Wyniki wyszukiwania dla: NONLINEAR SYSTEMS
-
application of linear quadratic regulator (lqr) for nonlinear systems based on the parameter sensitivity
PublikacjaMetoda LQR jest znaną metodą optymalizacyjną dla liniowych układów sterowania. W referacie przedstawiono oryginalny algorytm dotyczący zastosowania tej metody dla nieliniowych układów sterowania przy wykorzystaniu analizy wrażliwości układu. Algorytm ten poddany jest weryfikacji na przykładzie układu sterowania napędu statku.
-
Higher-order spectra for harmonics detection in nonlinear systems at presence of Gaussian noise.
PublikacjaPrzedstawiono metodę wykrywania harmonicznych w ukladach nieliniowych za pomocą funkcji bispektrum. Przebadano skuteczność proponowanej metody w porównaniu z metodą wykorzystującą gęstość widmową mocy. Badania przeprowadzono dla sygnałów będących sumą sygnału harmonicznego i realizacji szumu białego.
-
Mechatronic design o strongly nonlinear systems on a basis of three wheeled mobile platform
PublikacjaRemarkable grow in demand both of mobile platform operability performance and reduction of project leading time development encourage to apply modern algorithms and reliable engineering tools for the design process. The paper discusses the mechatronic design applied for the surveillance system based on the energy performance index algorithm. The exploited mechatronic techniques i.e. virtual prototyping, Hardware-In-the-Loop Simulation...
-
Systems of Nonlinear Fractional Differential Equations
PublikacjaUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
-
Nonlinear control systems modelling: global vs. local
Publikacja -
Numerical methods for systems of nonlinear differential functional equations
PublikacjaPraca dotyczy zagadnień początkowo brzegowych dla nieliniowych układów różniczkowo funkcyjnych. Rozważana jest aproksymacja rozwiązań rozważanego problemu różniczkowo funkcyjnego przez rozwiązania odpowiedniego problemu różnicowego. W pracy analizowana jest zbieżność prezentowanych metod. Dowód zbieżności opiera się na technice porównawczej z nieliniowym oszacowaniem typu Perron'a dla danych operatorów.
-
Nonlinear Analysis-Hybrid Systems
Czasopisma -
Nonlinear Dynamics and Systems Theory
Czasopisma -
Nonlinear Phenomena in Complex Systems
Czasopisma -
Discrete-time estimation of nonlinear continuous-time stochastic systems
PublikacjaIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
-
Discrete-time estimation of nonlinear continuous-time stochastic systems
PublikacjaIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
-
Multimode systems of nonlinear equations: derivation, integrability, and numerical solutions
PublikacjaWe consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearityinto account. We develop a method for transforming Maxwell's equations based on a complete set ofprojection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with thepropagation direction taken into account. The most important result of applying the method is a systemof equations describing the...
-
Properties of control systems based on nonlinear models of the induction motor.
PublikacjaW artykule przedstawiono zastosowanie obserwatora prędkości kątowej wirnika silnika indukcyjnego w nielinowych układach regulacji. Porównano dwa typy układów sterowania multiskalarnego. Przedstawiono przypadek niestabilnej pracy układu nieliniowego sterowania za pomocą symulacji komputerowej.W artykule przedstawiono dwa układy sterowania silnikiem asynchronicznym klatkowym, zasilanym z falownika napięcia, oparte na modelu multiskalarnym,...
-
Nonlinear Model of Synchronous Generator for Autonomous Electrical Power Systems Analysis
PublikacjaThis paper presents the nonlinear lookup table model for synchronous generator (SG) analysis. The saturation effects of the SG magnetic circuit have been considered. The saturated characteristic of the SG magnetic circuit are based on the open circuit saturation curve for magnetizing inductances. The model has been implemented into the Synopsys/Saber software using the MAST modelling language. To implement the no-load voltage characteristic...
