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Journal of the Alamire Foundation
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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
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The application of nonlinear curvature sections in the turnout diverging track
PublicationThe 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
PublicationWe 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
PublicationWithin 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...
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Project management for the construction sector in the field of foundation of buildings in complex conditions of the subsoil
PublicationAutorzy: Gwóźdź-Lasoń Monika, Kohutek...
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Features of Nonlinear Sound Propagation in Vibrationally Excited Gases
PublicationWeakly 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...
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Nonlinear Influence of Sound on the Vibrational Energy of Molecules in a Relaxing Gas
PublicationDynamics 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...
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SHORT REVIEW AND 3-D FEM ANALYSIS OF BASIC TYPES OF FOUNDATION FOR OFFSHORE WIND TURBINES
PublicationSome problems of the foundations of offshore wind turbines are considered in this paper. A short review is presented on the two basic types of foundations, i.e. monopiles and gravity foundations, including their basic features and applications as well as general design considerations. Also, some issues regarding analysis are discussed, including geotechnical problems and modelling techniques. A numerical model of offshores turbine...
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Nonlinear phenomena of small-scale sound in a gas with exponential stratification
PublicationThe 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...
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A Novel Approach to Fully Nonlinear Mathematical Modeling of Tectonic Plates
PublicationThe 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...
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Nonlinear Interaction of Magnetoacoustic Modes in a Quasi-Isentropic Plasma Flow
PublicationThe 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....
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NONLINEAR VIBRATION ANALYSIS OF BEAM AND PLATE WITH CLOSED CRACK: A REVIEW
PublicationThe 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...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn 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...
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Nonlinear increase in bubbles radii caused by sound in a bubbly liquid
PublicationThe 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...
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A comparison of the spectrophotometric Winkler method and HPLC technique in the determination of 5-Hydroxymethylfurfural in natural honey
PublicationPorównano technikę HPLC i klasyczną metodę spektrofotometryczną Winklera pod względem odzysku, precyzji, wykrywalności i oznaczalności 5-hydroksymetylofurfuralu (HMF) w miodach naturalnych. Zawartości HMF obiema metodami oznaczono w 15 różnych miodach naturalnych. Sześć miodów pochodziło z trójmiejskich punktów handlowych, 9 miodów pozyskano bezpośrednio od pszczelarzy z sześciu pasiek. Testem t-Studenta oszacowano istotność różnic...
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Olgun Aydin dr
PeopleOlgun Aydin finished his PhD by publishing a thesis about Deep Neural Networks. He works as a Principal Machine Learning Engineer in Nike, and works as Assistant Professor in Gdansk University of Technology in Poland. Dr. Aydin is part of editorial board of "Journal of Artificial Intelligence and Data Science" Dr. Aydin served as Vice-Chairman of Why R? Foundation and is member of Polish Artificial Intelligence Society. Olgun is...
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Generalized Euler method for nonlinear first order partial differential equations.
PublicationKlasyczne rozwiązania nieliniowych równań różniczkowych cząstkowych pierwszego rzędu są aproksymowane w tej pracy za pomocą rozwiązań quasiliniowych układów równań różnicowych. Podstawowa idea pracy jest oparta na teorii charakterystyk. Podane są warunki wystarczające dla zbieżności metody. Dowód stabilności schematu różnicowego wykorzystuje metodę porównawczą z nieliniowymi oszacowaniami typu Perrona dla danych funkcji.Podane...
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Optical rotation in the lithium triborate nonlinear crystal
PublicationA 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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Nonlinear resultant theory of shells accounting for thermodiffusion
PublicationThe 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...
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Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublicationThe 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...
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Nonlinear Engineering
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On the Nonlinear Effects of Magnetoacoustic Perturbations in Optically Thin Quasi-Isentropic Plasmas
PublicationNonlinear effects of planar magnetosound perturbations in a plasma are discussed. Plasma is non-adiabatic due to optically thin radiation and external heating. For these reasons, thermal instability of a plasma may appear which makes it acoustically active. The plasma is assumed to be initially homogeneous ideal gas with infinite electrical conductivity permeated by a straight magnetic field which is orthogonal to the trajectories...
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Nonlinear fuzzy control of the dissolved oxygen in activated sludge processes
PublicationWastewater 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...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn 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...
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Certain family of analytical solutions of nonlinear von Neumann equations
PublicationIn 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.
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Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation
PublicationTwo 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...
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Direct estimation of linear and nonlinear functionals of quantum state
PublicationWe 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...
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Method of lines for nonlinear first order partial functional differential equations.
PublicationClassical 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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Coupled nonlinear Schrödinger equations in optic fibers theory
PublicationIn 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...
