Search results for: DYNAMICAL STATE
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Weak forms of shadowing in topological dynamics
PublicationWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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Effect of vehicle motion stability after impact/crash on traffic safety
PublicationThe article presents the application of general stability theory to the study of road traffic stability immediately after an impact (crash, collision). It turns out that when modelling a collision, vehicles can be treated as colliding masses and dynamical systems can be assigned to this phenomenon.
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Transport of dangerous goods by rail, and threats to the subsoil of the railway surface in the event of a disaster
PublicationIn Poland, in 2020, the mass of dangerous goods (loads) transported by rail was 26 151.06 thousand tone. This translated into the performance of 8 899 691.89 thousand tone - km of transport performance. In 2020, these figures accounted for 11.72% of the weight of goods transported by rail. The situation is similar in other countries around the world. With such a large volume of transport of dangerous...
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The sensitiveness of the speed of pile displacement to speed variations of hammer in beating down process
PublicationIn this paper there is presented dynamical system described speed of pile displacement during beating down process. Its response is determined by using Heaviside operator. There is introduced the convergence with regulator in partially ordered space. There is given an answer to the question, whetdisplacement is sensitive to hammer's speed variations.
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Dynamics of cutting power during sawing with circular saw blades as an effect of wood properties changes in the cross section
PublicationIn the paper the effect of the method calculation upon the cutting power is presented. In computations were used models in which fracture toughness was incorporated. The comparison concerned models as follows: FM-CM – classic model in which the sum of all uncut chip thicknesses of the simultaneously teeth engaged represented the mean uncut chip thickness, FM-FDM – full dynamical model in which besides variable uncut chip thickness...
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Dynamical description of quantum computing: generic nonlocality of quantumnoise
PublicationWe develop a dynamical non-Markovian description of quantum computing in the weak-coupling limit, in the lowest-order approximation. We show that the long-range memory of the quantum reservoir (such as the 1/t4 one exhibited by electromagnetic vacuum) produces a strong interrelation between the structure of noise and the quantum algorithm, implying nonlocal attacks of noise. This shows that the implicit assumption of quantum error...
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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublicationIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
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Periodic and chaotic dynamics in a map‐based neuron model
PublicationMap-based neuron models are an important tool in modeling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on continuous or hybrid dynamical systems. However, due to their discrete nature, rigorous mathematical analysis might be challenging. We study a discrete model of neuronal dynamics introduced by Chialvo in 1995. In particular, we show that its reduced one-dimensional...
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One-dimensional chaos in a system with dry friction: analytical approach
PublicationWe introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of...
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Morse inequalities via Conley index theory
PublicationThe relation known as the Morse inequalities can be extended to a more general setting of flows on a locally compact metric spaces (Conley index) as well as dynamical systems on Hilbert spaces (LS-index). This paper is a discourse around this extension. Except the part concerning the LS-index the material is self-contained and has a character of a survey.
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Dynamical nonlocality in quantum time via modular operators
PublicationWe formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocality in time associated with the modular energy operator. Some applications of our...
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The ab initio and experimental study of the spectroscopic and magnetic properties of Ho(III)-EDTA
Open Research DataIn this dataset, the ab initio calculations of the electronic structure and the magnetic properties are discussed in the context of the experimental data for the Ho–EDTA complex. In the calculations different models of the cluster have been applied to examine the influence of various parts of the environment of the Ho(III)-EDTA complex on its properties....
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Connection matrix theory for discrete dynamical systems
PublicationIn [C] and [F1] the connection matrix theory for Morse decomposition is developedin the case of continuous dynamical systems. Our purpose is to study the case of discrete timedynamical systems.
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Curlicues generated by circle homeomorphisms
PublicationWe investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as boundedness, superficiality, local discrete radius of curvature are linked with dynamical properties of the circle homeomorphism which generates them: rotation number and its continued fraction...
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The Dynamical Projectors Method Hydro and Electrodynamics
PublicationThe dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book...
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The Effect of Circular Saw Blade Clamping Diameter on its Resonant Frequencies
PublicationIn this paper results of comparison of characteristic resonant frequencies of circular saw blades as a function of the saw clamping diameter from the impact test are presented. Obtained results revealed that proportionally with the increase of the saw clamping diameter also the dynamical stiffness of the saw blade increased. As a consequence of that the resonant frequencies of the saw blade move to higher values. Moreover, with...
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The effect of circular saw blade clamping diameter on its resonant frequencies
PublicationIn this paper results of comparison of characteristic resonant frequencies of circular saw blades as a function of saw clamping diameter from the impact test are presented. Obtained results revealed that proportionally with the increase of the saw clamping diameter also the dynamical stiffness of the saw blade increased. As a consequence of that the resonant frequencies of the saw blade move to higher values. Moreover, with the...
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Theoretical study of thermofrictional oscillations due to negative friction-temperature characteristic
PublicationAnalytical study on oscillations of a body on a moving counterbody has been done by assuming imperfect frictional thermal contact and friction that decreases with contact temperature. It has been shown that stick-slip oscillation occurs due to decrease of friction coefficient when the body moves in the opposite direction to the counterbody. Dynamical characteristics, such as conditions for stable sliding and limit cycles, have...
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On Computing Curlicues Generated by Circle Homeomorphisms
PublicationThe dataset entitled Computing dynamical curlicues contains values of consecutive points on a curlicue generated, respectively, by rotation on the circle by different angles, the Arnold circle map (with various parameter values) and an exemplary sequence as well as corresponding diameters and Birkhoff averages of these curves. We additionally provide source codes of the Matlab programs which can be used to generate and plot the...
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Multi-headed chimera states in coupled pendula
PublicationWe discuss the occurrence of the chimera states in the network of coupled, excited by the clock’s mechanisms pendula. We find the patterns of multi-headed chimera states in which pendula clustered in different heads behave differently (oscillate with different frequencies) and create different types of synchronous states (complete or phase synchronization). The mathematical model of the network shows that the observed chimera states...