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Wyniki wyszukiwania dla: NONLINEAR DYNAMICAL SYSTEMS
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A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
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Rich Bifurcation Structure in a Two-Patch Vaccination Model
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Subharmonic solutions for a class of Lagrangian systems
PublikacjaWe prove that second order Hamiltonian systems with a potential of class C1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [P. H. Rabinowitz, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38]. Indeed, we weaken...
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The Arnold conjecture in $ \mathbb C\mathbb P^n $ and the Conley index
Publikacjan this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in CP^n asserting that a Hamiltonian diffeomorphism of CP^n endowed with the Fubini-Study metric has at least (n+1) fixed points.
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Detecting coupling directions with transcript mutual information: A comparative study
PublikacjaCausal relationships are important to understand the dynamics of coupled processes and, moreover, to influence or control the effects by acting on the causes. Among the different approaches to determine cause-effect relationships and, in particular, coupling directions in interacting random or deterministic processes, we focus in this paper on information-theoretic measures. So, we study in the theoretical part the difference between...
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Nonlinear Fuzzy Control System for Dissolved Oxygen with Aeration System in Sequencing Batch Reactor
PublikacjaBiological processes at a wastewater treatment plant are complex, multivariable, time varying and nonlinear. Moreover, interactions between the components are very strong. Control of dissolved oxygen is one of most important task at the plant. The level of dissolved oxygen in aerobic tanks has significant influence on behaviour and activity of microorganisms at the plant. Air for aerated tanks is supplied by the aeration system...
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Robust Model Predictive Control for Autonomous Underwater Vehicle – Manipulator System with Fuzzy Compensator
PublikacjaThis paper proposes an improved Model Predictive Control (MPC) approach including a fuzzy compensator in order to track desired trajectories of autonomous Underwater Vehicle Manipulator Systems (UVMS). The tracking performance can be affected by robot dynamical model uncertainties and applied external disturbances. Nevertheless, the MPC as a known proficient nonlinear control approach should be improved by the uncertainty estimator...
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Robust Model Predictive Control for Autonomous Underwater Vehicle–Manipulator System with Fuzzy Compensator
PublikacjaThis paper proposes an improved Model Predictive Control (MPC) approach including a fuzzy compensator in order totrack desired trajectories of autonomous Underwater Vehicle Manipulator Systems (UVMS). The tracking performancecan be affected by robot dynamical model uncertainties and applied external disturbances. Nevertheless, the MPCas a known proficient nonlinear control approach should be improved by the...
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A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect
PublikacjaThe aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations...
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Topological invariants for equivariant flows: Conley index and degree
PublikacjaAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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Genetic Hybrid Predictive Controller for Optimized Dissolved-Oxygen Tracking at Lower Control Level
PublikacjaA hierarchical two-level controller for dissolvedoxygenreference trajectory tracking in activated sludge processeshas been recently developed and successfully validated on a realwastewater treatment plant. The upper level control unit generatestrajectories of the desired airflows to be delivered by theaeration system to the aerobic zones of the biological reactor. Anonlinear model predictive control algorithm is applied to designthis...
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Weak forms of shadowing in topological dynamics
PublikacjaWe 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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Survey on fuzzy logic methods in control systems of electromechanical plants
PublikacjaРассмотрены алгоритмы управления электромеханическими системами с использованием теории нечеткой логики, приводятся основные положения их синтеза, рассматриваются методы анализа их устойчивости на основе нечетких функций Ляпунова. Эти алгоритмы чаще всего реализуются в виде различных регуляторов, применение которых целесообразно в системах, математическая модель которых не известна, не детерминирована или является строго нелинейной,...
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Hierarchical dissolved oxygen control for activated sludge processes
PublikacjaA hierarchical controller for tracking the dissolved oxygen reference trajectory in activated sludge processes is proposed and investigated. The removal of nitrogen and phosphorous from wastewater is considered. Typically, an aeration system itself is a complicated hybrid nonlinear dynamical system with faster dynamics compared to the internal dynamics of the dissolved oxygen in a biological reactor. It is a common approach to...