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On rotational instability within the nonlinear six-parameter shell theory
PublicationWithin 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...
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Service and service decomposition model - theoretical foundation of it service management
PublicationThe publication contains different definitions of Service - one of the fundamental IT Service Management term. It describes types of Service attributes nad introduces so-called ''distinguish functions'' in order to propose different categories of Services. It proposes both general model of Service decomposition and practical model based on CMDB implementation limitations. In summarizes obtained results and gives some remarks about...
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Evaluation of Foundation Input Motions Based on Kinematic Interaction Models
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublicationWithin 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.
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Design of novel highly sensitive sensors for crack detection in metal surfaces: theoretical foundation and experimental validation
PublicationThe application of different types of microwave resonators for sensing cracks in metallic structures has been subject of many studies. While most studies have been focused on improving the sensitivity of planar crack sensors, the theoretical foundation of the topic has not been treated in much detail. The major objective of this study is to perform an exhaustive study of the principles and theoretical foundations for crack sensing...
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Geometrically nonlinear analysis of shells - Benchmark problems for Autocad Robot Analysis Professional
PublicationThe aim of this work is to verify the suitability of commercial engineering software for geometrically nonlinear analysis of shells. This paper deals with the static, geometrically nonlinear analysis of shells made of an isotropic material. The Finite Element Method (FEM) is chosen to solve the problem. The results of the commercial software Autocad Robot Structural Analysis Professional (ARSAP) are compared with the litera-ture...
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Nonlinear and linear impedance of bismuth vanadate ceramics and its relation to structural properties
PublicationThe nonlinear and linear electrical properties, topography, and microstructure of bismuth-vanadate ceramics, were studied. The structurewas observed with the use of X-ray diffraction (XRD), scanning electronmicroscopy (SEM), atomic force microscopy (AFM) and confocal microscopy methods. The obtained results showed that ceramic is porous. Two phase transitionswere determinedwith the use of DSC measurements. The linear and nonlinear ac...
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Nonlinear planar modeling of massive taut strings travelled by a force-driven point-mass
PublicationThe planar response of horizontal massive taut strings, travelled by a heavy point-mass, either driven by an assigned force, or moving with an assigned law, is studied. A kinematically exact model is derived for the free boundary problem via a variational approach, accounting for the singularity in the slope of the deflected string. Reactive forces exchanged between the point-mass and the string are taken into account via Lagrange...
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Control of nonlinear and linearized model of self-balancing electric motorcycle
PublicationSelf-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...
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Elastoplastic material law in 6-parameter nonlinear shell theory
PublicationWe 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...
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Existence of solutions with an exponential growth for nonlinear differential-functional parabolic equations
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence.We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution
PublicationAmong various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In...
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Searching of the buried objects into the sea bottom by means of nonlinear acouctic methods
PublicationThe main goal of this paper is to introduce the methodology of preparing the area for investigations that will be carried out at the sea. As the first step there is recognition of the basic method both in the theory as well as experimental investigation. There were taken into account the nonlinear methods. These ones are very promising methods that have very interesting features, very convenient for examinations of the seabed structure....
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Nonlinear Model of Synchronous Generator for Autonomous Electrical Power Systems Analysis
PublicationThis 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...
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Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas
PublicationTwo dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place. are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into...
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Ship Dynamic Positioning Based on Nonlinear Model Predictive Control
PublicationThe presented work explores the simulation test results of using nonlinear model predictive control algorithm for ship dynamic positioning. In the optimization task, a goal function with a penalty was proposed with a variable prediction step. The results of the proposed control algorithm were compared with backstepping and PID. The effect of estimation accuracy on the control quality with the implemented algorithms was investigated....
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Nonlinear Excitation of the Non-Wave Perturbations by the Magnetoacoustic Waves in the Non-Isentropic Plasma
PublicationNonlinear excitation of slow modes by the planar magnetosonic perturbations in a plasma is discussed. Plasma is an open system due to radiation and external heating. This may stipulate enhancement of wave perturbations and hence the acoustical activity of plasma. Plasma is assumed to be a homogeneous ideal gas with infinite electrical conductivity. The straight magnetic field is orthogonal to the velocity of fluid’s...
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Nonlinear Fuzzy Control System for Dissolved Oxygen with Aeration System in Sequencing Batch Reactor
PublicationBiological 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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Elastoplastic nonlinear FEM analysis of FGM shells of Cosserat type
PublicationThe paper is a continuation of [1] where the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter (the drilling degree of freedom) was presented. Here the formulation is extended to the elasto-plastic range. The material law is based on Cosserat plasticity and employs the well-known Tamura-Tomota-Ozawa (TTO) [2] mixture...