preprint, article
  17. Gaps in the spectrum of a periodic quantum graph with periodically distributed δ'-type interactions
    Diana Barseghyan, Andrii Khrabustovskyi
    Journal of Physics A: Mathematical and Theoretical, 48(25) (2015), 255201
    preprint, article
  18. Opening up and control of spectral gaps of the Laplacian in periodic domains
    Andrii Khrabustovskyi
    Journal of Mathematical Physics, 55(12) (2014), 121502
    preprint, article
  19. Gaps in the spectrum of the Neumann Laplacian generated by a system of periodically distributed traps
    Andrii Khrabustovskyi, Evgeni Khruslov
    Mathematical Methods in the Applied Sciences, 38(1) (2015), 11-26
    preprint, article
  20. Homogenization of spectral problem on Riemannian manifold consisting of two domains connected by many tubes
    Andrii Khrabustovskyi
    Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 143(6) (2013), 1255-1289
    preprint, article
  21. Periodic elliptic operators with asymptotically preassigned spectrum
    Andrii Khrabustovskyi
    Asymptotic Analysis, 82(1-2) (2013), 1-37
    preprint, article
  22. Periodic Riemannian manifold with preassigned gaps in spectrum of Laplace-Beltrami operator
    Andrii Khrabustovskyi
    Journal of Differential Equations, 252(3) (2012), 2339-2369
    preprint, article
  23. Homogenization of eigenvalue problem for Laplace-Beltrami operator on Riemannian manifold with complicated "bubble-like" microstructure
    Mathematical Methods in the Applied Sciences, 32(16) (2009), 2123-2137
    article
  24. On spectrum of Riemannian manifolds with attached thin handles
    Andrii Khrabustovskyi
    Journal of Mathematical Physics, Analysis, Geometry, 5(2) (2009), 145-169
    article (open access)
  25. Asymptotic behaviour of spectrum of Laplace-Beltrami operator on Riemannian manifolds with complex microstructure
    Andrii Khrabustovskyi
    Applicable Analysis, 87(12) (2008), 1357-1372
    article
  26. Positivity and time behavior of a linear reaction-diffusion system, non-local in space and time
    Andrii Khrabustovskyi, Holger Stephan
    Mathematical Methods in the Applied Sciences, 31(15) (2008), 1809-1834
    preprint, article
  27. Klein-Gordon equation as a result of wave equation averaging on the Riemannian manifold of complex microstructure
    Andrii Khrabustovskyi
    Journal of Mathematical Physics, Analysis, Geometry, 3 (2) (2007), 213-233
    article (open access)

Proceedings

  1. Asymptotically predefined spectral gaps for the Neumann Laplacian in periodic domain
    Andrii Khrabustovskyi
    Mathematical Results in Quantum Mechanics: Proceedings of the QMath12 Conference, World Scientific, 2014
    article

Conference talks

Plenary talks

  • 08/2019
  • 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES-2019), Vienna, Austria
  • 09/2019
  • 6th Najman Conference on Spectral Theory and Differential Equations, Sveti Martin na Muri, Croatia

    Invited talks

  • 11/2018
  • "Advances in Operator Theory with Applications to Mathematical Physics", Orange, US
  • 06/2017
  • "Analysis and Mathematical Physics" (AMPH 2017), Kharkiv, Ukraine
  • 05/2017
  • WTZ Workshop/Network Meeting "Schrodinger Operators and Boundary Value Problems", Graz, Austria
  • 09/2016
  • Conference & summer school "Spectral Theory, Differential Equations and Probability", Mainz, Germany
  • 06/2016
  • "Analysis and Mathematical Physics" (AMPH 2016), Kharkiv, Ukraine
  • 05/2015
  • "Waveguides: asymptotic methods and numerical analysis", Naples, Italy
  • 07/2014
  • Minisimposium "Asymptotic Analysis: Homogenization and ThinStructures" (in the framework of IMSE 2014), Karlsruhe, Germany
  • 06/2014
  • "Analysis and Mathematical Physics" (AMPH 2014), Kharkiv, Ukraine
  • 06/2013
  • "Analysis and Mathematical Physics" (AMPH 2013), Kharkiv, Ukraine

