Search results for: MAXWELL'S EQUATIONS

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 quasionedimensional waves.

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...

Infinite systems of hyperbolic functional differential equations. Ukr.Mat. Zurn.*2003 t. 55 nr 12 s. 16781696 bibliogr. 21 poz. Nieskończone układy hiperboliczne równań różniczkowofunkcyjnych.
PublicationWykazano istnienie prawie klasycznego rozwiązania zagadnienia Cauchy´ego.Dowód wykorzystuje metodę bicharakterystyk i nierówności całkowofunkcyjne.

If Gravity is Geometry, is Dark Energy just Arithmetic?
PublicationArithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are nonunique. The examples of fourdimensional spaces, R^4 and (−L/2,L/2)^4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a nonDiophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms...

Diagonalized Macromodels in Finite Element Method for Fast Electromagnetic Analysis of Waveguide Components
PublicationA new technique of local modelorder reduction (MOR) in 3D finite element method (FEM) for frequencydomain electromagnetic analysis of waveguide components is proposed in this paper. It resolves the problem of increasing solution time of the reducedorder system assembled from macromodels created in the subdomains, into which an analyzed structure is partitioned. This problem becomes particularly relevant for growing size and...

Au–Si plasmonic platforms: synthesis, structure and FDTD simulations
PublicationPlasmonic platforms based on Au nanostructures have been successfully synthesized by directional solidification of a eutectic from Au and the substrate. In order to determine homogeneous shape and space distribution, the influence of annealing conditions and the initial thickness of the Au film on the nanostructures was analyzed. For the surface morphology studies, SEM and AFM measurements were performed. The structure of platforms...

Single and DualGPU Generalized Sparse Eigenvalue Solvers for Finding a Few LowOrder Resonances of a Microwave Cavity Using the FiniteElement Method
PublicationThis paper presents two fast generalized eigenvalue solvers for sparse symmetric matrices that arise when electromagnetic cavity resonances are investigated using the higherorder finite element method (FEM). To find a few loworder resonances, the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm with nullspace deflation is applied. The computations are expedited by using one or two graphical processing...

Effective Permeability of Multi Air Gap Ferrite Core 3Phase Medium Frequency Transformer in Isolated DCDC Converters
PublicationThe magnetizing inductance of the medium frequency transformer (MFT) impacts the performance of the isolated dcdc power converters. The ferrite material is considered for high power transformers but it requires an assembly of type “I” cores resulting in a multi air gap structure of the magnetic core. The authors claim that the multiple air gaps are randomly distributed and that the average air gap length is unpredictable at the...

A GPU Solver for Sparse Generalized Eigenvalue Problems with Symmetric ComplexValued Matrices Obtained Using HigherOrder FEM
PublicationThe paper discusses a fast implementation of the stabilized locally optimal block preconditioned conjugate gradient (sLOBPCG) method, using a hierarchical multilevel preconditioner to solve nonHermitian sparse generalized eigenvalue problems with large symmetric complexvalued matrices obtained using the higherorder finiteelement method (FEM), applied to the analysis of a microwave resonator. The resonant frequencies of the loworder...

Selection of AHI + SC Hybrid Storage Based on Mathematical Models and Load Variation Characteristics
PublicationThe article deals with the design of a hybrid storage consisting of Aqueous Hybrid Ion battery (AHI) and supercapacitor (SC) modules. The selection of components is based on the knowledge of the load profile of the storage and the AHI battery and supercapacitor models. The paper presents the method of selecting components of the storage made of AHI batteries and supercapacitor modules The article includes an example of the hybrid...

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 nonacoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...

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 nonnewtonian 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...

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 nonnewtonian 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...

Injury Prediction Models for Onshore Road Network Development
PublicationIntegrating different modes of transport (road, rail, air and water) is important for port cities. To accommodate this need, new transport hubs must be built such as airports or sea ports. If ports are to grow, they must be accessible, a feature which is best achieved by building new roads, including fast roads. Poland must develop a network of fast roads that will provide good access to ports. What is equally important is to upgrade...

