prof. Ing. Václav Klika, Ph.D.

e-mail:	zobrazit e-mail
telefon:	+420 778 545 594
místnost:	107a
www:	http://kmlinux.fjfi.cvut.cz/~klikavac/

rozvrh
témata prací
publikace

Towards self-organisation in real systems: models and analysis

školitel:	doc. Ing. Václav Klika, Ph.D.
e-mail:	zobrazit e-mail
typ práce:	dizertační práce
zaměření:	MI_MM
přiložený soubor:	pdf
popis:	The aim of this topic is to extend the current models of spatial self-organisation and discuss the significance of these extensions in real systems via a combination of analytical and numerical tools. See the attachment for more details.
naposledy změněno:	09.09.2020 09:35:27

Semigroups and non-equilibrium thermodynamics

školitel:	doc. Ing. Václav Klika, Ph.D.
e-mail:	zobrazit e-mail
typ práce:	dizertační práce
zaměření:	MI_MM
přiložený soubor:	pdf
popis:	The aim of non-equilibrium thermodynamics is to present a rather general framework for formulation of thermodynamically consistent models. In an ideal world, we would like to guarantee the knowledge of mathematical well-posedness of the proposed models, which is almost perpendicular to the former approach (function spaces, boundary and initial conditions etc). See the attachment for more details.
naposledy změněno:	09.09.2020 09:37:36

Pokročilé partie gradované geometrie

školitel:	Ing. Jan Vysoký, Ph.D.
e-mail:	zobrazit e-mail
typ práce:	dizertační práce
zaměření:	MI_MM
popis:	Gradovaná geometrie představuje pozoruhodné rozšíření standardní diferenciální geometrie. Hlavním objektem jejího zájmu jsou gradované variety, matematické objekty popsané gradovaně komutativními algebrami svých funkcí. Vzhledem k nemožnosti jejich jednoduchého popisu jako množin s dodatečnou strukturou vyžaduje jejich studium použití metod vyvinutých v algebraické geometrii. Na rozdíl od klasické teorie obsahuje jejich popis proměnné, které spolu antikomutují. Díky tomu nachází gradovaná geometrie uplatnění v teoretické fyzice, zejména kvantové teorii pole obsahující fermiony. Možným cílem práce bude hledat v různých oblastech standardní diferenciální geometrie a snažit se nalézt možná zobecnění v kategorii gradovaných variet. Příkladem je gradovaná verze slavné Frobeniovy věty dávající do rovnosti involutivní a integrabilní hladké distribuce. Bylo by rovněž zajímavé rozšířit paletu aplikací gradované geometrie v teoretické fyzice.
literatura:	Doporučená literatura: [1] J. Vysoký: Global theory of graded manifolds, Reviews in Mathematical Physics 33, 22500335 (2022) [2] C. Carmeli, L. Caston, R. Fioresi: Mathematical foundations of supersymmetry, Vol. 15. European Mathematical Society, 2011 [3] C Bartocci, U Bruzzo, D Hernández-Ruipérez: The geometry of supermanifolds, Vol. 71. Springer Science & Business Media, 2012 [4] B. Jubin, A. Kotov, N. Poncin, V. Salnikov: Differential Graded Lie Groups and Their Differential Graded Lie Algebras, Transformation Groups 27, 497-523 (2022) [5] L. W. Tu: Differential Geometry: Connections, Curvature, and Characteristic Classes, Springer, 2017
naposledy změněno:	23.05.2023 11:04:23

Strojové učení jako špatně podmíněná úloha

školitel:	doc. Ing.Jaromír Kukal, Ph.D.
e-mail:	zobrazit e-mail
typ práce:	dizertační práce
zaměření:	MI_MM, MI_AMSM, MINF, APIN
přiložený soubor:	pdf
popis:	viz příloha
naposledy změněno:	24.05.2023 11:22:18