-
Adaptive fuzzy modelling and control for discrete-time nonlinear uncertain systems
PublikacjaReferat przedstawia metodę adaptacyjnego rozmytego modelowania i sterowania dla nieliniowego systemu dyskretnego z niepewnością. Proponowana metoda adaptacyjna składa się z dwóch części: rozmyte modelowanie on-line z zastosowaniem systemu Takagi - Sugeno (T-S) oraz sterowanie adaptacyjne z modelem referencyjnym. Model rozmyty T-S posiada samoorganizującą się strukturę, tzn. reguły rozmyte mogą być dodawane, zamieniane lub usuwane...
-
Softly Switched Robustly Feasible Model Predictive Control for Nonlinear Network Systems
PublikacjaIt is common that an efficient constrained plant operation under full range of disturbance inputs require meeting different sets of control objectives. This calls for application of model predictive controllers each of them being best fit into specific operating conditions. It further requires that not only designing robustly feasible model predictive controllers is needed to satisfy the real plant state/output constraints, but...
-
Nonlinear model of a synchronous generator for analysis of more electric aircraft power systems
PublikacjaA nonlinear model for studying a variable-speed synchronous generator (SG) in more electric aircraft (MEA) power system has been developed. The saturation effects of the SG magnetic circuit have been considered. The model has been implemented in the Synopys/Saber simulation environment. The modelling language MAST has been used to elaborate the SG model. The model exhibit a network with the same number of external terminals/ports...
-
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...
-
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...
-
Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models
PublikacjaExperimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretical attention has been devoted to the spontaneous activity of neurons, less is known about the dynamic mechanisms shaping their responses to transient inputs, although these bear significant physiological relevance. Here, we study responses to transient...
-
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...
-
Towards homoscedastic nonlinear cointegration for structural health monitoring
Publikacja -
Topological Methods in Nonlinear Analysis
Czasopisma -
Nonlinear viscoelasticity in Three Dimensional filler reinforced rubber composites and nanocomposites
PublikacjaThis chapter describes the influence of three-dimensional nanofillers used in elastomers on the nonlinear viscoelastic properties. In particular, this part focuses and investigates the most important three-dimensional nanoparticles, which are used to produce rubber nanocomposites. The rheological and the dynamic mechanical properties of elastomeric polymers, reinforced with spherical nanoparticles, like POSS, titanium dioxide and...
-
Linear and Nonlinear Optical Properties of Azobenzene Derivatives Modified with an (Amino)naphthalene Moiety
PublikacjaThe design of two-photon absorbing azobenzene (AB) derivatives has received much attention; however, the two-photon absorption (2PA) properties of bis-conjugated azobenzene systems are relatively less explored. Here, we present the synthesis of six azobenzene derivatives and three bisazobenzenes substituted (or not) at para position(s) with one or two amino group(s). Their linear and nonlinear absorption properties are studied...
-
Nonlinear Control of a Doubly Fed Generator Supplied by a Current Source Inverter
PublikacjaNowadays, wind turbines based on a doubly fed induction generator (DFIG) are a commonly used solution in the wind industry. The standard converter topology used in these systems is the voltage source inverter (VSI). The use of reverse-blocking insulated gate bipolar transistor (RB-IGBT) in the current source inverter topology (CSI), which is an alternative topology, opens new possibilities of control methods. This paper presents...
-
Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublikacjaIn 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...
-
Robust Parameter Estimation and Output Prediction for Reactive Carrier-Load Nonlinear Dynamic Networks
PublikacjaIn this paper an extension of on-line model simplification technique for a class of networked systems, namely reactive carrier-load nonlinear dynamic networked system (RCLNDNS), kept within point-parametric model (PPM) framework is addressed. The PPM is utilised to acquire a piece wise constant time-varying parameter linear structure for the RCLNDNS suitable for the on-line one step ahead prediction that may be applied to monitoring...
-
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...
