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Search results for: FRACTIONAL ORDER CIRCUITS MAXWELL’S EQUATIONS RIEMANN-LIOUVILLE DERIVATIVE
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Explicit and implicit difefrence methods for quasilinear first order partial functional differential equations.
PublicationInitial 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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Weighted difference schemes for systems of quasilinear first order partial functional differential equations
PublicationThe paper deals with initial boundary value problems of the Dirichlet type for system of quasilinear functional differential equations. We investigate weighted difference methods for these problems. A complete convergence analysis of the considered difference methods is given. Nonlinear estimates of the Perron type with respect to functional variables for given functions are assumed. The proof of the stability of difference problems...
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On the derivative of associated Le.gendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
PublicationW pracy podano szereg zamkniętych wyrażeń dla pochodnej stowarzyszonej funkcji Legendre'a o stopniu (dolnym indeksie) całkowitym względem jej rzędu (górnego indeksu). Wyniki zastosowano do wyprowadzenia kilku nowych reprezentacji, w tym typu Rodriguesa, stowarzyszonych funkcji Legendre'a drugiego rodzaju z całkowityni indeksani.
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On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order).
PublicationWyprowadzono szereg zamkniętych wyrażeń dla pochodnych stowarzyszonej funkcji Legendre'a pierwszego rodzaju względem jej dolnego indeksu w przypadku, gdy górny indeks jest liczbą całkowitą. Wyniki zastosowano do znalezienia pewnych nowych reprezentacji (w tym typu Rodriguesa) stowarzyszonych funkcji Legendre'a drugiego rodzaju o indeksach całkowitych.
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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublicationAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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Positive solutions to second order four-point boundary value problems for impulsive differential equations
PublicationPraca dotyczy problemów brzegowych dla równań różniczkowych drugiego rzędu z impulsami. Podane zostały warunki dostateczne na istnienie trzech dodatnich rozwiązań takich problemów z czteropunktowymi warunkami brzegowymi. W badaniach korzystano z twierdzenia Leggetta-Williamsa.
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Three positive solutions to second-order three-point impulsive differential equations with deviating arguments
PublicationStosując tw. Leggetta-Williamsa, pokazano że rozpatrywany trzypunktowy problem brzegowy z impulsami ma dodatnie rozwiązania (trzy). Otrzymane twierdzenia dotyczą przypadku opóźnionego oraz wyprzedzonego. W pracy podano przykład i pokazano, że przyjęte założenia są spełnione.
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Generalized solution of mixed problems for first order partial differential equations with state dependent delays
PublicationW pracy zostało udowodnione twierdzenie o istnieniu i jednoznaczności rozwiązań dla zagadnień początkowo-brzegowych z cząstkowym równaniem różniczkowo-funkcyjnym z opóźnionym argumentem zależnym od funkcji niewiadomej. Użyto metody bicharakterystyk. Jednoznaczność rozwiązań wykazano metodą porównawczą, istnienie - metodą ciągów przybliżeń.
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Solvability of three point boundary value problems for second order differential equations with deviating arguments
PublicationBadano problem istnienia rozwiązań dla równań różniczkowych rzędu drugiego z trzypunktowymi warunkami brzegowymi. Podano warunki dostateczne dla istnienia ekstremalnych lub kwazi-ekstremalnych rozwiązań powyższych problemów. Przedmiotem badań były również nierówności różniczkowe z odchylonymi argumentami.
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Existence of positive solutions to third order differential equations with advanced arguments and nonlocal boundary conditions
PublicationPraca dotyczy warunków dostatecznych na istnienie dodatnich rozwiązań dla równań różniczkowych z wyprzedzonymi argumentami i warunkami brzegowymi zawierającymi całki Stieltjesa.
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An Efficient Framework For Fast Computer Aided Design of Microwave Circuits Based on the Higher-Order 3D Finite-Element Method
PublicationIn this paper, an efficient computational framework for the full-wave design by optimization of complex microwave passive devices, such as antennas, filters, and multiplexers, is described. The framework consists of a computational engine, a 3D object modeler, and a graphical user interface. The computational engine, which is based on a finite element method with curvilinear higher-order tetrahedral elements, is coupled with built-in...
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Dataset of phase portraits of the fractional prey-predator model with Holling type-II interaction (without predator harvesting)
Open Research DataThe need for a fractional generalization of a given classical model is often due to new behaviors which cannot be taken into account by the model. In this situation, it can be useful to look for a fractional deformation of the initial system, trying to fit the fractional exponent of differentiation in order to catch properly the data.
