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Wyniki wyszukiwania dla: NONLINEAR ADVECTION EQUATIONS
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Modeling of Composite Shells in 6-Parameter Nonlinear Theory with Drilling Degree of Freedom
PublikacjaWithin the framework of a 6-parameter nonlinear shell theory, with strain measures of Cosserat type, constitutive relations are proposed for thin elastic composite shells. The material law is expressed in terms of five engineering constants of classical anisotropic continuum plus an additional parameter accounting for drilling stiffness. The theory allows for unlimited displacements and rotations. A number of examples are presented...
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On the Nonlinear Effects of Magnetoacoustic Perturbations in a Perfectly Conducting Viscous and Thermoconducting Gas
PublikacjaNonlinear effects of planar and quasi-planar magnetosound perturbations are discussed. The plasma is as- sumed to be a Newtonian thermoconducting gas with infinite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. Generation of the non-wave modes (magnetoacoustic heating and streaming) in the field of periodic and aperiodic magnetoacoustic perturbations is discussed. The results...
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Investigations of the optical activity of nonlinear crystals by means of dual-wavelength polarimeter
PublikacjaA dual-wavelength method in high accuracy polarimetry has been successfully tested and applied to measure optical activity (OA) of nonlinear crystals. In proposed polarimetric scheme two neighboring semiconductor laser wavelengths (635 and 650 nm) are used, which increases number of parameters measured simultaneously and improves the data processing. By neglecting dispersion of eigen wave ellipticity in crystals, more efficient...
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Simplified Dirac--Coulomb Equations
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On dynamic equations with deviating arguments
PublikacjaPraca dotyczy istnienia rozwiązań równań dynamicznych z odchylonymi argumentami. Podane zostały warunki dostateczne na istnienie rozwiązania. Dwa przykłady ilustrują otrzymane wyniki.
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Differential equations with delayed arguments
PublikacjaPraca dotyczy problemów brzegowych dla równań różniczkowych z opóźnionymi argumentami. Podane zostały warunki dostateczne na istnienie jednego rozwiązania bądź rozwiązań ekstremalnych. Dyskusja dotyczy również nierówności różniczkowych. Przykłady ilustrują otrzymane wyniki.
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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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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.
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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...
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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...
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Effectiveness of a mathematical model in simulating nonlinear mechanical behaviour of a seismic isolation system made of polymeric bearings
PublikacjaThe present study was focused on determining the effectives of a nonlinear mathematical model in simulating complex mechanical behaviour of a seismic isolation system made of Polymeric Bearings. The proposed mathematical model defines the lateral force as a nonlinear function of the shear displacement and the deformation velocity. The effectiveness of the proposed mathematical model was verified by comparing the seismic response...
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A measurement system for nonlinear surface spectroscopy with an atomic force microscope during corrosion process monitoring
PublikacjaIn addition to traditional imaging the surface, atomic force microscopy (AFM) enables wide variety of additional measurements. One of them is higher harmonic imaging. In tapping mode the nonlinear contact between tip and specimen results in higher frequency vibrations. More information available from the higher harmonics analysis proves to be helpful for more detailed imaging. Such visualization is espe-cially useful for heterogeneous...
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Linear Time-Varying Dynamic-Algebraic Equations of Index One on Time Scales
PublikacjaIn this paper, we introduce a class of linear time-varying dynamic-algebraic equations (LTVDAE) of tractability index one on ar- bitrary time scales. We propose a procedure for the decoupling of the considered class LTVDAE. Explicit formulae are written down both for transfer operator and the obtained decoupled system. A projector ap- proach is used to prove the main statement of the paper and sufficient conditions of decoupling...
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Studies of Nonlinear Sound Dynamics in Fluids Based on the Caloric Equation of State
PublikacjaThe sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting...
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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...
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Multiple Solutions to Third-Order Differential Equations with Derivative Dependence and Deviating Arguments
PublikacjaIn this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J ⊂ [0,1] and advanced...
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Nonlinear Biomedical Physics
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Nonlinear Analysis Forum
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Results in Nonlinear Analysis
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NONLINEAR PROCESSES IN GEOPHYSICS
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Nonlinear Physical Science
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JOURNAL OF NONLINEAR SCIENCE
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Novel hierarchical nonlinear control algorithm to improve dissolved oxygen control in biological WWTP
PublikacjaWastewater treatment is a problem known to humankind for centuries. The quality of treated sewage determines the condition of reservoirs around the world. Control of such a complex and nonlinear system as a wastewater treatment plant requires thorough knowledge of the process. The paper presents a hierarchical control system of a Sequencing Batch Reactor (SBR) in Wastewater Treatment Plant (WWTP) taking into account a model based...
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Nonlinear material identification of heterogeneous isogeometric Kirchhoff–Love shells
PublikacjaThis work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous materialdistributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable fordescribing incompressible material behavior as well as initially curved shells. The material distribution is discretized by bilinearelements such that the nodal values...
