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Wyniki wyszukiwania dla: NONLINEAR ADVECTION EQUATIONS
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On the Nonlinea Distortions of Sound and its Coupling with Other Modes in a Gasesous Plasma with Finite Electric Conductivity in a Magnetic Field
PublikacjaNonlinear phenomena of the planar and quasi-planar magnetoacoustic waves are considered. We focus on deriving of equations which govern nonlinear excitation of the non-wave motions by the intense sound in initially static gaseous plasma. The plasma is treated as an ideal gas with finite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. This introduces dispersion of a flow. Magnetoacoustic...
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Dane BadawczeThe presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Dane BadawczePresented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...
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Zastosowanie odcinków nieliniowej krzywizny w torze zwrotnym rozjazdu kolejowego
PublikacjaW pracy została przedstawiona analityczna metoda kształtowania toru zwrotnego rozjazdu kolejowego posiadającego na swojej długości odcinki nieliniowej krzywizny. Odcinki te służą łagodzeniu wykresu krzywizny w skrajnych strefach rozjazdu W omawianej metodzie dokonano identyfikacji problemu rozkładu krzywizny za pomocą równań różniczkowych. Uzyskane rozwiązania mają charakter uniwersalny; m. in. pozwalają na przyjmowanie dowolnych...
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Numerical Methods
Kursy OnlineNumerical Methods: for Electronics and Telecommunications students, Master's level, semester 1 Instructor: Michał Rewieński, Piotr Sypek Course description: This course provides an introduction to computational techniques for the simulation and modeling of a broad range of engineering and physical systems. Concepts and methods discussed are widely illustrated by various applications including modeling of integrated circuits,...
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Wybrane elementy nieliniowej dynamiki struktur kratowych
PublikacjaW pracy jest dyskutowany problem nieliniowej dynamiki struktur kratowych. Zastosowano stacjonarny opis Lagrange'a (ang. Total Lagrange), pokazano silne i słabe sformułowanie dla pręta kratowego, jego aplikację do MES. W zakresie całkowania równań ruchu przedstawiono metodę Newmarka i metodę-a dla problemów liniowych i nieliniowych. Załączony przykład numeryczny ilustruje cechy przedstawionych metod.
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Determination of time delay between ventricles contraction using impedance measurements
PublikacjaThe paper presents a novel approach to assessment of ventricular dyssynchrony basing on multichannel electrical impedance measurements. Using a proper placement of electrodes, the sensitivity approach allows estimating time difference between chambers contraction from over determined nonlinear system of equations. The theoretical considerations which include Finite Element Method simulations were verified using measurements on...
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Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by ε-Approximate Fixed-Point Method
PublikacjaIn this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline vh defined by its values vi = vh(ti) at grid points ti, i = 0, 1, ... ,N. The necessary for construction the cubic spline and missing the first derivatives at the boundary...
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Analysis of nonlinear eigenvalue problems for guides and resonators in microwave and terahertz technology
PublikacjaThis dissertation presents developed numerical tools for investigating waveguides and resonators' properties for microwave and terahertz technology. The electromagnetics analysis requires solving complex eigenvalue problems, representing various parameters such as resonant frequency or propagation coefficient. Solving equations with eigenvalue boils down to finding the roots of the determinant of the matrix. At the beginning, one...
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Modelling of joining route segments of differential curvature
PublikacjaThe paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph...
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MAGNETOACOUSTIC HEATING AND STREAMING IN A PLASMA WITH FINITE ELECTRICAL CONDUCTIVITY
PublikacjaNonlinear effects of planar and quasi-planar magnetosound perturbations are discussed. Plasma is assumed to be an ideal gas with a finite electrical conductivity permeated by a magnetic filed orthogonal to the trajectories of gas particles. the excitation of non-wave modes in the filed of intense magnetoacoustic perturbations, i.e., magnetoaciustic heating and streaming, is discussed. The analysis includes a derivation if instantaneous...
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On the generalized model of shell structures with functional cross-sections
PublikacjaIn the present study, a single general formulation has been presented for the analysis of various shell-shaped structures. The proposed model is comprehensive and a variety of theories can be used based on it. The cross-section of the shell structure can be arbitrarily analyzed with the presented equations. In other words, various types of shell structures, including cylindrical, conical, spherical, elliptical, hyperbolic, parabolic,...
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Introduction to Numerical Simulation
Kursy OnlineCourse description: This interdisciplinary course provides an introduction to computational techniques for the simulation of a broad range of engineering and physical systems. Concepts and methods discussed are widely illustrated by applications drawn from electrical, mechanical, and chemical engineering. Topics include: mathematical formulations of simulation problems; sparse direct and iterative linear system solution techniques,...
