Research
My main interests are – apart from my family – good reads, sports, and research. Regarding the last one, I consider myself as an applied mathematician with major interests in modelling in general, including the way how to formulate thermodynamically consistent models (non-equilibrium thermodynamics provides a means for such formulations; CIT, EIT, GENERIC) and how to analyse them (stability, symmetries of DEs, asymptotic methods), and the emergence of spatial organisation (diffusion-driven instability and beyond). Topics that attracted my attention up to now include non-equilibrium thermodynamics in general, (self-organisation) pattern formation, coupling phenomena, mixture theory, bone remodelling, cartilage, PEM membranes, or simple swimmers in Stokes flow. My research is described in higher detail below and can be followed on researchgate.
Teaching
Vážení studenti, detailnější stránky věnované předmětům, které učím, naleznete zde.
Equations of mathematical physics (RMF)
The theory of generalised functions and its usage to solve linear PDEs. Integral equations, Fredholm operators, and their counterparts in elliptic PDEs (Sturm-Liouville theory, orthonormal basis).
Introduction to semigroup theory (TPG)
Qualitative properties of solutions to abstract Cauchy problems in Banach spaces. The suitability of semigroup properties for wellposedness, various continuities of semigroups, Hille-Yosida theorem, Lumer-Philips theorem, types of solutions to the abstract Cauchy problem, spectral mapping theorem and its relation to Lyapunov stability.
Mathematical Biology (MBI)
Illustration of the learned mathematical tools to study qualitative properties of models inspired from population dynamics or biology, including discrete, continuous, and spatial models. Tools revealing key long-time behaviour include the identification of fixed points and their stability, periodic solutions and their stability, Poincare maps, asymptotics and we also venture briefly into non-equilibrium thermodynamics to gain some understanding of model formulations.
Calculus (ANB3, ANB4)
A rather standard course on the foundations of mathematical analysis.
New possible projects for student's
Vážení studenti, trochu podrobnější popis možných studentských témat ve spolupráci se mnou naleznete zde.
Non-equilibrium thermodynamics
There are many possible avenues here: boundary conditions in mixtures, biphasic and binary mixture model, functional constraints as an extension of Onsager-Casimir reciprocal relations, transport models beyond Fick or Stefan-Maxwell, symmetric hyperbolicity of models..
Self-organisation (pattern formation)
Although there has been a rapid development of this field, there are still many open problems including: the effect of growing domains, natural wave speed of pattern, nondiffusibles and their role in stratified systems, hyperbolic models of reaction-diffusion phenomena, thermodynamically consistent models such as the recent Burger's type model
Modelling of various physical phenomena
My approach to model formulation always stems from non-equilibrium thermodynamics but then the potential applications are accordingly wide and include: biomechanics (cartilage, bone), mechanochemical coupling, transport phenomena in PEM fuel cells, upscaled PNP equations as a replacement of Donnan theory,...
Contact
(office 107a)
Trojanova 13
120 00 Prague 2
Czech Republic
vaclav.klika (at) cvut.cz
+420 22435 8545
CV
Sep 2001 - Jun 2006
Master's degree in Applied Mathematics at FNSPE, CTU in Prague
MSc, CTU in Prague
Oct 2006 - Oct 2009
Doctoral degree in Applied Mathematics at FNSPE, CTU in Prague
PhD, CTU in Prague
Jan 2004 - Dec 2015
researcher in Institute of Thermomechanics, Czech Academy of Sciences
research scientist
Mar 2010 - Oct 2016
Applied Mathematics, Dept. Mathematics, FNSPE, CTU in Prague
Assist. prof.
Oct 2016 - May 2023
Applied Mathematics, Dept. Mathematics, FNSPE, CTU in Prague
Assoc. prof.
May 2023
Applied Mathematics, Dept. Mathematics, FNSPE, CTU in Prague
Full prof.
long-term
visits
Maths Institute (Oxford, UK), Isaac Newton Institute (Cambridge, UK), ETH, Ecole Polytechnique (Montreal), University of Zaragoza (Zaragoza)