-
Application of discrete wavelet transform in seismic nonlinear analysis of soil–structure interaction problems
PublikacjaSimulation of soil-structure interaction (SSI) effects is a time-consuming and costly process. However, ignoring the influence of SSI on structural response may lead to inaccurate results, especially in the case of seismic nonlinear analysis. In this paper, wavelet transform methodology has been utilized for investigation of the seismic response of soil-structure systems. For this purpose, different storey outrigger braced buildings...
-
Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
PublikacjaThis work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by...
-
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...
-
Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublikacjaIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
-
Nonlinear control of five phase induction motor with synchronized third harmonic flux injection
PublikacjaThe paper deals with the novel control system for five phase induction motor (IM) that enables the injection of the rotor flux 3rd harmonic component. Two multiscalar models are transformed from the 1-1 and 2-2 vector models developed in the 1st and 3rd harmonic planes. Based on the obtained multiscalar models the synthesis of dual multiscalar control is established. The obtained two multiscalar control systems can independently...
-
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Czasopisma -
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...
-
The experimental identification of the dynamic coefficients of two hydrodynamic journal bearings operating at constant rotational speed and under nonlinear conditions.
PublikacjaHydrodynamic bearings are commonly used in ship propulsion systems. Typically, they are calculated using numerical or experimental methods. This paper presents an experimental study through which it has been possible to estimate 24 dynamic coefficients of two hydrodynamic slide bearings operating under nonlinear conditions. During the investigation, bearing mass coefficients are identified by means of a newly developed algorithm....
-
Nonlinear Engineering
Czasopisma -
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.
-
Robust output prediction of differential – algebraic systems – application to drinking water distribution system
PublikacjaThe paper presents the recursive robust output variable prediction algorithm, applicable for systems described in the form of nonlinear algebraic-differential equations. The algorithm bases on the uncertainty interval description, the system model, and the measurements. To improve the algorithm efficiency, nonlinear system models are linearised along the nominal trajectory. The effectiveness of the algorithm is demonstrated on...
-
Approximation of Fractional Order Dynamic Systems Using Elman, GRU and LSTM Neural Networks
PublikacjaIn the paper, authors explore the possibility of using the recurrent neural networks (RNN) - Elman, GRU and LSTM - for an approximation of the solution of the fractional-orders differential equations. The RNN network parameters are estimated via optimisation with the second order L-BFGS algorithm. It is done based on data from four systems: simple first and second fractional order LTI systems, a system of fractional-order point...
-
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...
-
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...
-
Software tool for modelling of mechatronic systems with elastic continua
PublikacjaThe paper presents a systematic computational package for modelling and analysis of complex systems composed of multiple lumped and distributed parameter subsystems. The constructed computer program enables the frequency domain analysis of a class of linear systems and to obtain reduced order model in the form of bond graph. Obtained modal bond graph can be directly exported into 20-Sim package to further processing including nonlinear...
-
Communications in Nonlinear Science and Numerical Simulation
Czasopisma -
Fuzzy differential-algebraic systems
PublikacjaProblem istnienia i jednoznaczności rozwiązań oraz ciągła zależność jest dyskutowana. Powyższe rezultaty zostały otrzymane zakładając m.in. warunek Perrona oraz stosując metodę porównawczą. Przypadek liniowy warunku Perrona jest też badany.
-
Geometrically nonlinear analysis of shells
PublikacjaArtykuł porusza zagadnienia nieliniowej analizy powłok wykonanych z materiałów izotropowych. Obliczenia wykonano przy wykorzystaniu dwóch komercyjnych programów wykorzystujących Metodę Elementów Skończonych (Robot Millennium v. 19.0 i MSC.Marc v.2005r2 ). Główną uwagę skupiono na zjawisku zakleszczenia.
-
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...
-
Nonlinear Studies
Czasopisma -
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...
-
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...
-
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...