Existence and asymptotic behaviour of weakly bounded states

školitel:	prof Dirk Hundertmark, RNDr. Ing. Michal Jex, Ph.D.
e-mail:	zobrazit e-mail
typ práce:	dizertační práce
zaměření:	MI_MM
popis:	Stability of matter is one of the fundamental properties that governs the physics in our universe. On the microscopic scale the stability of quantum systems is directly related to the existence of eigenstates. The situation for eigenstates below the threshold of the essential spectrum is well studied. They exhibit exponential decay, their existence is linked to an energy gap, and they are stable under small perturbations of the system. However, the situation at the threshold of the essential spectrum is much more subtle. The existence of true bound states at this spectral phase transition is strongly correlated with the asymptotic behaviour of the potential part of the self-adjoint operator describing the quantum system. Moreover, these states are highly unstable under even small perturbations of the system. This makes it a challenging problem to tackle within the field of quantum mechanics and spectral theory. The objective of this PhD thesis is to deepen the understanding of weakly bounded states. The starting point will be recently developed method [HJL23a] which should be applied to more complicated systems and extended to other operators apart from standard Schrödinger operator. Especially useful would-be generalisation of the existence results for discrete and continuous Schrödinger operators [HJL23b, JŠ23] to Dirac operators. This would open a path to experimental verification of the properties of weakly bounded states on graphene-like structures for relativistic quantum mechanics setting.
literatura:	[HJL23a] D. Hundertmark, M. Jex, and M. Lange. „Quantum Systems at the Brink“. In: Springer INdAM Series. Springer Nature Singapore, 2023, pp. 259–273. ISBN: 9789819958948. DOI: 10.1007/978-981-99-5894-8_10. [HJL23b] D. Hundertmark, M. Jex, and M. Lange. „Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality“. In: Forum of Mathematics, Sigma 11 (2023), e61. DOI: 10.1017/fms.2023.39. [JŠ23] M. Jex and F. Štampach. „On the ground state of lattice Schrödinger operators“. In: arXiv: 2312.08081 (2023), p. 20.
naposledy změněno:	11.12.2024 10:03:28

Rekurence a transport v kvantových procházkách

školitel:	doc. Ing. Martin Štefaňák, Ph.D.
e-mail:	zobrazit e-mail
typ práce:	dizertační práce
zaměření:	MI_MM
popis:	Kvantové procházky v diskrétním čase [1,2] popisují šíření kvantové částice na grafu nebo mřížce. Obvyklý unitární model lze zobecnit na otevřenou kvantovou dynamiku, což umožňuje např. popis dynamicky se měnícího grafu a perkolace [3] nebo interpolaci mezi kvantovou a klasickou procházkou [4]. Další zvrat nastává, když je iterovaný vývoj proložen částečným projektivním měřením. Tímto způsobem lze např. sledovat návrat částice do počátečního vrcholu [5,6], tj. studovat rekurenci, nebo modelovat absorbující vrcholy a studovat kvantový transport [7,8]. Cílem práce je prohloubit porozumění iterované monitorované kvantové evoluce, ať už unitární, nebo stochastické. Možné rozšíření známých výsledků zahrnuje dvoučásticové efekty a roli interakce v kvantovém transportu nebo rekurenci diskrétních stochastických kvantových procházek.
literatura:	[1] Y. Aharonov, L. Davidovich, and N. Zagury, Quantum random walks, Phys. Rev. A 48, 1687 (1993). [2] M.Hillery, J. Bergou, and E. Feldman, Quantum walks based on an interferometric analogy, Phys. Rev. A 68, 032314 (2003). [3] B. Kollár, T. Kiss, J. Novotný, and I. Jex, Asymptotic Dynamics of Coined Quantum Walks on Percolation Graphs, Phys. Rev. Lett. 108, 230505 (2012). [4] J. D. Whitfield, C. A. Rodríguez-Rosario, and A. Aspuru-Guzik, Quantum stochastic walks: A generalization of classical random walks and quantum walks, Phys. Rev. A 81, 022323 (2010). [5] A. Grünbaum, L. Velázquez, A. H. Werner, and R. F. Werner, Recurrence for Discrete Time Unitary Evolutions, Commun. Math. Phys. 320, 543 (2013). [6] M. Štefaňák, Monitored recurrence of a one-parameter family of three-state quantum walks, Phys. Scr. 98, 064001 (2023). [7] J. Mareš, J. Novotný, M. Štefaňák, and I. Jex, Counterintuitive role of geometry in transport by quantum walks, Phys. Rev. A 101, 032113 (2020). [8] N. Konno, E. Segawa and M. Štefaňák, Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs Symmetry 13, 1169 (2021).
naposledy změněno:	14.04.2025 19:18:25

Databáze V3S

Aplikace V3S eviduje výsledky vědy a výzkumu a další aktivity vědecko-výzkumných pracovníků ve vědecké komunitě. Aplikace V3S slouží k odesílání výsledků do RIV, exportům pro statistické analýzy i k interním hodnocením vědecko-výzkumné činnosti.