Macroelements and Model Order Reduction for Efficient ThreeDimensional FEM Analysis
PublicationAn efficient model order reduction (MOR) methodology for three dimensional vector finite element method (FEM) is developed to accelerate simulations of the structures containing features that cause strong variations of mesh density. As the result of presented algorithm, FEM subsystems of equations corresponding to the selected refined region are converted into a very compact sets of linear equations, called macroelements.Numerical...

Pantographic metamaterials: an example of mathematically driven design and of its technological challenges
PublicationIn this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those...

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...

Preconditioners with Low Memory Requirements for HigherOrder FiniteElement 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 complexvalued, sparse systems obtained using the higher order finiteelement method applied to the solution of the timeharmonic Maxwell equations. In the first implementation, denoted PCGV, a classical Vcycle is applied and the system of equations on the lowest level is solved...

Thermophysical study of the binary mixtures of triethyl phosphate with Nmethylformamide, N,Ndimethylformamide and N,Ndimethylacetamide – Experimental and theoretical approach
PublicationDensities at (293.15, 298.15, 303.15 and 308.15) K, and viscosities and ultrasonic velocities at 298.15 K of binary liquid mixtures of triethyl phosphate with Nmethylformamide, N,Ndimethylformamide and N,Ndimethylacetamide have been measured over the entire range of composition at p = 0.1 MPa. From the experimental data, values of excess molar volume, excess isentropic compressibility, viscosity deviation and excess Gibbs energy...

Modelling of joining route segments of differential curvature
PublicationThe 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 Sshaped and Coval transitions. The obtained Sshaped curves have been compared to the cubic CBezier curves and to the Pythagorean hodograph...

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...

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...

The influence of stainless steels microstructure evolution on the mechanical properties of pressure installation elements
PublicationIn this paper results of FEM analysis performed for pipe and 90o elbow, made of super duplex stainless steel, after precipitation of sigma phase (s), were presented. Heat treatment conditions simulate accidental overheating that can occur in nuclear installations after cooling circulation fails. For initial and modified microstructure tensile test was performed and numerical description of work hardening curves was done. Verification...

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...

Types of Markov Fields and Tilings
PublicationThe method of types is one of the most popular techniques in information theory and combinatorics. However, thus far the method has been mostly applied to onedimensional Markov processes, and it has not been thoroughly studied for general Markov ﬁelds. Markov ﬁelds over a ﬁnite alphabet of size m ≥ 2 can be viewed as models for multidimensional systems with local interactions. The locality of these interactions is represented...

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...

Automatic Regularization by Quantization in Reducible Representations of CCR: PointForm Quantum Optics with Classical Sources
PublicationElectromagnetic fields are quantized in a manifestly covariant way by means ofa class of reducible "centerofmass Nrepresentations" of the algebra of canonical commutationrelations (CCR). The fourpotential Aa(x) transforms in these representations as aHermitian fourvector field in Minkowski fourposition space (without change of gauge), butin momentum space it splits into spin1 massless photons and two massless scalars. Whatwe...

Polynomial Chaos Expansion in Bio and Structural Mechanics
PublicationThis thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanicsbased approaches in the modelling and simulation of implants used in the repair...

Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...

Multimode systems of nonlinear equations: derivation, integrability, and numerical solutions
PublicationWe consider the propagation of electromagnetic pulses in isotropic media taking a thirdorder nonlinearityinto account. We develop a method for transforming Maxwell's equations based on a complete set ofprojection operators corresponding to wavedispersion 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...

Directed electromagnetic pulse dynamics: projecting operators method
PublicationIn this article, we consider a onedimensional 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...

Fractional Order Circuit Elements Derived from Electromagnetism
PublicationIn this paper, derivations of fractionalorder (FO) circuitelement equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasistatic (QS) approximations of Maxwell's equations in media with...