-
Nonlinear Biomedical Physics
Czasopisma -
Nonlinear Analysis Forum
Czasopisma -
Results in Nonlinear Analysis
Czasopisma -
NONLINEAR PROCESSES IN GEOPHYSICS
Czasopisma -
Nonlinear Physical Science
Czasopisma -
JOURNAL OF NONLINEAR SCIENCE
Czasopisma -
Stability by linear approximation for time scale dynamical systems
PublikacjaWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
-
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,...
-
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...
-
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...
-
Multiscalar Model Based Control Systems for AC Machines
PublikacjaContents of the Chapter: Nonlinear transformations and feedback linearization. Models of the squirrel cage induction machine: Vector model of the squirrel cage induction machine. Multiscalar models of the squirrel cage induction machine.Feedback linearization of multiscalar models of the induction motor.Models of the double fed induction machine: Vector model of the double fed induction machine. Multiscalar model of the...
-
Analysis of nonlinear generation in bubble layer
PublikacjaRozważano zagadnienie liniowego i nieliniowego rozpraszania w warstwie z pęcherzykami. Badania numeryczne dotyczyły rozpraszania koherentnego i różnych własności rozchodzenia się fal wewnątrz warstwy z pęcherzykami jak odbicie od brzegu, dyspersja, tłumienie. Badania dla różnych rozkładów pęcherzyków przeprowadzono w oparciu o równanie Rayleigha-Plesseta.
-
Nonlinear Backstepping Ship Course Controller
PublikacjaStatek, jako obiekt sterowania charakteryzuje się nieliniową manewrową funkcją opisującą. Metoda backstepping jest jedną z metod, które mogą być wykorzystane w procesie projektowania nieliniowych układu sterowania kursem statków. Metoda została zastosowana w celu zaprojektowania dwóch konfiguracji nieliniowych regulatorów kursu.Regulatory zostały przebadane w układach regulacji kursu statku. Jedna z konfiguracji w fazie projektowania...
-
Modeling of nonlinear generation in a bubble layer
PublikacjaPraca prezentuje numeryczne podejście do zagadnienia liniowego i nieliniowego rozpraszania w warstwie z pęcherzykami. Badania numeryczne niekoherentnego rozpraszania wykonano stosując metodę Monte Carlo. Propagację i wsteczne rozpraszanie sygnałów badano w oparciu o równanie Rayleigha-Plesseta.
-
Analysis of nonlinear effects as a diagnostic tool
PublikacjaMetody analizy efektów nieliniowych nieliniowej analizy sygnałów na wyjściu testowanych obiektów umożliwiają badanie występowania defektów i uszkodzeń w materiałach i elementach elektronicznych, co jest niezbędne w predykcji niezawodności. W odniesieniu do elementów biernych bardzo skutecznym narzędziem okazuje się być wskaźnik trzeciej harmonicznej (THI - Third Harmonic Index). W artykule bardziej szczegółowo opisano pomiary parametru...
-
Correlation experiments in nonlinear quantum mechanics
PublikacjaPokazano w jaki sposób należy obliczać wieloczasowe i wielocząstkowe funkcje korelacyjne w nieliniowej mechanice kwantowej, aby zagwarantować lokalność formalizmu.
-
Nonlinear modelling of eathquake induced pounding.
PublikacjaZaprezentowano nieliniowy model lepkosprężysty siły zderzenia w czasie kontaktu między konstrukcjami podczas trzęsień ziemi. Efektywność modelu sprawdzono przez porównanie wyników analizy numerycznej z wynikami eksperymentalnymi. Wyniki badań pokazują, iż rozważany model najdokładniej symuluje siłę zderzenia w czasie.
-
Nonlinear resultant theory of shells accounting for thermodiffusion
PublikacjaThe complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells...
-
Generalized quazilinearization for systems of degenerate singular perturbation problem
PublikacjaPraca dotyczy ogólnej metody kwazilinearyzacji dla układów równań różniczkowych z parametrami.
-
<title>Nonlinear glasses and metaglasses for photonics, a review: Part I. Nonlinear electrical susceptibility and refractive index</title>
Publikacja -
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...