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Positive solutions of three-point boundary value problems for second order impulsive differential equations with advanced arguments
PublicationW pracy dyskutowano problem istnienia dodatnich rozwiązań dla równań różniczkowych z impulsami rzędu drugiego i z argumentami typu wyprzedzonego. Podano warunki dostateczne na istnienie jednego lub dwóch rozwiązań dodatnich takich zagadnień.
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Positive solutions of one-dimensional p-Laplacian boundary value problems for fourth-order differential equations with deviating arguments
PublicationPraca dotyczy istnienia dodatnich rozwiązań dla równań różniczkowych rzędu czwartego z warunkami brzegowymi z odchylonymi argumentami. Stosując twierdzenie o punkcie stałym dla stożków podano warunki dostateczne na istnienia takich rozwiązań.
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Karolina Lademann mgr
PeopleCurriculum vitae
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An facile Fortran-95 algorithm to simulate complex instabilities in three-dimensional hyperbolic systems
Open Research DataIt is well know that the simulation of fractional systems is a difficult task from all points of view. In particular, the computer implementation of numerical algorithms to simulate fractional systems of partial differential equations in three dimensions is a hard task which has no been solved satisfactorily. Here, we provide a Fortran-95 code to solve...
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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublicationIn this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced....
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Joanna Janczewska prof. dr hab.
PeopleJoanna Janczewska obtained her PhD degree at the University of Gdansk in 2002. From October 1999 to September 2004 she was an assistant at the University of Gdansk. Since October 2004 she has been an assistant professor at the Gdansk University of Technology. Moreover, from October 2008 to September 2010 she had a visiting position in the Institute of Mathematics of the Polish Academy of Sciences. Her mathematical interests...
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A Note on Fractional Curl Operator
PublicationIn this letter, we demonstrate that the fractional curl operator, widely used in electromagnetics since 1998, is essentially a rotation operation of components of the complex Riemann–Silberstein vector representing the electromagnetic field. It occurs that after the wave decomposition into circular polarisations, the standard duality rotation with the angle depending on the fractional order is applied to the left-handed basis vector...
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublicationThis paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme...
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublicationThe 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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Numerical Test for Stability Evaluation of Analog Circuits
PublicationIn this contribution, a new numerical test for the stability evaluation of analog circuits is presented. Usually, if an analog circuit is unstable then the roots of its characteristic equation are localized on the right half-plane of the Laplace s- plane. Because this region is unbounded, we employ the bilinear transformation to map it into the unit disc on the complex plane. Hence, the existence of any root inside the unit disc...
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Marek Czachor prof. dr hab.
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The possibilities for application of new comminution circuits in order to improve technological indexes of KGHM Polska Miedź S.A. copper ore concentrators = Możliwości zastosowania nowych układów rozdrabniania w aspekcie wskaźników technologicznych w warunkach O/ZWR
PublicationArtykuł opisuje zagadnienia związane z efektywnością procesu przygotowania urobku do wzbogacania. Przeanalizowano w nim aktualne układy rozdrabniające, oparte o kruszarki młotkowe i młyny prętowe, jak również warianty układów rozdrabniania z aplikacjami najnowszych rozwiązań techniczno – technologicznych tj. wysokociśnieniowej kruszarki walcowej oraz kruszarki stożkowej. Omawiane aspekty oparte są na badaniach prowadzonych...
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Sensitive Demonstration of the Twin-Core Couplers including Kerr Law Non-Linearity via Beta Derivative Evolution
PublicationTo obtain new solitary wave solutions for non-linear directional couplers using optical meta-materials, a new extended direct algebraic technique (EDAT) is used. This model investigates solitary wave propagation inside a fiber. As a result, twin couplers are the subject of this study. Kerr law is the sort of non-linearity addressed there. Because it offers solutions to problems with large tails or infinite fluctuations, the resulting...
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A Fortran-95 algorithm to solve the three-dimensional Higgs boson equation in the de Sitter space-time
Open Research DataA numerically efficient finite-difference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space-time is designed. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0,1)U(1,2], which considers a generalized potential and a time-dependent diffusion...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublicationIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Numerical and quantitative analysis of HIV/AIDS model with modified Atangana-Baleanu in Caputo sense derivative
PublicationFractional calculus plays an important role in the development of control strategies, the study of the dynamical transmission of diseases, and some other real-life problems nowadays. The time-fractional HIV/AIDS model is examined using a novel method in this paper. Based on the Atangana-concept Baleanu’s of a derivative in the Caputo sense, the current modified fractional derivative operator uses singular and non-local kernels....
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Fractional problems with advanced arguments
PublicationThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
PublicationWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is...
