Andrii Khrabustovskyi

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, Czech Republic
Office tel.: +420 493332762
E-mail: andrii.khrabustovskyi[at]uhk.cz
Official webpage

Academic profiles


Research interests

  • Asymptotic analysis and homogenization of PDEs
  • Spectral theory
  • Periodic PDEs
  • Quantum graphs, waveguides
  • Schrödinger operators
  • Metamaterials


Publications

Submitted

  • The Neumann sieve problem revisited
    Andrii Khrabustovskyi
    preprint

Articles in peer-reviewed journals (published or accepted)

  1. Spectrum of the Laplacian on a domain perturbed by small resonators
    Giuseppe Cardone, Andrii Khrabustovskyi
    SIAM Journal on Mathematical Analysis 55(4) (2023), 3677-3712
    preprint, article
  2. Creating and controlling band gaps in periodic media with small resonators
    Andrii Khrabustovskyi, Evgen Khruslov
    Journal of Mathematical Physics, Analysis, Geometry 19(2) (2023), 456–481
    preprint, article (open access)
  3. Operator estimates for Neumann sieve problem
    Andrii Khrabustovskyi
    Annali di Matematica Pura ed Applicata 202(4) (2023), 1955-1990
    preprint, article
  4. Operator estimates for homogenization of the Robin Laplacian in a perforated domain
    Andrii Khrabustovskyi, Michael Plum
    Journal of Differential Equations 338 (2022), 474-517
    preprint, article
  5. Construction of self-adjoint differential operators with prescribed spectral properties
    Jussi Behrndt, Andrii Khrabustovskyi
    Mathematische Nachrichten 295(6) (2022), 1063-1095
    preprint, article (open access)
  6. Singular Schrödinger operators with prescribed spectral properties
    Jussi Behrndt, Andrii Khrabustovskyi
    Journal of Functional Analysis 282(1) (2022), 109252
    preprint, article (open access)
  7. A geometric approximation of δ-interactions by Neumann Laplacians
    Andrii Khrabustovskyi, Olaf Post
    Journal of Physics A: Mathematical and Theoretical 54(46) (2021), 465201
    preprint, article (open access)
  8. Higher order constitutive relations and interface conditions for metamaterials with strong spatial dispersion
    Fatima Z. Goffi, Andrii Khrabustovskyi, Ramakrishna Venkitakrishnan, Carsten Rockstuhl, Michael Plum
    Physics Letters A 412 (2021), 127570
    preprint, article
  9. The inverse problem of two-state quantum systems with non-adiabatic static linear coupling
    Andrii Khrabustovskyi, Imen Rassas, Eric Soccorsi
    Communications in Contemporary Mathematics 23(4) (2021), 2050002
    preprint, article
  10. Periodic quantum graphs with predefined spectral gaps
    Andrii Khrabustovskyi
    Journal of Physics A: Mathematical and Theoretical 53(40) (2020), 405202
    preprint, article (open access)
  11. 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
  12. 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
  13. 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
  14. 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
  15. Operator estimates for the crushed ice problem
    Andrii Khrabustovskyi, Olaf Post
    Asymptotic Analysis 110(3-4) (2018),137-161
    preprint, article
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. Periodic elliptic operators with asymptotically preassigned spectrum
    Andrii Khrabustovskyi
    Asymptotic Analysis, 82(1-2) (2013), 1-37
    preprint, article
  30. 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
  31. 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
  32. 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)
  33. Asymptotic behaviour of spectrum of Laplace-Beltrami operator on Riemannian manifolds with complex microstructure
    Andrii Khrabustovskyi
    Applicable Analysis, 87(12) (2008), 1357-1372
    article
  34. 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
  35. 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

09/20196th Najman Conference on Spectral Theory and Differential Equations, Sveti Martin na Muri, Croatia
08/201914th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES-2019), Vienna, Austria

Invited talks

12/2022Workshop "Challenges in Spectral Theory of Differential Operators", Graz, Austria
11/2018"Advances in Operator Theory with Applications to Mathematical Physics", Orange, US
06/2017"Analysis and Mathematical Physics" (AMPH 2017), Kharkiv, Ukraine
05/2017WTZ Workshop/Network Meeting "Schrodinger Operators and Boundary Value Problems", Graz, Austria
09/2016Conference & 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
07/2014Minisimposium "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

08/2023 "Analytic and Algebraic Methods in Physics XX", Prague, Czech Republic
08/2023 "International Workshop on Operator Theory and its Applications" (IWOTA2023), Helsinki, Finland
09/2022 "Asymptotic analysis and spectral theory", Oldenburg, Germany
09/2022 "Analytic and Algebraic Methods in Physics XIX", Prague, Czech Republic
07/2022 "Equadiff 2022", Brno, Czech Republic
09/2021 "Analytic and Algebraic Methods in Physics XIII", Prague, Czech Republic
09/2020 "VA2MP meeting", Prague, Czech Republic
12/2019"Operator Theory and Krein Spaces" (dedicated to the memory of Hagen Neidhardt), Vienna, Austria
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, 12/2016University of Trier (Department IV - Mathematics), Germany
03/2016Aix-Marseille University (Center of Theoretical Physics), France
05/2015University of Technology (Institute of Numerical Mathematics), Austria
03/2014, 09/2014University of Sannio (Department of Engineering), Benevento,Italy
11/2013 Nuclear Physics Institute of ASCR (Department of Theoretical Physics), Řež, Czech Republic
12/2009Pierre and Marie Curie University (Jussieu Institute of Mathematics), Paris, France
11/2009Weierstrass Institute for Applied Analysis and Stochastics (Re-search group "Numerical Mathematics and Scientific Computing"), Berlin, Germany
02/2007Darmstadt University of Technology (Research Group "Analysis"), Germany