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High performance super-twisting sliding mode control for a maritime autonomous surface ship (MASS) using ADP-Based adaptive gains and time delay estimation
PublikacjaThis research addresses two kinds of problems related to optimal trajectory tracking of a Maritime Autonomous Surface Ship (MASS): those caused by the time-varying external disturbances including winds, waves and ocean currents as well as those resulting from inherent dynamical uncertainties. As the paper shows, an accurate and robust optimal controller can successfully deal with both issues. An improved Optimal Adaptive Super-Twisting...
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Modelling of wastewater treatment plant for monitoring and control purposes by state - space wavelet networks
PublikacjaMost of industrial processes are nonlinear, not stationary, and dynamical with at least few different time scales in their internal dynamics and hardly measured states. A biological wastewater treatment plant falls into this category. The paper considers modelling such processes for monitorning and control purposes by using State - Space Wavelet Neural Networks (SSWN). The modelling method is illustrated based on bioreactors of...
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High performance super-twisting sliding mode control for a maritime autonomous surface ship (MASS) using ADP-Based adaptive gains and time delay estimation
PublikacjaThis research addresses two kinds of problems related to optimal trajectory tracking of a Maritime Autonomous Surface Ship (MASS): those caused by the time-varying external disturbances including winds, waves and ocean currents as well as those resulting from inherent dynamical uncertainties. As the paper shows, an accurate and robust optimal controller can successfully deal with both issues. An improved Optimal Adaptive Super-Twisting...
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Sterowanie predykcyjne i fuzja danych w systemie dynamicznego pozycjonowania statku
PublikacjaRozprawa doktorska poświęcona jest badaniu zastosowania fuzji danych oraz sterowania predykcyjnego w systemie dynamicznego pozycjonowania statku. W pierwszej części pracy przedstawiono historię rozwoju systemów dynamicznego pozycjonowania, różne metody estymacji położenia statku, metody sterowania oraz cel i tezę pracy. Następnie zaprezentowano model matematyczny statku, kinematykę oraz dynamikę. W kolejnej części przedstawiono...
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PROJEKTOWANIE WIELOWYMIAROWEGO REGULATORA BACKSTEPPING W UKŁADZIE DYNAMICZNEGO POZYCJONOWANIA STATKU
PublikacjaW komercyjnych systemach dynamicznego pozycjonowania statku, pomimo znacznego wzrostu poziomu automatyzacji, wykorzystywane jest nadal sterowanie typu PID. Poprawę jakości procesu pozycjonowania może umożliwić wykorzystanie bardziej efektywnych algorytmów, oferujących zaawansowane nieliniowe techniki sterowania. W artykule przedstawiono zagadnienie projektowania regulatora pozycji i kursu dla układu dynamicznego pozycjonowania...
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The Dynamical Projectors Method Hydro and Electrodynamics
PublikacjaThe 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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Two examples of Quantum Dynamical Semigroups
PublikacjaThe Hamiltonians of the considered bi-partite systems are of the form $$ H_{S,R} = H_S /times 1_R + Q_{S} /times M_R + 1_S /times H_R $$ Subindex $S$ corresponds to the observed system and $R$ to the reservoir (the enviroment of $S$). Two classes of systems are distinguished: the discrete-continuous...
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Dynamical objectivity in quantum Brownian motion
PublikacjaClassical objectivity as a property of quantum states —a view proposed to explain the observer-independent character of our world from quantum theory, is an important step in bridging the quantum-classical gap. It was recently derived in terms of spectrum broadcast structures for small objects embedded in noisy photon-like environments. However, two fundamental problems have arisen: a description of objective motion and applicability...
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Dynamical description of quantum computing: generic nonlocality of quantumnoise
PublikacjaWe 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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Dynamical nonlocality in quantum time via modular operators
PublikacjaWe 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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Nonlinear Viscoelastic Properties of Polyurethane Nanocomposites
PublikacjaIn recent years, the nonlinear viscoelastic behaviors of elastomeric nanocomposites have been examined, especially for a wide range of rubbery composite (including natural rubber) materials. This chapter describes the influence of fillers and nanofillers on the nonlinear viscoelastic properties of elastomeric polyurethane systems. These filled elastomers (similar to the classic natural rubber reinforced elastomers), also exhibit...