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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublicationThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
PublicationIn 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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Variable Order Differential Models of Bone Remodelling * *This work was supported by FCT, through IDMEC, under LAETA, projects UID/EMS/50022/2013, BoneSys, joint Polish-Portuguese project Modelling and controlling cancer evolution using fractional calculus, PERSEIDS (PTDC/EMS-SIS/0642/2014) and IF/00653/2012
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Karolina Lademann Mgr
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Analiza sterowania ułamkowego PIλDμ mocą reaktora jądrowego
PublicationW artykule przedstawiono syntezę regulatora PIλDμ niecałkowitego rzędu dla potrzeb sterowania mocą reaktora jądrowego lekko wodnego określanego, jako typu PWR (Pressurized Water Reactor). W tym celu wykorzystano nieliniowy model matematyczny reaktora PWR o parametrach skupionych obejmujący procesy generacji i wymiany ciepła oraz termicznych efektów reaktywnościowych. Nastawy regulatora PIλDμ niecałkowitego rzędu dobrano w sposób...
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A review on analytical models of brushless permanent magnet machines
PublicationThis study provides an in-depth investigation of the use of analytical and numerical methods in analyzing electrical machines. Although numerical models such as the finite-element method (FEM) can handle complex geometries and saturation effects, they have significant computational burdens, are time-consuming, and are inflexible when it comes to changing machine geometries or input values. Analytical models based on magnetic equivalent...
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Crank–Nicolson FDTD Method in Media Described by Time-Fractional Constitutive Relations
PublicationIn this contribution, we present the Crank-Nicolson finite-difference time-domain (CN-FDTD) method, implemented for simulations of wave propagation in media described by time-fractional (TF) constitutive relations. That is, the considered constitutive relations involve fractional-order (FO) derivatives based on the Grünwald-Letnikov definition, allowing for description of hereditary properties and memory effects of media and processes....
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Vortex flow caused by periodic and aperiodic sound in a relaxing maxwell fluid
PublicationThis paper concerns the description of vortex flow generated by periodic and aperiodic sound in relaxing Maxwell fluid. The analysis is based on governing equation of vorticity mode, which is a result of decomposition of the hydrodynamic equations for fluid flow with relaxation and thermal conductivity into acoustical and non-acoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis 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
PublicationThis 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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A Compact Basis for Reliable Fast Frequency Sweep via the Reduced-Basis Method
PublicationA reliable reduced-order model (ROM) for fast frequency sweep in time-harmonic Maxwell’s equations by means of the reduced-basis method is detailed. Taking frequency as a parameter, the electromagnetic field in microwave circuits does not arbitrarily vary as frequency changes, but evolves on a very low-dimensional manifold. Approximating this low-dimensional manifold by a low dimension subspace, namely, reduced-basis space, gives...
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Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment
PublicationWe study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k_{B}T, which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar...
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Efficiency of acoustic heating in the Maxwell fluid
PublicationThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Efficiency of acoustic heating in the Maxwell fluid
PublicationThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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Krzysztof Nyka dr hab. inż.
PeopleKrzysztof Nyka, received MSc (1986) PhD (2002) and DSc (2020) degrees in telecommunication and electrical engineering from the Faculty of Electronics, Telecommunications and Informatics (ETI) of Gdańsk University of Technology (GUT), Poland. He is currently an Associate Professor at the Department of Microwaves and Antenna Engineering, Faculty of ETI, GUT. Before his academic career, he worked for the electronic industry (1984-1986). Research...
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Efficiency of acoustic heating produced in the thermoviscous flow of a fluid with relaxation
PublicationInstantaneous acoustic heating of a fluid with thermodynamic relaxation is the subject of investigation. Among others, viscoelastic biological media described by the Maxwell model of the viscous stress tensor, belong to this type of fluid. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in...
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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks
PublicationIn this article, we formulate and solve the representation problem for diffusion equations: giving a discretization of the Laplace transform of a diffusion equation under a space discretization over a space scale determined by an increment h > 0, can we construct a continuous in h family of Cauer ladder networks whose constitutive equations match for all h > 0 the discretization. It is proved that for a finite differences discretization...
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Ladder-Based Synthesis and Design of Low-Frequency Buffer-Based CMOS Filters
PublicationBuffer-based CMOS filters are maximally simplified circuits containing as few transistors as possible. Their applications, among others, include nano to micro watt biomedical sensors that process physiological signals of frequencies from 0.01 Hz to about 3 kHz. The order of a buffer-based filter is not greater than two. Hence, to obtain higher-order filters, a cascade of second-order filters is constructed. In this paper, a more...