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Mitigating the seismic pounding of multi-story buildings in series using linear and nonlinear fluid viscous dampers
PublikacjaSeismic-induced pounding between adjacent buildings may have serious consequences, ranging from minor damage up to total collapse. Therefore, researchers try to mitigate the pounding problem using different methods, such as coupling the adjacent buildings with stiff beams, connecting them by using viscoelastic links, and installing damping devices in each building individually. In the current paper, the effect of using linear and...
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ON DYNAMICS OF ELASTIC NETWORKS WITH RIGID JUNCTIONS WITHIN NONLINEAR MICRO-POLAR ELASTICITY
PublikacjaWithin the nonlinear micropolar elasticity we discuss effective dynamic (kinetic) properties of elastic networks with rigid joints. The model of a hyperelastic micropolar continuum is based on two constitutive relations, i.e., static and kinetic ones. They introduce a strain energy density and a kinetic energy density, respectively. Here we consider a three-dimensional elastic network made of three families of elastic fibers connected...
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Linear and nonlinear impedance of iron containing silicate glasses
Dane BadawczeThe linear and nonlinear impedance ofglasses doped with iron oxide were measured. Glass samples (50 SiO2-50-xPbO-xFe2O3 in mol%) were prepared by the conventional melt quenching technique. The substrates were powdered in a mortar and melted in Al2O3 crucibles. The melting was conducted in air at 1623K. The melts were poured out on plate heated up to...
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Drilling couples and refined constitutive equations in the resultant geometrically non-linear theory of elastic shells
PublikacjaIt is well known that distribution of displacements through the shell thickness is non-linear, in general. We introduce a modified polar decomposition of shell deformation gradient and a vector of deviation from the linear displacement distribution. When strains are assumed to be small, this allows one to propose an explicit definition of the drilling couples which is proportional to tangential components of the deviation vector....
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Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions
PublikacjaIn this paper we investigate integral boundary value problems for fourth order differentialequations with deviating arguments.Wediscuss our problem both for advanced or delayedarguments. We establish sufficient conditions under which such problems have positivesolutions. To obtain the existence of multiple (at least three) positive solutions, we use afixed point theorem due to Avery and Peterson. An example is also included to...
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Positive solutions for fourth-order differential equations with deviating arguments and integral boundary conditions
PublikacjaBadane są problemy brzegowe dla równań różniczkowych rzędu czwartego z odchylonymi argumentami i z warunkami brzegowymi typu całkowego. Sformułowano twierdzenie dotyczące istnienia dodatnich rozwiązań takich problemów. W dowodzie korzystano z tw. Avery-Petersona o punktach stałych dla stożków. Podano przykład ilustrujący otrzymane wyniki.
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Variational principles for bound states of Schrödinger and Dirac equations allowing the use of discontinuous trial functions
PublikacjaWe present systematic constructions of variational principles for energies of bound states of the Schroedinger and Dirac equations. The principles allow the use of discontinuous trial functions. The method employed is based on a generalized Lagrange procedure. Relationships between our variational principles and those available in the literature are established.
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Numerical analysis of open channel steady gradually varied flow using the simplified saint-venant equations
PublikacjaFor one-dimensional open-channel flow modeling, the energy equation is usually used. There exist numerous approaches using the energy equation for open-channel flow computations, which resulted in the development of several very efficient methods for solving this problem applied to channel networks. However, the dynamic equation can be used for this purpose as well. This paper introduces a method for solving a system of non-linear...
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Nonlinear Modeling in Time Domain Numerical Analysis of Stringed Instrument Dynamics
PublikacjaMusical instruments are very various in terms of sound quality with their timbre shaped by materials and geometry. Materials' impact is commonly treated as dominant one by musicians, while it is unclear whether it is true or not. The research proposed in the study focuses on determining influence of both these factors on sound quality based on their impact on harmonic composition. Numerical approach has been chosen to allowed independent...
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Accuracy of Trajectory Tracking Based on Nonlinear Guidance Logic for Hydrographic Unmanned Surface Vessels
PublikacjaA new trend in recent years for hydrographic measurement in water bodies is the use of unmanned surface vehicles (USVs). In the process of navigation by USVs, it is particularly important to control position precisely on the measuring profile. Precise navigation with respect to the measuring profile avoids registration of redundant data and thus saves time and survey costs. This article addresses the issue of precise navigation...
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Nonlinear free and forced vibrations of a dielectric elastomer-based microcantilever for atomic force microscopy
PublikacjaThe majority of atomic force microcode (AFM) probes work based on piezoelectric actuation. However, some undesirable phenomena such as creep and hysteresis may appear in the piezoelectric actuators that limit their applications. This paper proposes a novel AFM probe based on dielectric elastomer actuators (DEAs). The DE is modeled via the use of a hyperelastic Cosserat model. Size effects and geometric nonlinearity are included...
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Nonlinear secondary arc model use for evaluation of single pole auto-reclosing effectiveness
PublikacjaPurpose – The purpose of this paper is to discuss two evaluation methods of single pole autoreclosing process effectiveness in HV transmission lines. Secondary arc current and recovery voltage results obtained by load flow calculation are compared to the results obtained by the time domain simulations. Moreover, a nonlinear secondary arc implementation is presented. Design/methodology/approach – A computer simulation studies were...
