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Search results for: NONLINEAR ADVECTION EQUATIONS
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Simulations of flows in the coastal zone of the Baltic Sea
Open Research DataThe study area is located in the Southern Baltic, within Polish Marine Areas, adjacent to the coastline in the vicinity of Lubiatowo village, where The Coastal Research Station (CRS) – a field laboratory of the Institute of Hydro-Engineering of the Polish Academy of Sciences (IBW PAN) –is situated. The numerical reconstruction of the coastal flow was...
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Isogeometric Shell FE Analysis of the Human Abdominal Wall
PublicationIn this paper a nonlinear isogeometric Kirchhoff-Love shell model of the human abdominal wall is proposed. Its geometry is based on in vivo measurements obtained from a polygon mesh that is transformed into a NURBS surface, and then used directly for the finite element analysis. The passive response of the abdominal wall model under uniform pressure is considered. A hyperelastic membrane model based on the Gasser-Ogden-Holzapfel...
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Data on solutions of Hes1 system
Open Research DataHes1 protein (hairy and enhancer of split 1) belongs to the helix-loop-helix (bHLH) family of transcription proteins, i.e. DNA-binding proteins in the promoter region or in another region where regulation of transcription processes occurs. The database collects data on solutions of the Hes1 systems with multiple binding sites and the dimer formation...
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Analytical Steady-State Model of the Pipeline Flow Process
PublicationThe paper addresses the issue of modeling the flow process in transmission pipelines. A base model used for numerical simulation is introduced. Under certain assumptions concerning steady state analysis, the differential equations describing the process are solved analytically for two cases: zero and nonzero inclination angle α. These equations describe a constant flow rate and a corresponding distribution of the pressure along...
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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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Numerical solution of threshold problems in epidemics and population dynamics
PublicationA new algorithm is proposed for the numerical solution of threshold problems in epidemics and population dynamics. These problems are modeled by the delay-differential equations, where the delay function is unknown and has to be determined from the threshold conditions. The new algorithm is based on embedded pair of continuous Runge–Kutta method of order p = 4 and discrete Runge–Kutta method of order q = 3 which is used for the...
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Analytical method of determining dynamic properties of thermocouples used in measurements of quick – changing temperatures of exhaust gases in marine diesel engines
PublicationThe article presents selected issues of mathematical modeling of heat exchange between the thermocouple and the exhaust gas flowing them, in unsteady conditions. On the way of energy balancing consideration of thermodynamic processes developed differential equations describing the dynamic properties for three versions of the design sheathed thermocouples: with weld isolated from the sheath, with weld welded the sheath and with...
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Macro-elements and Model Order Reduction for Efficient Three-Dimensional 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 macro-elements.Numerical...
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On a 3D material modelling of smart nanocomposite structures
PublicationSmart composites (SCs) are utilized in electro-mechanical systems such as actuators and energy harvesters. Typically, thin-walled components such as beams, plates, and shells are employed as structural elements to achieve the mechanical behavior desired in these composites. SCs exhibit various advanced properties, ranging from lower order phenomena like piezoelectricity and piezomagneticity, to higher order effects including flexoelectricity...
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Stochastic resonance in measurements
PublicationNoise is usually associated with the negative phenomenon, hampering the measurements data and their analysis. This view has been broken in the '80s when the phenomenon of stochastic resonance (Stochastic Resonance - SR) was discovered. It is a phenomenon that occurs in nonlinear dynamic measurement systems when the selected input noise can optimize system performance. SR became a way to improve efficiency of weak signals detection....
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Accurate Computation of IGBT Junction Temperature in PLECS
PublicationIn the article, a new method to improve the accuracy of the insulated-gate bipolar transistor (IGBT) junction temperature computations in the piecewise linear electrical circuit simulation (PLECS) software is proposed and described in detail. This method allows computing the IGBT junction temperature using a nonlinear compact thermal model of this device in PLECS. In the method, a nonlinear compact thermal model of the IGBT is...
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Transition curve with smoothed curvature at its ends for railway roads
PublicationIn the paper, in view of a railway ballasted track, a new concept of transition curve of linear form of curvature along its length and smoothed extreme regions is presented. For this purpose use has been made of an original, universal method for identifying transition curves by means of differential equations. Some general curvature equations for three regions investigated have been determined to be followed by appropriate parametric...
