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Search results for: COMPLEX LINEAR SYSTEM OF EQUATIONS
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Free Convection Heat Transfer from Horizontal Cylinders
PublicationThe results of experimental investigation of free convection heat transfer in a rectangular container are presented. The ability of the commonly accepted correlation equations to reproduce present experimental data was tested as well. It was assumed that the examined geometry fulfils the requirement of no-interaction between heated cylinder and bounded surfaces. In order to check this assumption recently published correlation equations...
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Investigations of the Working Process in a Dual-Fuel Low-Emission Combustion Chamber for an FPSO Gas Turbine Engine
PublicationThis investigation is devoted to an analysis of the working process in a dual-fuel low-emission combustion chamber for a floating vessel’s gas turbine. The low-emission gas turbine combustion chamber with partial pre-mixing of fuel and air inside the outer and inner radial-axial swirlers was chosen as the object of research. When modelling processes in a dual-flow low-emission gas turbine combustion chamber, a generalized method...
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Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance
PublicationThe 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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Design of reverse curves adapted to the satellite measurements
PublicationThe paper presents a new method for designing railway route in the direction change area adapted to the Mobile Satellite Measurements technique. The method may be particularly useful in the situations when both tangents cannot be connected in an elementary way using a circular arc with transition curves. Thus, the only solution would be the application of two circular arcs of opposite curvature signs, that is, the use of an inverse...
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Correlations between organic pollution indicators in municipal wastewater
PublicationThe paper presents the results of a study of parameters used for determining the amount of organic pollutants in wastewater flowing into a collective wastewater treatment plant with a population equivalent of about 120 000 PE. The plant constituted part of a sewage system. Assays were performed for biochemical oxygen demand (BOD5), chemical oxygen demand (CODCr), permanganete index (CODMn) and total organic carbon (TOC). In addition,...
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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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One-Dimensional Modeling of Flows in Open Channels
PublicationIn this chapter, modeling of the unsteady open channel flow using one-dimensional approach is considered. As this question belongs to the well-known and standard problems of open channel hydraulic engineering, comprehensively presented and described in many books and publications, our attention is focused on some selected aspects only. As far as the numerical solution of the governing equations is considered, one can find out that...
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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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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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On Nonlinear Dynamic Theory of Thin Plates with Surface Stresses
PublicationWe discuss the modelling of dynamics of thin plates considering surface stresses according to Gurtin–Murdoch surface elasticity. Taking into account the surface mass density we derive the two-dimensional (2D) equations of motion. For the reduction of the three-dimensional (3D) motion equations to the 2D ones we use the trough-the-thickness integration procedure. As a result, the 2D dynamic parameters of the plate depend not only...
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<title>Cavity control system model simulations for the TESLA linear accelerator</title>
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<title>Cavity control system essential modeling for the TESLA linear accelerator</title>
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Non-classical operational calculus applied to certain linear discrete time-system
PublicationW pracy zastosowano nieklasyczny rachunek operatorów do wyznaczania odpowiedzi pewnego dyskretnego układu dynamicznego. Pokazano metodę szczególnie przydatną do wyznaczania odpowiedzi pewnych dyskretnych niestacjonarnych układów dynamicznych, przy których zastosowanie przekształcenia Z sprawia duże trudności.
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Supply current signal and artificial neural networks in the induction motor bearings diagnostics
PublicationThis paper contains research results of the diagnostics of induction motor bearings based on measurement of the supply current with usage of artificial neural networks. Bearing failure amount is greater than 40% of all engine failures, which makes their damage-free operation crucial. Tests were performed on motors with intentionally made bearings defects. Chapter 2 introduces the concept of artificial neural networks. It presents...
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Thermo-resonance analysis of an excited graphene sheet using a new approach
PublicationForced vibration of graphene nanoplate based on a refined plate theory in conjunction with higher-order nonlocal strain gradient theory in the thermal environment has been investigated. Regarding the higher-order nonlocal strain gradient theory, both stress nonlocality and size-dependent effects are taken into account, so the equilibrium equations which are governing on the graphene sheet have been formulated by the theory....
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Irreversible thermodynamics model equations for heterogeneous solute flows in a double-membrane system
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INVESTIGATIONS OF THE EMISSION CHARACTERISTICS OF A DUAL-FUEL GAS TURBINE COMBUSTION CHAMBER OPERATING SIMULTANEOUSLY ON LIQUID AND GASEOUS FUELS
PublicationT his study is dedicated to investigations of the working process in a dual-fuel low-emission combustion chamber for a floating vessel’s gas turbine. As the object of the research, a low-emission gas turbine combustion chamber with partial premixing of fuel and air inside the outer and inner radial-axial swirls was chosen. The method of the research is based on the numerical solution of the system of differential...