-
Features of Nonlinear Sound Propagation in Vibrationally Excited Gases
PublikacjaWeakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to...
-
Direct estimation of linear and nonlinear functionals of quantum state
PublikacjaWe present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of...
-
Coupled nonlinear Schrödinger equations in optic fibers theory
PublikacjaIn this paper a detailed derivation and numerical solutions of CoupledNonlinear Schr¨odinger Equations for pulses of polarized electromagnetic wavesin cylindrical fibers has been reviewed. Our recent work has been compared withsome previous ones and the advantage of our new approach over other methods hasbeen assessed. The novelty of our approach lies is an attempt to proceed withoutloss of information within the frame of basic...
-
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,...
-
Ordinar differential equations with nonlinear boundary conditions
PublikacjaPraca dotyczy zwyczajnych równań różniczkowych z nieliniowymi warunkami brzegowymi. Sformułowano warunki dostateczne na istnienie rozwiązania (jedynego lub ekstremalnych) zakładając pewną regularność na prawe strony równania i warunek brzegowy. Warunki brzegowe typu okresowego lub antyokresowego są szczególnymi przypadkami ogólnego warunku dyskutowanego w tej pracy.
-
Linear and nonlinear Stark effect in a triangular molecule
Publikacja -
Identification of nonlinear viscoelastic properties of the ''Panama'' fabric
PublikacjaTkanina techniczna Panama wytwarzana przez firmę Sattler (Niemcy)wykazuje cechy nieliniowe w tym właściwości lepkosprężyste w czasie testów długoterminowych. Na podstawie jednoosiowych testów płynięcia i regeneracji przeprowadzonych dla pięciu poziomów obciążenia przeprowadzono identyfikacje nieliniowych lepkosprężystych właściwości tkaniny. Do opisu zależności konstytutywnych użyto całkowego modelu Schapery'ego. Zastosowano funkcję...
-
<title>Measurements of nonlinear optical fibers</title>
Publikacja -
A nonlinear approach to modelling gas bubble deformation.
PublikacjaPrzedstawiono model wyjaśniający wpływ deformacji pęcherzyka na występowanie zjawiska chaosu podczas generowania pęcherzyków gazowych z pojedynczej dyszy zanurzonej w cieczy.
-
On delay differential equations with nonlinear boundary conditions
PublikacjaStosując metodę iteracji monotonicznych podano warunki dostateczne na istnienie kwazirozwiązań lub ekstremalnych rozwiązań rozpatrywanego zagadnienia. Problem jednoznaczności rozwiązania był również przedmiotem badań. Zajmowano się również nierównościami różniczkowymi z opóżnionymi argumentami.
-
Advanced differential equations with nonlinear boundary conditions.
PublikacjaBadano problemy istnienia rozwiązań dla równań różniczkowych z nielinowymi warunkami brzegowymi. Podano też warunki dostateczne na istnienie rozwiązań ekstremalnych. Przedmiotem badań były również nierówności różniczkowe z wyprzedzonym argumentem.
-
Homoclinics for singular strong force Lagrangian systems
PublikacjaWe study the existence of homoclinic solutions for a class of generalized Lagrangian systems in the plane, with a C1-smooth potential with a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin.Under a strong force condition around the singular point ξ, via minimization of an action integral, we will prove the existence of at least two geometrically distinct homoclinic solutions.
-
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Czasopisma -
Nonlinear Influence of Sound on the Vibrational Energy of Molecules in a Relaxing Gas
PublikacjaDynamics of a weakly nonlinear and weakly dispersive flow of a gas where molecular vibrational relaxation takes place is studied. Variations in the vibrational energy in the field of intense sound is considered. These variations are caused by a nonlinear transfer of the acoustic energy into energy of vibrational degrees of freedom in a relaxing gas. The final dynamic equation which describes this is instantaneous, it includes a...