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The Doppler effect in a bistatic system for determining the position of moving targets
PublicationThe article presents the theoretical analysis and the results of numerical calculations of the Doppler effect it occurs in a system designed to determine the position and speed of a moving target. The transmitter is the source of the signal and it emits a sinusoidal, acoustic and continuous wave. Signal reflected off a moving target is received by four hydrophones. Based on the signals, four Doppler shifts are determined and inserted...
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Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method
PublicationIn this paper, bending analysis of rectangular functionally graded (FG) nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory (HSDT). The set of coupled equations are solved using the dynamic relaxation (DR) method combined with finite difference (FD) discretization technique...
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A high-accuracy method of computation of x-ray waves propagation through an optical system consisting of many lenses
PublicationThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated...
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Local buckling of thin-walled channel member flange made of aluminum alloy
PublicationThe paper deals with local stability of the thin-walled compressed flange of channel columns and beams made of aluminum alloy. The aim of paper is to find critical stress of local buckling of the flange member taking into account the web-flange interaction in linear and nonlinear elastic range of the member material. The governing differential equation of the problem is derived with aid of the principle of stationary total potential...
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Random field modelling of mechanical behaviour of corroded thin steel plate specimens
PublicationThe objective of this work is to explore the possibility of corrosion degradation modelling of thin steel plate specimens with the use of random field approach. The mechanical properties are obtained via the nonlinear Finite Element Analysis with the use of an explicit dynamic solver. The fully nonlinear material model is adopted to obtain the proper stress-strain response. Sensitivity analysis considering the main statistical...
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Fluid–solid interaction on a thin platelet with high-velocity flow: vibration modelling and experiment
PublicationThe paper concerns the nonlinear behaviour of a thin platelet that is streamlined in an aerodynamic tunnel. The air velocity in the aerodynamic tunnel was at 858.9 km/h or 0.7 Ma (Ma—Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound). This experiment was numerically simulated using FSI (fluid–solid interaction) tools, namely the coupling...
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Rapid Design Tuning of Miniaturized Rat-Race Couplers Using Regression-Based Equivalent Network Surrogates
PublicationA simple technique for fast design tuning of compact rat-race couplers is presented. Our approach involves equivalent circuit representation, corrected by nonlinear functions of frequency with coefficients extracted through nonlinear regression. At the same time, the tuning process connects two levels of coupler representation: EM simulation of the entire circuit and re-optimization of the coupler building blocks (slow-wave cells...
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Inline Microwave Filters With N+1 Transmission Zeros Generated by Frequency-Variant Couplings: Coupling-Matrix-Based Synthesis and Design
PublicationA general coupling-matrix-based synthesis methodology for inline Nth-order microwave bandpass filters (BPFs) with frequency-variant reactive-type couplings that generate N+1 transmission zeros (TZs) is presented in this brief. The proposed approach exploits the formulation of the synthesis problem as three inverse nonlinear eigenvalue problems (INEVPs) so that the coupling matrix is built from their sets of eigenvalues. For this...
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Synthesis of coupled lossy resonator filters.
PublicationA technique for fast synthesis of coupling matrix low-pass prototypes of generalized. Chebyshev bandpass filters with lossy resonators is presented in this letter. The coupling matrix is found by solving a nonlinear least squares problem based on zeros and poles of filter's transfer functions.
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Ellipticity in couple-stress elasticity
PublicationWe discuss ellipticity property within the linear couple-stress elasticity. In this theory, there exists a deformation energy density introduced as a function of strains and gradient of macrorotations, where the latter are expressed through displacements. So the couple-stress theory could be treated as a particular class of strain gradient elasticity. Within the micropolar elasticity, the model is called Cosserat pseudocontinuum...
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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublicationIn this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their...
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Wpływ błędów parametrów modelu maszyny indukcyjnej na działanie rozszerzonego obserwatora prędkości
PublicationW artykule opisano metodę odtwarzania prędkości wirnika maszyny indukcyjnej przy wykorzystaniu rozszerzonego obserwatora prędkości. Zbadano wpływ błędów parametrów modelu maszyny indukcyjnej na właściwości dynamiczne obserwatora poprzez porównanie macierzy stanu obserwatora obarczonego oraz nieobarczonego błędami parametrów. Zbadany został także wpływ błędów parametrów na jakość odtwarzania zmiennych maszyny w stanie ustalonym.