Seznam publikaci ve V3S

Knihy

2011

Klika, V. and Maršík, F., Feasible Simulation of Diseases Related to Bone Remodelling and of Their Treatment, Theoretical Biomechanics, InTech, 2011,
BiBTeX

@INBOOK{Klika11:1854,
  title = {{Feasible Simulation of Diseases Related to Bone Remodelling and of Their Treatment}},
  author = {Klika, V. and Mar{\v s}{\'\i}k, F.},
  address = {Rijeka},
  booktitle = {{Theoretical Biomechanics}},
  publisher = {InTech},
  year = {2011},
  pages = {187--210}
}

2010

Klika, V. and Maršík, F. and Mařík, I., Influencing the Effect of Treatment of Diseases Related to Bone Remodelling by Dynamic Loading, Dynamic Modelling, In-Teh, 2010,
BiBTeX

@INBOOK{Klika10:1704,
  title = {{Influencing the Effect of Treatment of Diseases Related to Bone Remodelling by Dynamic Loading}},
  author = {Klika, V. and Mar{\v s}{\'\i}k, F. and Ma{\v r}{\'\i}k, I.},
  address = {Viena},
  booktitle = {{Dynamic Modelling}},
  publisher = {In-Teh},
  year = {2010},
  pages = {263--290}
}

Články v časopisech

2014

Klika, V., A Guide through Available Mixture Theories for Applications, Critical Reviews in Solid State and Materials Sciences 39 (2014) , 154-174
BiBTeX

@ARTICLE{Klika14:2116,
  title = {{A Guide through Available Mixture Theories for Applications}},
  author = {Klika, V.},
  journal = {Critical Reviews in Solid State and Materials Sciences},
  year = {2014},
  volume = {39},
  number = {2},
  pages = {154--174},
  month = {FEB}
}

2013

Klika, V. and Grmela, M., Coupling between chemical kinetics and mechanics that is both nonlinear and compatible with thermodynamics, Physical Review E 87 (2013) , 012141-1-012141-9
BiBTeX

@ARTICLE{Klika13:2014,
  title = {{Coupling between chemical kinetics and mechanics that is both nonlinear and compatible with thermodynamics}},
  author = {Klika, V. and Grmela, M.},
  journal = {Physical Review E},
  year = {2013},
  volume = {87},
  number = {1},
  pages = {012141-1--012141-9}
}

2012

Klika, V. and Baker, RE and Headon, D. and Gaffney, EA, The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation, BULLETIN OF MATHEMATICAL BIOLOGY 74 (2012) , 935-957
BiBTeX

@ARTICLE{Klika12:1850,
  title = {{The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation}},
  author = {Klika, V. and Baker, RE and Headon, D. and Gaffney, EA},
  journal = {BULLETIN OF MATHEMATICAL BIOLOGY},
  year = {2012},
  volume = {74},
  number = {4},
  pages = {935--957}
}

2011

Myslivec, R. and Klika, V. and Zemková, D. and Maříková, A. and Mařík, I., Prediction of suitable time instant for external fixation removal in distraction osteogenesis according to a simple biomechanical model, Pohybové ústrojí. Pokroky ve výzkumu, diagnostice a terapii 18 (2011) , 328-333
BiBTeX

@ARTICLE{Myslivec11:1,
  title = {{Prediction of suitable time instant for external fixation removal in distraction osteogenesis according to a simple biomechanical model}},
  author = {Myslivec, R. and Klika, V. and Zemkov{\' a}, D. and Ma{\v r}{\'\i}kov{\' a}, A. and Ma{\v r}{\'\i}k, I.},
  journal = {Pohybov{\' e} {\' u}stroj{\'\i}. Pokroky ve v{\' y}zkumu, diagnostice a terapii},
  year = {2011},
  volume = {18},
  number = {3+4},
  pages = {328--333}
}

Klika, V. and Maršík, F., Feasible prediction of bone remodelling using modelling techniques, Pohybové ústrojí. Pokroky ve výzkumu, diagnostice a terapii 18 (2011) , 26-41
BiBTeX