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Formation of carbon monoxide by radiative association: a quantum dynamical study
PublikacjaRate coefficients for the formation of carbon monoxide (CO) by radiative association of carbon and oxygen atoms are computed using quantum dynamical simulations. At temperatures above 10 K CO radiative association is dominated by C(3P) and O(3P) approaching on the A1Π potential energy curve. The rate coefficient is estimated as k=A(T/300 K)αexp−β/T with A= 1.39 × 10−18 cm3 s−1, α=−0.016 and β= 92.2 for temperatures between 6 and...
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Nonlinear Properties of Seawater as a Factor Determining Nonlinear Wave Propagation
PublikacjaTaking practical advantage of nonlinear acoustical interactions occurring in seawater [1, 2] requires knowledge of the parameter of nonlinearity B=A of this medium. The literature does not offer much reports on B=A parameter value for seawater. In the few papers concerning that address the issue, results concerning ocean waters with high salinity and at large depths are given [3], while studies concerning seawater with low salinity...
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Wieloobszarowa regulacja systemu turbogeneratora elektrowni jądrowej =Multiregional control of nuclear power plant turbogenerator system
PublikacjaW artykule przedstawiono propozycję zaawansowanej struktury sterowania układem turbogeneratora w szerokim zakresie zmian zapotrzebowania na moc czynną. Dla potrzeb syntezy tej struktury wykorzystano nieliniowe, dynamiczne modele turbiny parowej i generatora synchronicznego współpracującego z systemem elektroenergetycznym. Zaproponowane algorytmy sterowania oparte są odpowiednio o wieloobszarowe regulatory rozmyte, z lokalnymi regulatorami...
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Dynamical Aspects of Knowledge Evolution
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Optical rotation in the lithium triborate nonlinear crystal
PublikacjaA dual-wavelength polarimetric technique at 633 and 661 nm has been used for the characterization of a nonlinear lithium triborate (LiB3O5) nonenantiomorphous biaxial crystal. The mismatch of the crystallographic and optical coordinate systems was taken into account. The optical rotatory power for light propagation along one of the optical axes is ρ = 7.06° mm−1. The gyration tensor component along the bisector between the x and...
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A dynamical model for plasma confinement transitions
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Numerical modeling of quantum dynamical processes
PublikacjaIn this dissertation I present a high-precision (15, 18 or 33 decimal places) C++ implementation of quantum dynamics time propagation algorithms for both time-independent and time-dependent Hamiltonian with an inhomogeneous source term. Moreover I present an extension of both algorithms for time propagation to handle arbitrary number of coupled electronic levels. I have performed a careful validation of these implementations comparing...
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Systems of boundary value problems of advanced differential equations
PublikacjaThis paper considers the existence of extremal solutions to systems of advanced differential equations with corresponding nonlinear boundary conditions. The monotone iterative method is applied to obtain the existence results. An example is provided for illustration.
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Comparative analysis of switched reluctance motor control algorithms
PublikacjaПредмет исследования. Развитие микропроцессорной техники и силовой электроники позволило создавать недорогие и эффективные системы управления различными электромеханическими объектами, которые ранее широко не использовались из-за сложности управления. К таким устройствам можно отнести вентильно-индукторные электрические машины. Данные машины широко применяются в различных практических разработках, например, в тяговом электроприводе,...
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Comparative analysis of switched reluctance motor control algorithms
PublikacjaПредмет исследования. Развитие микропроцессорной техники и силовой электроники позволило создавать недорогие и эффективные системы управления различными электромеханическими объектами, которые ранее широко не использовались из-за сложности управления. К таким устройствам можно отнести вентильно-индукторные электрические машины. Данные машины широко применяются в различных практических разработках, например, в тяговом электроприводе,...
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Comparison of Two Nonlinear Predictive Control Algorithms for Dissolved Oxygen Tracking Problem at WWTP
PublikacjaThe wastewater treatment plant is classified as a complex system, due to its nonlinear dynamics, large uncertainty of disturbance inputs, multiple time scales in the internal process dynamics, and multivariable structure. The aeration process, in turn, is an important and expensive part of wastewater treatment plant operation. All operating parameters of the aeration in biological processes are to be precisely controlled to provide...
