Dr. Petr Pelech

Phone:  +420 951 553 409
Email:  pelech(Strudel)karlin.mff.cuni.cz
ORCID:   0000-0002-2271-7147  

Scientific interests

I have done my reasearch mainly in the area of the calculus of variations, partial differential equations, and continuum thermodynamics.

In particular, I have been studying rate-independent processes in solids with the focus on inelastic behaviour of materials in a large-strain regime. The works have addressed on one side the proper notion of a weak solution and the question of its existence (stress has been put on variational mathods), on the other thermodynamic consistency of the model under consideration, building mainly on the concept of generalized standard solid.

More recently, I have started to investigate gradient flows in Banach spaces, to larger extend using the minimizing movement scheme, and to study their limiting behaviour for various time scales.

Last but not least, I have been also interested in GENERIC (General Equation for Nom-Equilibrium Reversible-Irreversible Coupling), focusing mainly on modeling of complex, visco-elasto-plastic fluid-solids, and mathematical analysis of static models in Peridynamics, a nonlocal theory of the mechanics of solids.


Publications and Preprints

  1. Petr Pelech, Paula P. Navarro, Andrea Vettiger, Luke H. Chao, Christoph Allolio.  Stress-mediated growth determines E. coli division site morphogenesis.  bioRxiv.,  2024.09.11.612282v1.
  2. Martin Horák, Martin Kružík, Petr Pelech, Anja Schlömerkemper.  Gradient polyconvexity and modeling of shape memory alloys.  Variational Views in Mechanics.,  10.1007/978-3-030-90051-9_5,  WIAS Preprint No. 2851.
  3. Petr Pelech, Karel Tůma, Michal Pavelka, Martin Šípka, Martin Sýkora.  On compatibility of the Natural configuration framework with GENERIC: Derivation of anisotropic rate-type models.  J. Non-New. Fluid Mech.,  10.1016/j.jnnfm.2022.104808,  WIAS Preprint No. 2856,  arXiv:2010.06903.
  4. Elisa Davoli, Martin Kružík, Petr Pelech.  Separately Global Solutions to Rate-Independent Processes in Large-Strain Inelasticity.  Nonlinear Analysis.,  10.1016/j.na.2021.112668,  arXiv:2008.02244.
  5. Martin Kružík, Petr Pelech, Anja Schlömerkemper.  Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys.  J. Optim. Theory Appl.,  184,  2020. 10.1007/s10957-019-01489-9,  arXiv:1807.09855.
  6. Petr Pelech.  The peridynamic stress tensors and the non-local to local passage.  Z. Angew. Math. Mech.,  2019. 10.1002/zamm.201800010  arXiv:1711.08445.

Thesis

PELECH, Petr. Variational Methods in Thermomechanics of Solids. Praha, 2020. Dizertační práce. Univerzita Karlova, Matematicko-fyzikální fakulta. Vedoucí práce Kružík, Martin. (Charles Univerzity Digital Repository)


Short CV

Jan 2023 Member of the Biomembrane Remodeling Group at the Faculty of Mathematics and Physics, Charles University.
Oct 2020 – Dec 2022 Member of the research group Partial Differential Equations at the Weierstrass Institute, Forschungsverbund Berlin e.V.
Sep 2020 Doctoral defense at Charles University, Faculty of Mathematics and Physics.
Advisor: Doc. Martin Kružík;
Oct 2014 – Sep 2016 Studies M.Sc. Mathematical Modelling at Charles University, Faculty of Mathematics and Physics
Oct 2011 – Sep 2014 Studies B.Sc. Mathematics at Charles University, Faculty of Mathematics and Physics



Last modified: 2023-10-15 by Petr Pelech