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Importance of sign conventions on analytical solutions to the wave-induced cyclic response of a poro-elastic seabed
PublicationThis paper discusses the influence of different sign conventions for strains and stresses, i.e. the solid mechanics sign convention and the soil mechanics sign convention, on the form of governing partial differential equations (the static equilibrium equations and the continuity equation) used to describe the wave-induced cyclic response of a poro-elastic seabed due to propagation of a sinusoidal surface water-wave. Some selected...
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ANALIZA MOŻLIWOŚCI ZASTOSOWANIA STEROWANIA PREDYKCYJNEGO TURBINĄ PAROWĄ ELEKTROWNI JĄDROWEJ
PublicationArtykuł przedstawia wyniki wstępnej analizy możliwości zastosowania sterowania predykcyjnego MPC turbiną parową elektrowni jądrowej. Tradycyjnie przyjmuje się, że turbina pracuje w jednym punkcie pracy odpowiadającym jej mocy nominalnej, co pozwala na stosowanie klasycznych regulatorów PID. Synteza sterowania dla warunków zmiennego punktu pracy wymaga uwzględnienia nieliniowego charakteru procesów turbiny oraz możliwości naruszania...
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Vibro-Electrical Behavior of a Viscoelastic Piezo-Nanowire in an Elastic Substrate Considering Stress Nonlocality and Microstructural Size-Dependent Effects
PublicationThis research deals with dynamics response of a Pol/BaTiO3 nanowire including viscosity influences. The wire is also impressed by a longitudinal electric field. Hamilton's principle and Lagrangian strains are employed in conjunction with a refined higher-order beam theory in order to derive equations of motion. By combining nonlocality and small size...
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On analytical solution of stationary two dimensional boundary problem of natural convection
PublicationApproximate analytical solution of two dimensional problem for sta- tionary Navier-Stokes, continuity and Fourier-Kirchho equations describ- ing free convective heat transfer from isothermal surface of half innite vertical plate is presented. The problem formulation is based on the typ- ical for natural convection assumptions: the uid noncompressibility and Boussinesq approximation. We also assume that orthogonal to the plate component...
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Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory
PublicationThis article is intended to analyze forced vibrations of a piezoelectric-piezomagnetic ceramic nanoplate by a new refined shear deformation plate theory in conjunction with higher-order nonlocal strain gradient theory. As both stress nonlocality and strain gradient size-dependent effects are taken into account using the higher-order nonlocal strain gradient theory, the governing equations of the composite nanoplate are formulated....
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Sensor Position Estimation Method for IoT Using Mobile Reference Node
PublicationThe paper proposes an innovative method of locating objects for the Internet of Things (IoT). The proposed method allows the position of a fixed measuring sensor (MS) to be estimated using one mobile base station with a known position moving around the MS. The mathematical analysis of the method, and three algorithms — Newton’s (NA), gradient descent (GD) and genetic (GA) — for solving the system of non-linear positional equations...
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On forced vibrations of piezo-flexomagnetic nano-actuator beams
PublicationThe effect of excitation frequency on the piezomagnetic Euler-Bernoulli nanobeam taking the flexomagnetic material phenomenon into consideration is investigated in this chapter. The magnetization with strain gradients creates flexomagneticity. We couple simultaneously the piezomagnetic and flexomagnetic properties in an inverse magnetization. Resemble the flexoelectricity, the flexomagneticity is also size-dependent. So, it has...
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Mathematical Modelling of a Seismic Isolation System to Protect Structures During Damaging Earthquakes
PublicationThe present study aims to determine the effectiveness of a nonlinear mathematical model in simulating complex mechanical behaviour of a seismic isolation system to protect structures during strong and damaging earthquakes. In order to construct the Polymeric Bearings considered in this research, a specially prepared flexible polyurethane elastomer with increased damping properties has been used. The usefulness of the proposed mathematical...
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Flexural behavior of composite structural insulated panels with magnesium oxide board facings
PublicationThe current report is devoted to the flexural analysis of a composite structural insulated panel (CSIP) with magnesium oxide board facings and expanded polystyrene (EPS) core, that was recently introduced to the building industry. An advanced nonlinear FE model was created in the ABAQUS environment, able to simulate the CSIP’s flexural behavior in great detail. An original custom code procedure was developed, which allowed to include...