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Modeling and simulation of blood flow under the influence of radioactive materials having slip with MHD and nonlinear mixed convection
PublikacjaRadioactive materials are widely in industry, nuclear plants and medical treatments. Scientists and workers in these fields are mostly exposed to such materials, and adverse effects on blood and temperature profiles are observed. In this regard, objective of the current study is to model and simulate blood based nanofluid with three very important radioactive materials, named as Uranium dioxide (UO2), Thorium dioxide (ThO2) and...
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generation of the vorticity mode by sound in a bingham plastic
PublikacjaThis study investigates interaction between acoustic and non-acoustic modes, such as vorticity mode,in some class of a non-newtonian fluid called Bingham plastic. The instantaneous equations describinginteraction between different modes are derived. The attention is paid to the nonlinear effects in the fieldof intense sound. The resulting equations which describe dynamics of both sound and the vorticity modeapply to both periodic...
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublikacjaIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublikacjaThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublikacjaThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublikacjaIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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State Observer for Doubly-fed Induction Generator
PublikacjaIn the paper a new state observer for doubly-fed generator has been proposed. In the new approach an extended mathematical model of the doubly fed generator is used to form equations of the introduced z type observer. Stability of the observer has been verified through poles placement analyses. The active and reactive powers of the generator are controlled by a nonlinear multiscalar control method. Simulation and experimental results...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublikacjaIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublikacjaIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Higher harmonics of the intensity modulated Photocurrent/Photovoltage spectroscopy response - a tool for studying photoelectrochemical nonlinearities
PublikacjaIn this work, a higher harmonic analysis (HHA) of the intensity modulated photocurrent/photovoltage (IMPS/IMVS) spectroscopy data is proposed as a potent tool for studying nonlinear phenomena in photoelectrochemical and photovoltaic systems. Analytical solutions of kinetic equations were constructed for cases of single and double resonance accounting for various sources of higher harmonics. These sources correspond to the physical...
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Excitation of Non-Wave Modes by Sound of Arbitrary Frequency in a Chemically Reacting Gas
PublikacjaThe nonlinear phenomena in the field of high intensity sound propagating in a gas with a chemical reaction, are considered. A chemical reaction of A → B type is followed by dispersion and attenuation of sound which may be atypical during irreversible thermodynamic processes under some conditions. The first and second order derivatives of heat produced in the chemical reaction evaluated at the equilibrium temperature, density and...
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Ultrashort Opposite Directed Pulses Dynamics with Kerr Effect and Polarization Account
PublikacjaWe present the application of projection operator methods to solving the problem of the propagation and interaction of short optical pulses of different polarizations and directions in a nonlinear dispersive medium. We restrict ourselves by the caseof one-dimensional theory, taking into account material dispersion and Kerr nonlinearity. The construction of operators is delivered in two variants: for the Cauchy problem and for the...
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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...
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Computationally Effcient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems
PublikacjaThis paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed...
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublikacjaThe paper presents the neutron point kinetics and heat exchange models for the nuclear reactor. The models consist of a nonlinear system of fractional ordinary differential and algebraic equations. Two numerical algorithms are used to solve them. The first algorithm is application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. The second involves building an analog scheme in the FOMCON Toolbox...
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Genetic Algorithm Approach for Gains Selection of Induction Machine Extended Speed Observer
PublikacjaThe subject of this paper is gains selection of an extended induction machine speed observer. A high number of gains makes manual gains selection difficult and due to nonlinear equations of the observer, well-known methods of gains selection for linear systems cannot be applied. A method based on genetic algorithms has been proposed instead. Such an approach requires multiple fitness function calls; therefore, using a quality index...
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Standing Waves and Acoustic Heating (or Cooling) in Resonators Filled with Chemically Reacting Gas
PublikacjaStanding waves and acoustic heating in a one-dimensional resonator filled with chemically reacting gas, is the subject of investigation. The chemical reaction of A ! B type, which takes place in a gas, may be reversible or not. Governing equations for the sound and entropy mode which is generated in the field of sound are derived by use of a special mathematical method. Under some conditions, sound waves propagating in opposite...
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An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
PublikacjaAn isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space R3, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive equations without zero...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
PublikacjaIn this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element method (f-SEM) and fractional Finite element method (f-FEM) are crucial in various branches of science and play a significant role. In this review, we discuss the advantages and adaptability of FEM and SEM, which provide the simulations of fractional...
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On time-dependent nonlinear dynamic response of micro-elastic solids
PublikacjaA new approach to the mechanical response of micro-mechanic problems is presented using the modified couple stress theory. This model captured micro-turns due to micro-particles' rotations which could be essential for microstructural materials and/or at small scales. In a micro media based on the small rotations, sub-particles can also turn except the whole domain rotation. However, this framework is competent for a static medium....