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Tuning of microstructure in engineered poly (trimethylene terephthalate) based blends with nano inclusion as multifunctional additive
PublicationImmiscible blends and their composites are heterogeneous and have variable morphology due to variation in mesophase regions. Tuning, i.e. controlling the phase dimension is important, thereof we report a “super-combo” effect of multiwalled carbon nanotubes (MWCNTs) in poly (trimethylene terephthalate)/polypropylene (PTT/ PP) blend system. MWCNTs act as a good reinforcing agent and compatibilizer in the otherwise immiscible PTT/...
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Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model
PublicationWe develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6-parameter shell theory. The Cosserat plane stress equations are integrated through-the- thickness under assumption of the Reissner-Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus Gc and the micropolar...
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Integrable zero-range potentials in a plane
PublicationWe examine general statements in the Wronskian representation of Darboux transformations for plane zero-range potentials. Such expressions naturally contain scattering problem solution. We also apply Abel theorem to Wronskians for differential equations and link it to chain equations for Darboux transforms to fix conditions for further development of the underlying distribution concept. Moutard transformations give a convenient...
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Reduction of Computational Complexity in Simulations of the Flow Process in Transmission Pipelines
PublicationThe paper addresses the problem of computational efficiency of the pipe-flow model used in leak detection and identification systems. Analysis of the model brings attention to its specific structure, where all matrices are sparse. With certain rearrangements, the model can be reduced to a set of equations with tridiagonal matrices. Such equations can be solved using the Thomas algorithm. This method provides almost the same values...
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Ellipticity of gradient poroelasticity
PublicationWe discuss the ellipticity properties of an enhanced model of poroelastic continua called dilatational strain gradient elasticity. Within the theory there exists a deformation energy density given as a function of strains and gradient of dilatation. We show that the equilibrium equations are elliptic in the sense of Douglis–Nirenberg. These conditions are more general than the ordinary and strong ellipticity but keep almost all...
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Design of a complex multiplier based on the convolution with the use of the polynomial residue number system
Publicationzaproponowano realizację mnożnika zespolonego opartego na algorytmie dekompozycyjnym skavantzosa i stouraitisa. mnożenie zespolone jest wykonywane jako splot 8-punktowy. przedstawiono przykład obliczeniowy i architekturę mnożnika dla małych liczb.
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The analysis of the operational process of a complex fire alarm system used in transport facilities
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Towards the autonomy of urban management: simple system as a solution for complex urban environment
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Fractional Order Circuit Elements Derived from Electromagnetism
PublicationIn this paper, derivations of fractional-order (FO) circuit-element 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 quasi-static (QS) approximations of Maxwell's equations in media with...
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Method of lines for nonlinear first order partial functional differential equations.
PublicationClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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On neutral differential equations and the monotone iterative method
PublicationThe application of the monotone iterative method to neutral differential equations with deviating arguments is considered in this paper. We formulate existence results giving sufficient conditions which guarantee that such problems have solutions. This approach is new and to the Authors' knowledge, this is the first paper when the monotone iterative method is applied to neutral first-order differential equations with deviating...
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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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The FEM analysis of pressure installation elements after simulated accidental overheating
PublicationThe paper presents innovative analysis focused on the safety aspects of existing pressure installation operation after overheating accidents. Results presented here can be applied in decision-making process concerning further operation of existing pressure installation after cooling system failure. In this paper the results of FEM analysis performed for a straight pipe and 90 degrees elbow, made of super duplex stainless steel,...
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Adsorptive Removal of Aqueous Phase Crystal Violet Dye by Low-Cost Activated Carbon Obtained from Date Palm (L.) Dead Leaflets
PublicationUp to now, water pollution is still one of the important issues and challenges worldwide, due to its environmental, economic and human life impacts. It is also remains a challenge to environment scientists and technologists. Nowadays, the textile dyeing industry is considered one of the largest water consuming industries and produces large volumes of colored wastewater in its dyeing and finishing process. In this study, date palm...