-
Nonlinear phenomena of small-scale sound in a gas with exponential stratification
PublikacjaThe nonlinear dynamics of perturbations, quickly varying in space, with comparatively large characteristic wavenumbers k: k>1/H, is considered. H is the scale of density and pressure reduction in unperturbed gas, as the coordinate (H is the so-called height of the uniform equilibrium gas). Coupling nonlinear equations which govern the sound and the entropy mode in a weakly nonlinear flow are derived. They describe the dynamics...
-
A Novel Approach to Fully Nonlinear Mathematical Modeling of Tectonic Plates
PublikacjaThe motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the...
-
Nonlinear Interaction of Magnetoacoustic Modes in a Quasi-Isentropic Plasma Flow
PublikacjaThe nonlinear interaction of magnetoacoustic waves in a plasma is analytically studied. A plasma is an open system. It is affected by the straight constant equilibrium magnetic flux density forming constant angle with the wave vector which varies from 0 till . The nonlinear instantaneous equation which describes excitation of secondary wave modes in the field of intense magnetoacoustic perturbations is derived by use of projecting....
-
NONLINEAR VIBRATION ANALYSIS OF BEAM AND PLATE WITH CLOSED CRACK: A REVIEW
PublikacjaThe effect of nonlinearity is high sensitivity in damage detection, especially for closed cracks and delamination. This review illustrates the results of several researchers dealing with nonlinear effects caused by the closure of cracks in the structure, i.e., beam and plate structures. Early detection of damage is an important aspect for the structure and, therefore, continuous progress is being made in developing new and effective...
-
Nonlinear increase in bubbles radii caused by sound in a bubbly liquid
PublikacjaThe nonlinear interaction of acoustic and entropy modes in a bubbly liquid is considered. The reasons for interaction are both nonlinearity and dispersion. In the field of intense sound, a decrease in the mixture density is predicted. That corresponds to the well-established growth of bubbles volumes due to rectified diffusion. The nonlinear interaction of modes as a reason for a bubble to grow due to sound, is discovered. The...
-
Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublikacjaThe focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow...
-
Nonlinear fuzzy control of the dissolved oxygen in activated sludge processes
PublikacjaWastewater treatment plant is generally a complex, multivariable, time varying and nonlinear large scale industrial system. Moreover, interactions between the components are very strong. The dissolved oxygen tracking problem is one of the most complex and fundamental issues of biological processes. Air for the aerated tanks is supplied by aeration system (blowers, pipes, diffusers). It is a complex dynamic system. The new control...
-
Certain family of analytical solutions of nonlinear von Neumann equations
PublikacjaIn this paper we present a slight generalization of certain type of Darboux transformation, that may be used sub-sequently in a convenient way. This method allows to obtain families of solutions of nonlinear von Neumann equations, that are used in particular in DNA modeling.
-
Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation
PublikacjaTwo nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It...
-
On rotational instability within the nonlinear six-parameter shell theory
PublikacjaWithin the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which oc- curs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we con- sidered here both large translations and rotations. The constitutive relations contain some additional mi- cropolar parameters...
-
On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublikacjaWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
-
Control of nonlinear and linearized model of self-balancing electric motorcycle
PublikacjaSelf-Balancing Electric Motorcycle (SBEM) is a dynamic and nonlinear electro-mechanical system. In this paper, the process of mathematical modelling and line-arization of SBEM is presented. The model of the control system in Matlab envi-ronment is implemented. The control system using the PID controller is designed. The operation of particular structures of the PID controller on the simulation model is compared. Due to simulation...
-
Elastoplastic material law in 6-parameter nonlinear shell theory
PublikacjaWe develop the elastoplastic constitutive relations for nonlinear exact 6-parameter shell theory. A J2-type theory with strain hardening is formulated that takes into account asymmetric membrane strain measures. The incremental equations are solved using implicit Euler scheme with closest point projection algorithm. The presented test example shows the correctness of the proposed approach. Influence of micropolar material parameters...