    Contributed talks

  • 07/2019
  • "International Workshop on Operator Theory and its Applications" (IWOTA2018), Lisbon, Portugal
  • 09/2018
  • "Analytic and Algebraic Methods in Physics XV", Prague, Czech Republic
  • 08/2018
  • "Applications of Mathematics 2018", Prague, Czech Republic
  • 07/2018
  • Conference on Mathematics of Wave Phenomena, Karlsruhe, Germany
  • 09/2017
  • "Asymptotic Analysis and Spectral Theory" (Aspect’17), Trier, Germany
  • 05/2016
  • "Operators, Operator Families and Asymptotic", Bath, UK
  • 11/2015
  • "Asymptotic Analysis and Spectral Theory" (Aspect’15), Orsay, France
  • 09/2015
  • 4th Najman Conference on Spectral Problems for Operators and Matrices,Opatija, Croatia
  • 07/2015
  • 12th International Conference on Mathematical and Numerical Aspects of Waves(Waves 2015), Karlsruhe, Germany
  • 07/2014
  • "International Workshop on Operator Theory and its Applications" (IWOTA2014), Amsterdam, Netherlands
  • 07/2014
  • "Operator Theory, Analysis and Mathematical Physics" (OTAMP 2014), Stockholm, Sweden
  • 09/2013
  • "QMath12: Mathematical Results in Quantum Mechanics", Berlin, Germany
  • 08/2013
  • "Equadiff 2013", Prague, Czech Republic
  • 09/2012
  • International conference dedicated to the 120th anniversary of Stephan Banach,Lviv, Ukraine
  • 08/2012
  • Spectral Theory and Differential Equations (International Conference in honor of Vladimir A. Marchenko’s 90th birthday), Kharkiv, Ukraine
  • 09/2011
  • "Partial Differential Equations", Caputh, Germany
  • 01/2011
  • 10th GAMM Seminar on Microstructures, Darmstadt, Germany
  • 11/2009
  • International Conference on Elliptic and Parabolic Equations, Berlin, Germany
  • 06/2009
  • "Geometry "in large", topology and applications", Kharkiv, Ukraine
  • 02/2009
  • First Winter School at IMDEA on PDEs and Inequalities, Madrid, Spain

    Poster presentations

  • 11/2013
  • "New Trends in Calculus of Variations and PDEs", Naples, Italy
  • 07/2012
  • 6th European Congress of Mathematics, Krakow, Poland
  • 08/2009
  • Ukrainian Mathematical Congress, Kyiv, Ukraine
  • 08/2008
  • CIMPA-UNESCO School "Nolinear Analysis, Geometrical PDE", Tsaghadzor,Armenia
  • 07/2007
  • Liapunov Memorial International Conference, Kharkiv, Ukraine

    Research visits

  • 07/2018, 12/2016
  • University of Trier (Department IV - Mathematics), Germany1 week
  • 03/2016
  • Aix-Marseille University (Center of Theoretical Physics), France1 week
  • 05/2015
  • University of Technology (Institute of Numerical Mathematics), Austria1 week
  • 03/2014, 09/2014
  • University of Sannio (Department of Engineering), Benevento,Italy1 week
  • 11/2013
  • Nuclear Physics Institute of ASCR (Department of Theoretical Physics), Řež, Czech Republic1 week
  • 12/2009
  • Pierre and Marie Curie University (Jussieu Institute of Mathematics), Paris, France1 month
  • 11/2009
  • Weierstrass Institute for Applied Analysis and Stochastics (Re-search group "Numerical Mathematics and Scientific Computing"), Berlin, Germany2 weeks
  • 02/2007
  • Darmstadt University of Technology (Research Group "Analysis"), Germany1 month

    Participation in research projects

  • 2018 - 2020
  • Principal investigator in the project M 2310-N32 "Periodic quantum graphs and open waveguides" funded by Austrian Science Fund (FWF)
  • 2015 - 2017
  • Team member in the project "Effective characterization of optical metama-terials beyond a local response" within DFG Collaborative Research Centre 1173 "Wave phenomena: analysis and numerics"
  • 2009 - 2011
  • Team member of the joint French-Ukrainian project "PICS 2009-2011. Mathematical Physics: Methods and Applications" (CNRS and NAS of Ukraine)

