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Access status: Open Access ,
Mieszanie topologiczne w dyskretnych układach dynamicznych - krótkie wprowadzenie
(Wydawnictwa AGH, 2008) Oprocha, Piotr
When we study processes evolving in time, we usually consider two directions of research: we look for regularity (stability) of dynamics and we try to understand irregular behavior (chaos) which is present in the system. Intuitively, unpredictability of dynamics is related to some kind of »mixing« in the phase space. The aim of this article is to present notions which try to describe this phenomena on a basis of topological approach.
Access status: Open Access ,
Thermal-mechanical finite element simulation of flat bar rolling coupled with a stochastic model of microstructure evolution
(Wydawnictwa AGH, 2022) Szeliga, Danuta; Czyżewska, Natalia; Kusiak, Jan; Kuziak, Roman; Morkisz, Paweł M.; Oprocha, Piotr; Pietrzyk, Maciej; Piwowarczyk, Michał; Poloczek, Łukasz; Przybyłowicz, Paweł; Rauch, Łukasz; Wolańska, Natalia
It is generally recognized that the kinetics of phase transformations during the cooling of steel products depends to a large extent on the state of the austenite after rolling. Austenite deformation (when recrystallization is not complete) and grain size have a strong influence on the nucleation and growth of low-temperature phases. Thus, the general objective of the present work was the formulation of a numerical model which simulates thermal, mechanical and microstructural phenomena during multipass hot rolling of flat bars. The simulation of flat bar rolling accounting for the evolution of a heterogeneous microstructure was the objective of the work. A conventional finite-element program was used to calculate the distribution of strains, stresses, and temperatures in the flat bar during rolling and during interpass times. The FE program was coupled with the stochastic model describing austenite microstructure evolution. In this model, the random character of the recrystallization was accounted for. Simulations supplied information about the distributions of the dislocation density and the grain size at various locations through the thickness of the bars.
Access status: Open Access ,
A study of chaos for processes under small perturbations II - rigorous proof of chaos
(2010) Oprocha, Piotr; Wilczyński, Paweł
In the present paper we prove distributional chaos for the Poincaré map in the perturbed equation $\dot{z}=\left(1 + e^{i\kappa t} |z|^2\right)\bar{z}^2 - N e^{-i\frac{\pi}{3}}.$ Heteroclinic and homoclinic connections between two periodic solutions bifurcating from the stationary solution $0$ present in the system when $N = 0$ are also discussed.
Access status: Open Access ,
Topological approach to chain recurrence in continuous dynamical systems
(2005) Oprocha, Piotr
In this paper we present equivalent definitions of chain recurrent set for continuous dynamical systems. This definitions allow us to define chain recurrent set in topological spaces.

Oprocha, Piotr

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