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Simulation Studies of Control Systems for Doubly Fed Induction Generator Supplied by the Current Source Converter
PublicationThe control system for a Doubly Fed Induction Generator (DFIG) supplied by a grid-connected Current Source Converter (CSC) is presented in this paper. Nonlinear transformation of DFIG model to the multi-scalar form is proposed. The nonlinear control strategy of active and reactive power of DFIG is realized by feedback linearization. In the proposed control scheme, the DFIG model and CSI parameters are included. Two Proportional-Integral...
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Determination of the optimal curvature of the turnout diverging track for HSR using dynamic analysis
PublicationThe paper presents an analytical method of identifying the curvature of the turnout diverging track consisting of sections of varying curvature. Such turnout is mainly applied on High Speed Railway. Both linear and nonlinear (polynomial) curvatures of the turnout diverging track are considered in the paper. Obtained solutions enable to assume curvature values at the beginning and end point of the geometrical layout of the turnout.The...
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Plasmon resonance in gold-silver nanoalloys
Open Research DataSurface plasmon resonance (SPR) can lead to improve or formation a new linear or nonlinear optical phenomena. Especially it can enhance a light emission from luminescence materials. The presence of metal nanostructures or nanoparticles is necessary to excitation of the SPR. It is well known that gold and silver nanostructures exhibit plasmon resonance...
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Electromagnetic Control and Dynamics of Generalized Burgers’ Nanoliquid Flow Containing Motile Microorganisms with Cattaneo–Christov Relations: Galerkin Finite Element Mechanism
PublicationIn our research work, we have developed a model describing the characteristics of the bio-convection and moving microorganisms in the flows of a magnetized generalized Burgers’ nanoliquid with Fourier’s and Fick’s laws in a stretchable sheet. Considerations have been made to Cattaneo–Christov mass and heat diffusion theory. According to the Cattaneo–Christov relation, the Buongiorno phenomenon for the motion of a nanoliquid in...
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Numeryczna analiza hydrauliki toru kajakarstwa górskiego w Drzewicy
PublicationW artykule zaproponowano wykorzystanie do analizy hydrodynamiki toru kajakarstwa górskiego symulacji numerycznej, wykorzystującej dwuwymiarowe równania ruchu wody w warunkach przepływu szybkozmiennego. Rozwiązanie równań hydrodynamiki wykonano samodzielnie z zastosowaniem metody objętości skończonych. Jako przykład zastosowania zaproponowanej metody przedstawiono analizę przepływu wzdłuż istniejącego, poddanego modernizacji toru...
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Modelowanie zmiennej krzywizny na długości toru zwrotnego rozjazdu
PublicationW pracy została przedstawiona analityczna metoda wyznaczania krzywizny toru zwrotnego rozjazdu kolejowego posiadającego na swojej długości odcinki zmiennej krzywizny. Taki rozjazd jest dedykowany w głównym stopniu kolejom dużych prędkości. Rozpatrzono dwa odrębne przypadki obejmujące liniowy przebieg krzywizny oraz przebieg nieliniowy, w postaci wielomianowej. Uzyskane rozwiązania problemu pozwalają na przyjmowanie dowolnych wartości...
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On the theorem of Tverberg
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Borsuk-Ulam type theorems on product spaces II
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Fixed point index for $G$-equivariant multivalued maps
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The Conley index and spectral sequences
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On the space of equivariant local maps
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Spectral sequences and detailed connection matrices
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Topology of vibro-impact systems in the neighborhood of grazing
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
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Computer assisted method for proving existence of periodic orbits
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On homotopy Conley index for multivalued flows in Hilbert spaces
PublicationPodano aproksymacyjną definicję indeksu homotopijnego, otrzymując naturalne związki z podobnymi niezmiennikami. Zbadano własności tego niezmiennika i zastosowano do badania gradientowych potoków wykazując pewne geometryczne własności zbiorów niezmienniczych
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Selections and approximations of convex-valued equivariant mappings
PublicationUdowodniono szereg twierdzeń o współzmienniczych selekcjach i aproksymacjach ciągłych, mierzalnych i typu Caratheodory'ego dla odwzorowań G-współzmienniczych o wartościach wypukłych, gdzie G jest grupą zwartą Liego. Tw. typu Michaela, Celliny, Browdera, Kuratowskiego-Ryll-Nardzewskiego, Castaing itd.