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Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing
PublikacjaThe grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for the existence of a grazing family of periodic solutions, is given. The properties of these periodic solutions are discussed. A plenty of results on the topological structure of attractors of vibro-impact systems is known. However, since the considered system is strongly nonlinear, these attractors...
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Nonlinear properties of the Gotland Deep – Baltic Sea
PublikacjaThe properties of the nonlinear phenomenon in water, including sea water, have been well known for many decades. The feature of the non homogeneous distribution of the speed of sound along the depth of the sea is very interesting from the physical and technical point of view. It is important especially in the observation of underwater area by means of acoustical method ( Grelowska et al ., 2013; 2014). The observation of the underwater...
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Method of lines for nonlinear first order partial functional differential equations.
PublikacjaClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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The nonlinear effects of sound in a liquid with relaxation losses
PublikacjaThe nonlinear effects of sound in electrolyte with a chemical reaction are examined. The dynamic equations that govern non-wave modes in the field of intense sound are derived, and acoustic forces of vortex, entropy, and relaxation modes are determined in the cases of low-frequency sound and high-frequency sound. The difference in the nonlinear effects of sound in electrolyte and in a gas with excited vibrational degrees of molecules,...
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Security and Anonymity in Agent Systems
PublikacjaMany agent systems have been developed and suggested for commercial application. However, in spite of the significant potential offered by the agent paradigm, the lack of such important properties as security, anonymity and untracebility especially in open dynamical environment, such as the Internet, has blocked the active implementation of agent technologies. Protecting agent systems poses a more demanding challenge comparing...
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A Nonlinear Model of a Mesh Shell
PublikacjaFor a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration...
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Generation and Propagation of Nonlinear Waves in a Towing Tank
PublikacjaThe paper presents the results of the research focused on linear and nonlinear wave generation and propagation in a deepwater towing tank equipped with a single flap-type wavemaker of variable draft. The problem of wave generation and propagation has been theoretically formulated and solved by applying an analytical method; linear and nonlinear solutions were obtained. The linear solution has been verified experimentally. The...
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Dynamical properties of ordered Fe–Pt alloys
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Dimensionally Consistent Nonlinear Muskingum Equation
PublikacjaAlthough the Muskingum equation was proposed nearly 75 years ago, it is still a subject of active research. Despite of its simple form, the real properties of this equation have not been comprehensively explained. This paper proposes a new interpretation of the linear McCarthy’s relation. This relation can be interpreted only together with the storage equation, whereas the Muskingum equation can be derived directly from the system...
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A non-adiabatic wavepacket dynamical study of the low energy chargetransfer process in the S3+ + H collision
PublikacjaThe collisional system S3+ + H?S2+ + H+ has been studied using a time-dependent wavepacket methodologyin two-dimensions. Using available potential energy surfaces and coupling matrix elementsobtained from multireference ab initio calculations, five non-adiabatically coupled electronic states of1P symmetry have been included in the dynamical simulations. The collision has been studied in thelow energy regime of 1-10 eV. The wavepacket...
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On the geometrically nonlinear vibration of a piezo-flexomagnetic nanotube
PublikacjaIn order to describe the behavior of thin elements used in MEMS and NEMS, it is essential to study a nonlinear free vibration of nanotubes under complicated external fields such as magnetic environment. In this regard, the magnetic force applied to the conductive nanotube with piezo-flexomagnetic elastic wall is considered. By the inclusion of Euler-Bernoulli beam and using Hamilton’s principle, the equations governing the system...
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The application of nonlinear curvature sections in the turnout diverging track
PublikacjaThe paper presents the analytical method of modelling the diverging track of railway turnout with nonlinear curvature sections. These sections were used for smoothing the graph of curvature in the extreme areas of turnout. The problem of the curvature distribution was identified with the use of differential equations. The resulting solutions are of universal nature for example the ability of assuming any values of curvature at...
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On nonlinear dilatational strain gradient elasticity
PublikacjaWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the...
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Acceleration waves in the nonlinear micromorphic continuum
PublikacjaWithin the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for...