Barbora Benešová

I am a postdoctoral research associate in the Department for Mathematics in the Sciences, Institute for Mathematics at the University of Würzburg.
My research is concentrated upon mathematical modeling of solid microstructure-forming materials and general questions in mathematical elasticity.

In the summer semester 2018, I am a teaching assistant for Mathematics 2 for Physicists and Engineers.

Research

Mathematical Elasticity & Calculus of Variations

My work in this area focuses on the long-standing question in mathematical hyperelasticity on how to combine known convexity notions (quasiconvexity in particular) with requirements on the injectivity and orientation-preservation of the admissible deformations.
I currently approach this question only for planar deformations by trying to combine conformal analysis and its generalizations with calculus of variations; results include the first explicit characterizations of Young measures generated by gradients of homeomorphisms.
I also work on questions concerning lower-semicontinuity of functionals in general, for example when connected to quasiconvexity on the boundary

Related publications and preprints:

  • [16] B. BENEŠOVÁ, M. KRUŽÍK, A. SCHLÖMERKEMPER: A note on locking materials and gradient polyconvexity, accepted to M3AS. (Preprint at arXiv)
  • [13] B. BENEŠOVÁ, M. KRUŽÍK: Weak lower semicontinuity of integral functionals and applications, SIAM Review 59 (2017), 703-766. (Preprint at arXiv)
  • [11] B. BENEŠOVÁ, M. KAMPSCHULTE: Gradient Young measures generated by quasiconformal maps the plane, SIAM J.Math. Anal. 47 (2015) 4404-4435. (Preprint at RWTH Aachen)
  • [10] B. BENEŠOVÁ, S KRÖMER, M. KRUŽÍK: Boundary effects and weak* lower semicontinuity for signed integral functionals on BV, ESAIM:COCV 21 (2015), 513-534. (Preprint at RWTH Aachen),
  • [9] B. BENEŠOVÁ, M. KRUŽÍK: Characterization of gradient Young measures generated by homeomorphisms in the plane, ESAIM:COCV 22 (2016), 267-288. (Preprint at RWTH Aachen)
  • [5] B. BENEŠOVÁ, M. KRUŽÍK, G. PATHÓ: Young measures supported on invertible matrices. Appl. Anal., 93 (2014), 105-123.(ArXiv Link)



Microstructure Formation & Shape-memory Alloys

Convexity conditions in calculus of variations are strongly linked to microstructure formation in so-called “smart” solids like shape-memory alloys or ferromagnets. My research concerns proposing suitable models for these materials on the single- and polycrystalline scale and their mathematical analysis.
My results include thermomechanical extensions of established single-crystalline models of SMA or polycrystalline models with a refined description of the dissipation.
My ongoing projects in this area include modeling of modulated martensite in NiMnGa.


Related publications and preprints:

  • [12] B. BENEŠOVÁ, M. FROST, M. KAMPSCHULTE, C. MELCHER, P. SEDLÁK, H. SEINER: Incommensurateness in nanotwinning models of modulated martensites, Phys. Rev. B (Rapid Commun.), 92, 180101(R) (2015) - Chosen as editor´s suggestion.
  • [8] M. FROST, B. BENEŠOVÁ, P. SEDLÁK: A microscopically motivated constitutive model for shape memory alloys: formulation, analysis and computations, Math. Mech. Solids, 21(3) (2016), 358-382. Preprint at RWTH Aachen
  • [6] B. BENEŠOVÁ, M. KRUŽÍK, G. PATHÓ: A mesoscopic thermomechanically-coupled model for thin-film shape-memory alloys by dimension reduction and scale transition, Cont. Mech.Thermodyn., 26(5) (2014):683–713. (Preprint at RWTH Aachen)
  • [4] P. SEDLÁK, M. FROST, B.BENEŠOVÁ, T. BEN ZINEB, P. ŠITTNER: Thermomechanical model for NiTi-based shape memory alloys including R-phase and material anisotropy under multi-axial loadings, Int. J. Plasticity, 39 (2012), 132-151.
  • [3] B. BENEŠOVÁ, T. ROUBÍČEK: Micro-to-meso scale limit for shape-memory-alloy models with thermal coupling. Multiscale Model. Simul., 10 (2012), 1059–1089. (Preprint at the Nečas centre, Charles University in Prague)
  • [2] B. BENEŠOVÁ, M. KRUŽÍK, T. ROUBÍČEK: Thermodynamically-consistent mesoscopic model of the ferro/paramagnetic transition. Zeit. angew. Math. Phys., 64 (2013), 1-28. (Preprint at ArXiv)



Numerical Studies

I work on the design and implementation of efficient as well as reliable numerical methods for solving PDE’s describing microstructure formation. Results include improved algorithms for dissipative, rate-independent systems and design of an unconditionally stable implicit midpoint spectral scheme for the Cahn-Hilliard equation.




Related publications and preprints:





Miscellaneous

During my collaborations with physicist or mathematicians, results were obtained that lie outside of my main research focus. Examples include analysis of a simple model in magnetoelasticity (which is not focused on pattern formation) or uniqueness of a fitting procedure in ultrafast spectroscopy.




Related publications and preprints:

  • [15] B. BENEŠOVÁ, J. FORSTER, C. LIU, A. SCHLÖMERKEMPER: Existence of weak solutions to an evolutionary model for magnetoelasticity. SIAM J. Math. Anal., 50 (2018), 1200-1236.(Preprint at ArXiv)
  • [14] J. DOSTÁL, B. BENEŠOVÁ, T. BRIXNER: Two-Dimensional Electronic Spectroscopy Can Fully Characterize the Population Transfer in Molecular Systems , J. Chem. Phys., 145, 124312 (2016).



CV

Academic positions

Postdoctoral research associate, University of Würzburg
2014-present
In the group of Anja Schlömerkemper

PostDoc, RWTH Aachen University
2012-2014
In the group of Christof Melcher.
Work on variational methods in elasticity (incorporating the det > 0 constraint into quasiconvexity) and numerical solution of the Cahn–Hilliard equation by spectral methods. Also served as seminar organizer and teaching assistant

Research associate, Institute of Thermomechanics, Academy of Sciences of the Czech Republic
2009 - present (since 2012 on leave)
Collaborating with among others Tomáš Roubíček, Martin Kružík, Petr Šittner.
Work on in single- and polycrystalline models in shape-memory alloys

Education

PhD. in Applied Analysis, Charles University in Prague, Czech Republic
2008-2012
Advised by Tomáš Roubíček and co-advised by Martin Kružík and Hanuš Seiner.
Thesis: Mathematical and computational modeling of shape-memory alloys

M.Sc. (Mgr.), Charles University in Prague, Czech Republic.
2006-2008
M.Sc. in Mathematical modeling in science and technology focusing on partial differential equations in continuum mechanics.

B.Sc. (Bc.), Charles University in Prague, Czech Republic.
2003-2006
B.Sc. in General Physics.

Recognition and Outreach

Teaching/Lehre

Current/Aktuell

I am currently a teaching assistant for Mathematics for Physicists and Engineers.

Previous semesters

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