@ARTICLE{Klika11:1877,
  title = {{Feasible prediction of bone remodelling using modelling techniques}},
  author = {Klika, V. and Mar{\v s}{\'\i}k, F.},
  journal = {Pohybov{\' e} {\' u}stroj{\'\i}. Pokroky ve v{\' y}zkumu, diagnostice a terapii},
  year = {2011},
  volume = {18},
  number = {1+2},
  pages = {26--41}
}

Klika, V., Počítačové modelování tká\v nové přestavby, Československý časopis pro fyziku 61 (2011) , 272-277
BiBTeX

@ARTICLE{Klika11:1854,
  title = {{Po{\v c}{\'\i}ta{\v c}ov{\' e} modelov{\' a}n{\'\i} tk{\' a}{\v n}ov{\' e} p{\v r}estavby}},
  author = {Klika, V.},
  journal = {{\v C}eskoslovensk{\' y} {\v c}asopis pro fyziku},
  year = {2011},
  volume = {61},
  number = {5},
  pages = {272--277},
  month = {11}
}

2010

Klika, V. and Maršík, F., A thermodynamic model of bone remodelling: the influence of dynamic loading together with biochemical control, Journal of Musculoskeletal & Neuronal Interactions 10 (2010) , 220-230
BiBTeX

@ARTICLE{Klika10:1704,
  title = {{A thermodynamic model of bone remodelling: the influence of dynamic loading together with biochemical control}},
  author = {Klika, V. and Mar{\v s}{\'\i}k, F.},
  journal = {Journal of Musculoskeletal \& Neuronal Interactions},
  year = {2010},
  volume = {10},
  number = {3},
  pages = {220--230},
  month = {Sep}
}

Klika, V., Comparison of the Effects of Possible Mechanical Stimuli on the Rate of Biochemical Reactions, The Journal of Physical Chemistry B 114 (2010) , 10567-10572
BiBTeX

@ARTICLE{Klika10:1704,
  title = {{Comparison of the Effects of Possible Mechanical Stimuli on the Rate of Biochemical Reactions}},
  author = {Klika, V.},
  journal = {The Journal of Physical Chemistry B},
  year = {2010},
  volume = {114},
  number = {32},
  pages = {10567--10572},
  month = {Aug}
}

Bougherara, H. and Klika, V. and Maršík, F. and Mařík, IA and Yahia, L., New Predictive Model for Monitoring Bone Remodeling, Journal of Biomedical Materials Research Part A 95A (2010) , 9-24
BiBTeX

@ARTICLE{Bougherara10,
  title = {{New Predictive Model for Monitoring Bone Remodeling}},
  author = {Bougherara, H. and Klika, V. and Mar{\v s}{\'\i}k, F. and Ma{\v r}{\'\i}k, IA and Yahia, L.},
  journal = {Journal of Biomedical Materials Research Part A},
  year = {2010},
  volume = {95A},
  number = {1},
  pages = {9--24},
  month = {Oct}
}

Maršík, F. and Klika, V. and Chlup, H., Remodelling of living bone induced by dynamic loading and drug delivery-Numerical modelling and clinical treatment, Mathematics and Computers in Simulation 80 (2010) , 1278-1288
BiBTeX

@ARTICLE{Marsik10:158,
  title = {{Remodelling of living bone induced by dynamic loading and drug delivery-Numerical modelling and clinical treatment}},
  author = {Mar{\v s}{\'\i}k, F. and Klika, V. and Chlup, H.},
  journal = {Mathematics and Computers in Simulation},
  year = {2010},
  volume = {80},
  number = {6},
  pages = {1278--1288},
  month = {6}
}

2009

Klika, V. and Maršík, F., Coupling Effect between Mechanical Loading and Chemical Reactions, JOURNAL OF PHYSICAL CHEMISTRY B 113 (2009) , 14689-14697
BiBTeX

@ARTICLE{Klika09:1588,
  title = {{Coupling Effect between Mechanical Loading and Chemical Reactions}},
  author = {Klika, V. and Mar{\v s}{\'\i}k, F.},
  journal = {JOURNAL OF PHYSICAL CHEMISTRY B},
  year = {2009},
  volume = {113},
  number = {44},
  pages = {14689--14697}
}