    Organizational activities

  • 07/2019
  • Organizer (together with O. Post and C. Trunk) of the special session "Spectral Theory and Differential Operators" on IWOTA 2019 at University of Lisbon, Portugal
  • 02/2019
  • Organizer (together with J. Behrndt) of the conference "Differential Operators on Graphs and Waveguides" at Graz University of Technology
  • 11/2012 - 10/2014
  • Coordinator of the seminar of the Research Training Group 1294 at Karlsruhe Institute of Technology

    Teaching activities

    Teaching

  • 03/2019 - 06/2019
  • Partial Differential Equationslecture course and exercise classes for bachelor studentsTU Graz
  • 10/2018 - 01/2019
  • Advanced functional analysislecture course and exercise classes for bachelor studentsTU Graz
  • 03/2018 - 06/2018
  • Asymptotic analysislecture course for master studentsTU Graz
  • 04/2017 - 07/2017
  • Eigenvalue problems in complicated domainslecture course for master studentsKIT Karlsruhe
  • 04/2017 - 07/2017
  • Analysispro-seminar for bachelor studentsKIT Karlsruhe
  • 10/2015 - 02/2016
  • Differential equations and Hilbert spacesseminar for bachelor and master studentsKIT Karlsruhe
  • 10/2014 - 02/2015
  • Homogenization of PDEslecture course and exercise classes for master studentsKIT Karlsruhe
  • 10/2013 - 02/2014
  • Introduction to the homogenization theorylecture course for master studentsKIT Karlsruhe

    Supervision of students

    CV

    Degrees and education

  • 2019
  • Habilitation (mathematics) Graz University of Technology, Austria
    Thesis: Spectral and asymptotic properties of periodic media
  • 2017
  • Habilitation (mathematics) Karlsruhe University of Technology, Germany
    Thesis: Spectral and asymptotic properties of periodic media
  • 2010
  • PhD (mathematical physics) B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
    Thesis: Homogenization of spectral and evolution problems on Riemannian manifolds of complex microstructure
    Advisor: Prof. Ievgen Khruslov
  • 2006
  • Master (applied mathematics) V.N. Karazin Kharkiv National University, Ukraine

    Professional career

  • since 08/2020
  • Assistant professorDepartment of Physics, Faculty of Science, University of Hradec Králové, Czech Republic
  • 11/2019 - 07/2020
  • ResearcherDepartment of Physics, Faculty of Science, University of Hradec Králové, Czech Republic
  • 05/2018 - 07/2020
  • FWF Senior PostdocInstitute of Applied Mathematics, Graz University of Technology, Austria
  • 11/2017 - 04/2018
  • Project assistantInstitute of Applied Mathematics, Graz University of Technology, Austria
  • 07/2015 - 10/2017
  • Postdoctoral researcherDFG Collaborative Research Centre 1173 "Wave phenomena: analysis and numerics", Karlsruhe Institute of Technology, Germany
  • 11/2014 - 06/2015
  • Research assistantInstitute for Analysis, Karlsruhe Institute of Technology, Germany
  • 11/2012 - 10/2014
  • Postdoctoral researcherDFG Research Training Group 1294 "Analysis, Simulation and Design of Nanotechnological Processes", Karlsruhe Institute of Technology, Germany
  • 11/2009 - 10/2012
  • Junior research fellowB. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv

    Grants and scholarships

  • 2018 - 2020
  • Lise Meitner fellowship, Austrian Science Fund (FWF)
  • 2012
  • Best Poster Prize of the 6th European Congress of Mathematics
  • 2011
  • M.V. Ostrogradsky scholarship for young mathematicians, Ukraine
  • 2009
  • Scholarship of French Embassy in Ukraine
  • 2009 - 2010
  • Scholarship of the President of Ukraine
  • 2007 - 2008
  • Grant of the National Academy of Sciences of Ukraine
  • 2007
  • Grant DAAD, Germany
  • 2006
  • Grant of Akhiezer's Fund, Ukraine