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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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RANS-based design optimization of dual-rotor wind turbines
PublicationPurpose An improvement in the energy efficiency of wind turbines can be achieved using dual rotors. Because of complex flow physics, the design of dual-rotor wind turbines (DRWTs) requires repetitive evaluations of computationally expensive partial differential equation (PDE) simulation models. Approaches for solving design optimization of DRWTs constrained by PDE simulations are investigated. The purpose of this study is to determine...
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Identification of transition curves in vehicular roads and railways
PublicationIn the paper attention is focused on the necessity to systematize the procedure for determining the shape of transition curves used in vehicular roads and railway routes. There has been presented a universal method of identifying curvature in transition curves by using differential equations. Curvature equations for such known forms of transition curves as clothoid, quartic parabola, the Bloss curve, cosinusoid and sinusoid, have...
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Networked Object Monitor - A distributed system for monitoring, diagnostics and control of complex industrial facilities
PublicationRozwój mobilności i technologii internetowych, a także globalizacji gospodarki światowej, uwzględniający kluczowe aspekty zarządzania przepływem informacji, otworzył zupełnie nowe możliwości opracowywania i konstruowania innowacyjnych rozwiązań technicznych. Z taką myślą powstał prototyp Sieciowego Monitora Obiektu, aplikacji umożliwiającej nie tylko ciągłą kontrolę parametrów obiektów przemysłowych i biznesowych, ale również zarządzanie...
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Balance errors in numerical solutions of shallow water equations
PublicationThe analysis of the conservative properties of the shallow water equations is presented in the paper. The work focuses on the consistency of numerical solution of these equations with the conservation laws of mass and momentum. The investigations involve two different conservative forms which are solved by an implicit box scheme. The theoretical analysis supported by numerical experiments is carried out for rectangular channel...
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Absorbing Boundary Conditions Derived Based on Pauli Matrices Algebra
PublicationIn this letter, we demonstrate that a set of absorbing boundary conditions (ABCs) for numerical simulations of waves, proposed originally by Engquist and Majda and later generalized by Trefethen and Halpern, can alternatively be derived with the use of Pauli matrices algebra. Hence a novel approach to the derivation of one-way wave equations in electromagnetics is proposed. That is, the classical wave equation can be factorized...
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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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Nonlinear resultant theory of shells accounting for thermodiffusion
PublicationThe complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells...
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On the Peano Theorem for Some Functional Differential Equations on Time Scale
PublicationThe Peano Theorem for some functional differential equations on time scale is proved. Assumptions are of Caratheodory type. Two counter examples for false Peano theorems in the literature are presented.
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Influence and development of new kinematic systems in flat surface lapping
PublicationThe face grinding and lapping technology is widely used in the field of the precise and ultraprecise manufacturing. It has become an indispensable technology in the manufacture of many parts. An absence of material restrictions allows machining both metal and non-metallic materials, including technical ceramics [1]. Nowadays there are mainly two kinematic systems in lapping machines [2]. The machining plane-parallel surfaces is...
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Novel analysis methods of dynamic properties for vehicle pantographs
PublicationTransmission of electrical energy from a catenary system to traction units must be safe and reliable especially for high speed trains. Modern pantographs have to meet these requirements. Pantographs are subjected to several forces acting on their structural elements. These forces come from pantograph drive, inertia forces, aerodynamic effects, vibration of traction units etc. Modern approach to static and dynamic analysis should...
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A Nonlinear Model of a Mesh Shell
PublicationFor a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration...
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Electromagnetic-based derivation of fractional-order circuit theory
PublicationIn this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order...
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Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory
PublicationThe paper presents the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter being the drilling degree of freedom. The material law is derived by through-the-thickness integration of the Cosserat plane stress equations. The constitutive equations are formulated with respect to the neutral physical surface. The influence of...
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Systems of boundary value problems of advanced differential equations
PublicationThis paper considers the existence of extremal solutions to systems of advanced differential equations with corresponding nonlinear boundary conditions. The monotone iterative method is applied to obtain the existence results. An example is provided for illustration.
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ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING
PublicationThe paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection-diffusion equations. For the numerical solution of the 1D advection-diffusion equation a method, originally proposed for solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and consequently, to reduce...
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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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Use of a Least Squares with Conditional Equations Method in Positioning a Tramway Track in the Gdansk Agglomeration
PublicationSatellite measurement techniques have been used for many years in different types of human activity, including work related to staking out and making use of rail infrastructure. First and foremost, satellite techniques are applied to determine the tramway track course and to analyse the changes of its position during its operation. This paper proposes using the least squares with conditional equations method, known in geodesy (LSce)....
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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...