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Krzysztof Jamroziak Prof. dr hab. inż.
OsobyKrzysztof Jamroziak is Full Professor of the Wroclaw University of Scinece and Technology in Department Mechanic, Materials and Biomedical Engineering. His interests relate to composite materials, mechanical properties, ballistic impact, ballistic shields, nonlinear dynamics, strength of composite materials. Attention is focused on research on innovative composite structures subjected to impact loads, physico-mechanical properties...
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Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance
PublikacjaThe impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made...
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Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator
PublikacjaIn the paper, numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator...
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Discussion of “Development of an Accurate Time integration Technique for the Assessment of Q-Based versus h-Based Formulations of the Diffusion Wave Equation for Flow Routing” by K. Hasanvand, M.R. Hashemi and M.J. Abedini
PublikacjaThe discusser read the original with great interest. It seems, however, that some aspects of the original paper need additional comments. The authors of the original paper discuss the accuracy of a numerical solution of the diffusion wave equation formulated with respect to different state variables. The analysis focuses on nonlinear equations in the form of a single transport equation with the discharge Q (volumetric flow rate)...
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Asynchronous Method of Simultaneous Object Position and Orientation Estimation with Two Transmitters
PublikacjaThis paper proposes an object location method for all types of applications, including the Internet of Things. The proposed method enables estimations of the position and orientation of an object on a plane or in space, especially during motion, by means of location signals transmitted simultaneously from two transmitters placed on the object at a known distance from each other. A mathematical analysis of the proposed method and...
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An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split
PublikacjaThis work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system,which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff–Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface...
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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...
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Nieliniowa statyka 6-parametrowych powłok sprężysto plastycznych. Efektywne obliczenia MES
PublikacjaGłównym zagadnieniem omawianym w monografii jest sformułowanie sprężysto-plastycznego prawa konstytutywnego w nieliniowej 6-parametrowej teorii powłok. Wyróżnikiem tej teorii jest występujący w niej w naturalny sposób tzw. stopień 6 swobody, czyli owinięcie (drilling rotation). Podstawowe założenie pracy to przyjęcie płaskiego stanu naprężenia uogólnionego na ośrodek typu Cosseratów. Takie podejście stanowi oryginalny aspekt opracowania....
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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...
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Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force
PublikacjaIn this article, we have tried to simulate nonlinear bending analysis of a double-layered graphene sheet which contains a geometrical imperfection based on an eccentric hole. The first-order shear deformation theory is considered to obtain the governing equations. Also, the nonlinear von Kármán strain field has been assumed in order to obtain large deformations. Whereas the double-layered graphene sheet has been considered, the...
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Mechanical simulation of artificial gravity in torus-shaped and cylindrical spacecraft
PublikacjaLarge deformations and stress analyses in two types of space structures that are intended for people to live in space have been studied in this research. The structure under analysis is assumed to rotate around the central axis to create artificial gravitational acceleration equal to the gravity on the Earth's surface. The analysis is fully dynamic, which is formulated based on the energy method by using the first-order shear deformation...
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Buckling Analysis of a Micro Composite Plate with Nano Coating Based on the Modified Couple Stress Theory
PublikacjaThe present study investigates the buckling of a thick sandwich plate under the biaxial non-uniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (S-FSDT) is employed and the governing differential...
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Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory
PublikacjaIn the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle into account. On the other hand, a...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublikacjaWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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Forced vibrations in a dynamic system that is damped by a mechanism that trans-pass through its singular position
PublikacjaIn the paper, vibrations of a hybrid multibody-continuous system are investigated. For all the mechanical devices, effective damping methods are crucial in the design process. To obtain it, installation of viscous dampers or elasto-viscous elements is dominant. In the paper, an alternative method is investigated. It is based on modal disparity. To describe the method briefly, when structural damping is present in continuous systems,...
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On analysis of nanocomposite conical structures
PublikacjaThis research examines the analysis of rotating truncated conical baskets reinforced by carbon nanotubes around the two independent axes. A time-dependent analysis is considered, and the nonlinear dynamic governing equations are extracted using the energy method. Carbon nanotubes (CNTs) reinforced the conical basket, and the structure's mechanical properties are determined based on the several distributions of carbon nanotubes....
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On instabilities and post-buckling of piezomagnetic and flexomagnetic nanostructures
PublikacjaWe focus on the mechanical strength of piezomagnetic beam-like nanosize sensors during post-buckling. An effective flexomagnetic property is also taken into account. The modelled sensor is selected to be a Euler-Bernoulli type beam. Long-range interactions between atoms result in a mathematical model based on the nonlocal strain gradient elasticity approach (NSGT). Due to possible large deformations within a post-buckling phenomenon,...