Klika, V. and Pérez, MA and García-Aznar, JM and Maršík, F. and Doblaré, M., A coupled mechano-biochemical model for bone adaptation, Journal of Mathematical Biology () , -
BiBTeX

@ARTICLE{Klika:211667,
  title = {{A coupled mechano-biochemical model for bone adaptation}},
  author = {Klika, V. and P{\' e}rez, MA and Garc{\'\i}a-Aznar, JM and Mar{\v s}{\'\i}k, F. and Doblar{\' e}, M.},
  journal = {Journal of Mathematical Biology},
  pages = {--}
}

Články ve sbornících

2009

Klika, V. and Maršík, F., Simulation/prediction of osteogenic effects of vibration plates using thermodynamics model-a preliminary study, Sympozjum Naukowe "Latest archievements in orthopedics and in pediatrics orthopedics. Prophylatics programs in 'Bone and Joint Decade 2000-2010", (2009) , 148-151, Wydavnictwo AGATKA
BiBTeX

@INPROCEEDINGS{Klika09:1705,
  title = {{Simulation/prediction of osteogenic effects of vibration plates using thermodynamics model-a preliminary study}},
  author = {Klika, V. and Mar{\v s}{\'\i}k, F.},
  address = {Kloczew},
  booktitle = {{Sympozjum Naukowe "Latest archievements in orthopedics and in pediatrics orthopedics. Prophylatics programs in 'Bone and Joint Decade 2000-2010"}},
  publisher = {Wydavnictwo AGATKA},
  year = {2009},
  pages = {148--151}
}

2008

Klika, V., Towards real prediction of bone adaptation, Doktorandské dny 2008, (2008) , 83-92, Česká technika - nakladatelství ČVUT
BiBTeX

@INPROCEEDINGS{Klika08:1509,
  title = {{Towards real prediction of bone adaptation}},
  author = {Klika, V.},
  address = {Praha},
  booktitle = {{Doktorandsk{\' e} dny 2008}},
  publisher = {{\v C}esk{\' a} technika - nakladatelstv{\'\i} {\v C}VUT},
  year = {2008},
  pages = {83--92}
}

2007

Klika, V., Thermodynamic Model of Bone Adaptation, Doktorandské dny 2007, (2007) , 93-104, Česká technika - nakladatelství ČVUT
BiBTeX

@INPROCEEDINGS{Klika07:1376,
  title = {{Thermodynamic Model of Bone Adaptation}},
  author = {Klika, V.},
  address = {Praha},
  booktitle = {{Doktorandsk{\' e} dny 2007}},
  publisher = {{\v C}esk{\' a} technika - nakladatelstv{\'\i} {\v C}VUT},
  year = {2007},
  pages = {93--104}
}

Klika, V. and Maršík, F., Tissue adaptation driven by chemo-mechanical coupling with application to bone, , () , 337-338,
BiBTeX

@INPROCEEDINGS{Klika:184903,
  title = {{Tissue adaptation driven by chemo-mechanical coupling with application to bone}},
  author = {Klika, V. and Mar{\v s}{\'\i}k, F.},
  booktitle = {{}},
  pages = {337--338}
}

Ostatní publikace

2009

Klika, V., Towards longterm prediction of tissue remodelling, České vysoké učení technické v Praze, Fakulta jaderná a fyzikálně inženýrská, 2009
BiBTeX

@PHDTHESIS{Klika09:1588,
  title = {{Towards longterm prediction of tissue remodelling}},
  author = {Klika, V.},
  address = {Praha},
  year = {2009},
  pages = {103},
  school = {{\v C}esk{\' e} vysok{\' e} u{\v c}en{\'\i} technick{\' e} v Praze, Fakulta jadern{\' a} a fyzik{\' a}ln{\v e} in{\v z}en{\' y}rsk{\' a}}
}

2001

Klika, V., Biochemical model of bone remodelling including mechano-chemical coupling, 2001
BiBTeX

@UNPUBLISHED{Klika01:1704,
  title = {{Biochemical model of bone remodelling including mechano-chemical coupling}},
  author = {Klika, V.},
  year = {2001},
  note = {Unpublished Lecture}
}

za obsah této stránky zodpovídá: Radek Fučík | naposledy změněno: 7.8.2011