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Explicit and implicit difefrence methods for quasilinear first order partial functional differential equations.
PublikacjaInitial boundary value problems of the Dirichlet type for quasilinear functional differential equations are considered. Explicit difference schemes of the Euler type and implicit difference methods are investigated. Suffcient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both classes...
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Ordinary differential equations with deviated arguments
PublikacjaPraca dotyczy istnienia i przybliżonych rozwiązań dla problemów brzegowych z opóźnionymi oraz wyprzedzonymi argumentami. Dyskutowano też pewne nierówności różniczkowe powyższego typu.
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Approximate methods for functional differential equations
PublikacjaW pracy przedstawione są dwie klasy przybliżonych metod rozwiązywania równań różniczkowo funkcyjnych ze szczególnym uwzględnieniem równań różniczkowych z opóźnieniem. Do pierwszej klasy należą metody bezpośrednie reprezentowane w przedkładanej rozprawie przez dwukrokowe metody Rungego-Kutty. Należą one do klasy ogólnych metod liniowych rozwiązywania równań różniczkowych. Druga klasę przybliżonych metod rozwiązywania równań różniczkowo...
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Scalar- and vector-source wave equations
PublikacjaW analizie zjawisk akustyki liniowej i obliczeniach pola, powszechnie stosowane są równania falowe skalarne dotyczące ciśnienia akustycznego lub potencjału prędkości, natomiast rzadko są choćby tylko wspominane równania wektorowe operujące prędkością cząstek. Jest to przejaw asymetrii w traktowaniu skalarnych i wektorowych wielkości akustycznych. Artykuł przypomina dwa zestawy dualnych równań falowych, jednorodnych i niejednorodnych,...
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On some constitutive equations for micropolar plates
PublikacjaW pracy porównano równania konstytutywne dla płyt podane przez Altenbacha i Eremeyeva. Na podstawie ich wyprowadzeń określono zakres zmienności współczynnika momentów owinięcia i jego możliwy wpływ na wyniki otrzymane w rozwiązaniach MES w zakresie liniowym
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First-order advanced difference equations
PublikacjaBadano istnienie rozwiązań równań różnicowych rzędu pierwszego z wyprzedzonymi argumentami. Podano warunki na istnienie jedynego rozwiązania. Przedmiotem badań były też nierówności różnicowe związane z w/w równaniami różnicowymi. Otrzymane wyniki zilustrowano na przykładzie.
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Fractional differential equations with deviating arguments
PublikacjaDla równań różniczkowych typu ułamkowego, zostały podane warunki dostateczne na istnienie jednego rozwiązania lub rozwiazań ekstremalnych. Nierówności różniczkowe są też doskutowane.
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On delay differential equations with boundary conditions
PublikacjaPodano warunki na istnienie rozwiązania zagadnienia brzegowego typu opóźnionego, zakładając pewne warunki monotoniczności funkcji występującej po prawej stronie naszego zagadnienia. Pokazano, że dwa ciągi monotoniczne są zbieżne do rozwiązania dokładnego.
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Functional differential equations of second order.
PublikacjaPraca dotyczy problemu brzegowego dla równań różniczkowo-funkcyjnych 2-go rzędu. Stosując metodę kwasilinearyzacji pokazano, że odpowiednio skonstruowane ciągi monotoniczne są zbieżne do jedynego rozwiązania danego problemu i ustalono szybkość tej zbieżności. Pokazano również pewną relację pomiędzy rozwiązaniami odpowiednich liniowych równań różniczkowo-funkcyjnych z warunkami brzegowymi.
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Systems of differential equations with a singular matrix
PublikacjaPraca dotyczy układów równań różniczkowych z macierzą osobliwą. Szczególnymi przypadkami takich układów są równania różniczkowo-algebraiczne. Korzystając z odpowiedniej nierówności różniczkowej dla układów równań i metody quasi linearyzacji pokazano, iż odpowiednie monotoniczne ciągi są zbieżne do rozwiązania naszego problemu i jest to zbieżność kwadratowa. O funkcji f występującej po prawej stronie zagadnienia zakładano...
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Differential equations with integral boundary conditions
PublikacjaStosuje się metodę iteracji monotonicznych opartą na dolnym i górnym rozwiązaniu. Przy jednostronnym warunku Lipschitza uzyskano pewne wyniki dotyczące rozwiązań zwyczajnych równań różniczkowych z całkowym warunkiem brzegowym. Sformułowano warunki dostateczne na istnienie jedynego rozwiązania (lub rozwiązań ekstremalnych) w pewnym segmencie. Podano przykłady ilustrujące przyjęte założenia.
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On integro-differential equations with delayed arguments
PublikacjaPraca dotyczy problemów różniczkowo-całkowych z warunkami początkowymi oraz brzegowymi typu okresowego. Podano warunki na istnienie i jednoznaczność rozwiązania. Badania dotyczyły również nierówności różniczkowo-całkowych z argumentami typu opóżnionego. Podano przykłady, które mogą mieć zastosowanie w problemach inżynierskich.
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Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
PublikacjaWe propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...
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Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
PublikacjaWe propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...