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Search results for: MAXWELL'S EQUATIONS
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GENERAL DYNAMIC PROJECTING OF MAXWELL EQUATIONS
PublicationA complete – system of Maxwell equations is splitting into independent subsystems by means of a special dynamic projecting technique. The technique relies upon a direct link between field components that determine correspondent subspaces. The explicit form of links and corresponding subspace evolution equations are obtained in conditions of certain symmetry, it is illustrated by examples of spherical and quasi-one-dimensional waves.
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Multiple bifurcation in the solution set of the von Karman equations with S^{1}-symmetries
PublicationRozważmy cienką, sprężystą, kołową płytę, położoną na sprężystym podłożu, poddawaną działaniu sił ściskających koncentrycznie wzdłuż jej brzegu. Formy równowagi takiej płyty są rozwiązaniami równań von Karmana z dwoma parametrami określonych na dysku w R^{2}. Są to równania różniczkowe cząstkowe rzędu czwartego. Można je zapisać jako równanie operatorowe F(x,p)=0 w przestrzeniach Höldera, gdzie zmienna x odpowiada formom równowagi...
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Infinite systems of hyperbolic functional differential equations. Ukr.Mat. Zurn.*2003 t. 55 nr 12 s. 1678-1696 bibliogr. 21 poz. Nieskończone układy hiperboliczne równań różniczkowo-funkcyjnych.
PublicationWykazano istnienie prawie klasycznego rozwiązania zagadnienia Cauchy´ego.Dowód wykorzystuje metodę bicharakterystyk i nierówności całkowo-funkcyjne.
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublicationIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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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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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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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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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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Marek Czachor prof. dr hab.
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Multimode systems of nonlinear equations: derivation, integrability, and numerical solutions
PublicationWe consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearityinto account. We develop a method for transforming Maxwell's equations based on a complete set ofprojection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with thepropagation direction taken into account. The most important result of applying the method is a systemof equations describing the...
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Preconditioners with Low Memory Requirements for Higher-Order Finite-Element Method Applied to Solving Maxwell’s Equations on Multicore CPUs and GPUs
PublicationThis paper discusses two fast implementations of the conjugate gradient iterative method using a hierarchical multilevel preconditioner to solve the complex-valued, sparse systems obtained using the higher order finite-element method applied to the solution of the time-harmonic Maxwell equations. In the first implementation, denoted PCG-V, a classical V-cycle is applied and the system of equations on the lowest level is solved...
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Ruch wirowy wywoływany przez ultradźwięk w płynach z relaksacją
PublicationRozprawa doktorska poświęcona jest badaniu ruchu wirowego wywoływanego przez ultradźwięk w różnych modelach płynów z relaksacją. Ma ona charakter teoretyczny, jednak wykorzystanie uzyskanych dzięki niej wyników może przynieść lepsze zrozumienie ruchu wirowego wywoływanego przez siłę akustyczną. W I rozdziale rozprawy przedstawione zostały ogólne rozważania dotyczące akustyki nieliniowej. Rozdział II dotyczy ruchu wirowego wywoływanego...
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The influence of frequency separation on imaging properties in DFEIT
PublicationW artykule przedstawiono wpływ wyboru składowych częstotliwościowych dla różnicowej tomografii impedancyjnej na wynik i własności obrazowania w dwuczęstotliwościowej różnicowej tomografii impedancyjnej.A Dual Frequency EIT is an extension of a traditional EIT that uses two sinusoidal signals for imaging. Appropriate selection of signals' frequency allows to achieve reasonable contrast of imaged structure. It has already been shown...
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Karolina Lademann mgr
PeopleCurriculum vitae
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Karolina Lademann Mgr
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...
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MODELOWANIE TURBINY WIATROWEJ Z DWOMA PRZECIWBIEŻNIE OBRACAJĄCYMI SIĘ WIRNIKAMI
PublicationW artykule przedstawiono sposoby modelowania dwuwirnikowej turbiny wiatrowej z wykorzystaniem technik Obliczeniowej Mechaniki Płynów. Omówiono uproszczone metody modelowania Actuator Disc i Actuator Line Method oraz aspekty związane z dokładnym odwzorowaniem turbiny na siatce obliczeniowej. Zaprezentowano przykładowe wyniki obliczeń turbiny dwuwirnikowej złożonej z wirników NREL o mocy nominalnej 5 MW każdy. Do wykonania badań...
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Directed electromagnetic pulse dynamics: projecting operators method
PublicationIn this article, we consider a one-dimensional model of electromagnetic pulse propagation in isotropic media, takinginto account a nonlinearity of the third order. We introduce a method for Maxwell's equation transformation on thebasis of a complete set of projecting operators. The operators correspond to wave dispersion branches including thedirection of propagation. As the simplest result of applying the method, we derive a system...
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Simulating coherent light propagation in a random scattering materials using the perturbation expansion
PublicationMultiple scattering of a coherent light plays important role in the optical metrology. Probably the most important phenomenon caused by multiple scattering are the speckle patterns present in every optical imaging method based on coherent or partially coherent light illumination. In many cases the speckle patterns are considered as an undesired noise. However, they were found useful in various subsurface imaging methods such as...