Degrees & education

Habilitation (mathematics)

Graz University of Technology, Austria
Thesis: Spectral and asymptotic properties of periodic media
March 2019

Habilitation (mathematics)

Karlsruhe Institute of Technology, Germany
Thesis: Spectral and asymptotic properties of periodic media
January 2017

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
July 2006

Master (applied mathematics)

V.N. Karazin Kharkiv National University, Ukraine
December 2010

Professional experience

University of Hradec Králové, Czech Republic

Department of Physics, Faculty of Science
Assistant professor
Since August 2020

Nuclear Physics Institute of the CAS, Řež, Czech Republic

Department of Theoretical Physics
Researcher (part-time)
March 2021 -- December 2023

University of Hradec Králové, Czech Republic

Department of Physics, Faculty of Science
Researcher
November 2019 -- July 2020

Graz University of Technology, Austria

Institute of Applied Mathematics
FWF Senior postdoc (Lise Meitner fellowship)
May 2018 -- July 2020

Graz University of Technology, Austria

Institute of Applied Mathematics
Project assistant
November 2017 -- April 2018

Karlsruhe Institute of Technology, Germany

Institute of Analysis, Department of Mathematics
Postdoc at DFG Collaborative Research Centre 1173 "Wave phenomena: analysis and numerics"
July 2015 -- October 2017

Karlsruhe Institute of Technology, Germany

Institute of Analysis, Department of Mathematics
Research assistant
November 2014 -- June 2015

Karlsruhe Institute of Technology, Germany

Department of Mathematics
Postdoc at DFG Research Training Group 1294 "Analysis, Simulation and Design of Nanotechnological Processes"
November 2012 -- October 2014

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

Department of Mathematical Modelling of Physical Processes
Junior research fellow
November 2009 -- October 2012

Grants & scholarships

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

Projects participation

Project 22-18739S "Asymptotic and spectral analysis of operators in mathematical physics"

Czech Science Foundation (GAČR)
Team member
2022 - 2024

Project 21-07129S "New Effects from Time-Reversal Non-Invariance"

Czech Science Foundation (GAČR)
Team member
2021 - 2023

Project M 2310-N32 "Periodic quantum graphs and open waveguides"

Austrian Science Fund (FWF)
Principal investigator
2018 - 2020

Project 258734477 - SFB 1173 "Effective characterization of optical metamaterials beyond a local response"

German Research Foundation (DFG)
Team member
2015 - 2017

Joint French-Ukrainian project PICS 2009-2011 "Mathematical Physics: Methods and Applications"

CNRS & NAS of Ukraine
Team member
2009 - 2011

Teaching

Math II: Analysis in Several Variables

University of Hradec Králové
Lecture course and exercise classes for master students
Summer semesters 2023, 2024

Math I: Analysis in Several Variables

University of Hradec Králové
Lecture course and exercise classes for master students
Winter semesters 2022/2023, 2023/2024

Theory of Electromagnetic Field

University of Hradec Králové
Lecture course and exercise classes for master students
Winter semesters 2021/2022

Partial Differential Equations

Graz University of Technology
Lecture course and exercise classes for bachelor students
Summer semestr 2018/2019

Advanced functional analysis

Graz University of Technology
Lecture course and exercise classes for bachelor students
Winter semestr 2018/2019

Asymptotic analysis

Graz University of Technology
Lecture course for master students
Summer semestr 2017/2018

Eigenvalue problems in complicated domains

Karlsruhe Institute of Technology
Lecture course for master students
Summer semestr 2016/2017

Analysis

Karlsruhe Institute of Technology
Seminar for bachelor students
Winter semestr 2015/2016

Differential equations and Hilbert spaces

Karlsruhe Institute of Technology
Seminar for bachelor and master students
Winter semestr 2014/2015

Homogenization of PDEs

Karlsruhe Institute of Technology
Lecture course and exercise classes for master students
Winter semestr 2014/2015

Introduction to the homogenization theory

Karlsruhe Institute of Technology
Lecture course for master students
Winter semestr 2013/2014

Supervision of students

  • 1 bachelor student was supervised at Graz University of Technology
  • 3 bachelor students were co-supervised at Karlsruhe Institute of Technology

Organizational activities

  • 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, July 2019
  • Organizer (together with J. Behrndt) of the conference "Differential Operators on Graphs and Waveguides" at Graz University of Technology, February 2019
  • Coordinator of the seminar of the Research Training Group 1294 at Karlsruhe Institute of Technology, November 2012 - October 2014