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Characterization of the Functionally Graded Shear Modulus of a Half-Space
PublikacjaIn this article, a method is proposed for determining parameters of the exponentialy varying shear modulus of a functionally graded half-space. The method is based on the analytical solution of the problem of pure shear of an elastic functionally graded half-space by a strip punch. The half-space has the depth-wise exponential variation of its shear modulus, whose parameters are to be determined. The problem is reduced to an integral...
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Hyperbolic heat conduction at a microscopic sliding contact with account of adhesion-deformational heat generation and wear
PublikacjaDifferent non-Fourier models were proposed to simulate temperatures in materials subjected to extremely fast thermal disturbances, when the speed of heat propagation should be concerned. The present study investigated temperature and heat balance at a microscopic sliding contact during a single frictional interaction based on the Cattaneo-Vernotte hyperbolic heat conduction equation. Two fundamental features of friction, namely,...
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Krzywa przejściowa z wygładzoną krzywizną dla dróg kolejowych
PublikacjaW pracy przedstawiono koncepcję nowej postaci krzywej przejściowej, o liniowym przebiegu krzywizny na długości i wygładzonymi rejonami skrajnymi. Może ona stanowić alternatywę dla tzw. gładkich krzywych przejściowych, o nieliniowym przebiegu krzywizny na całej długości. Została tutaj wykorzystana uniwersalna metoda identyfikacji krzywych przejściowych za pomocą równań różniczkowych. Wyznaczono ogólne równania krzywizny oraz odpowiednie...
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One-Dimensional Modeling of Flows in Open Channels
PublikacjaIn 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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Topological invariants for equivariant flows: Conley index and degree
PublikacjaAbout 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...
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Entrepreneurial competencies and intentions among students of technical universities
PublikacjaThe study investigates the entrepreneurial competencies and intentions of students. Their formation is a requirement of modern times. The question arises whether students of modern technical universities get entrepreneurial competencies and whether they transform these competencies into their entrepreneurial intentions. More than 3.6 thousand students from six technical universities from Poland, Ukraine, Latvia, Bulgaria, and Lithuania...
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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublikacjaAbstract—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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Fractional problems with advanced arguments
PublikacjaThis 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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On Nonlinear Dynamic Theory of Thin Plates with Surface Stresses
PublikacjaWe 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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RANS-based design optimization of dual-rotor wind turbines
PublikacjaPurpose 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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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublikacjaIn 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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Thermo-resonance analysis of an excited graphene sheet using a new approach
PublikacjaForced 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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Ellipticity of gradient poroelasticity
PublikacjaWe 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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Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model
PublikacjaWe 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
PublikacjaWe 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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Analysis of a gene expression model
PublikacjaWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the number of active binding sites, the way in which dimers bind to DNA and time delay in translation process. For a simplified model that consist of three ordinary differential equations with time delay we derive conditions for stability of the positive steady state and for the...
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Reduction of Computational Complexity in Simulations of the Flow Process in Transmission Pipelines
PublikacjaThe 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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Application of the distributed transfer function method and the rigid finite element method for modelling of 2-D and 3-D systems
PublikacjaIn the paper application of the Distributed Transfer Function Method and the Rigid Finite Element Method for modelling of 2-D and 3-D systems is presented. In this method an elastic body is divided into 1-D distributed parameter elements (strips or prisms). The whole body (divided into strips or prism) is described by a set of coupled partial differential equations. Solving this equations in the state space form it is possible...
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Experimental and predicted physicochemical properties of monopropanolamine-based deep eutectic solvents
PublikacjaIn this work, the novel deep eutectic solvents (DESs) based on 3-amino-1-propanol (AP) as hydrogen bond donor (HBD) and tetrabutylammonium bromide (TBAB) or tetrabutylammonium chloride (TBAC) or tetraethylammonium chloride (TEAC) as hydrogen bond acceptors (HBAs) were synthesized with different molar ratios of 1: 4, 1: 6 and 1: 8 salt to AP. Fourier Transform Infrared Spectroscopy measurements were performed to provide an evidence...
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Supply current signal and artificial neural networks in the induction motor bearings diagnostics
PublikacjaThis 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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Experimental and predicted physicochemical properties of monopropanolamine-based deep eutectic solvents
PublikacjaIn this work, the novel deep eutectic solvents (DESs) based on 3-amino-1-propanol (AP) as hydrogen bond donor (HBD) and tetrabutylammonium bromide (TBAB) or tetrabutylammonium chloride (TBAC) or tetraethylammonium chloride (TEAC) as hydrogen bond acceptors (HBAs) were synthesized with different molar ratios of 1:4, 1:6 and 1:8 salt to AP. Fourier Transform Infrared Spectroscopy measurements were performed to provide an evidence...
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Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum
PublikacjaIn this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets were modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear...
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Modal Adjustment of Rayleigh Based Structural Damping and Coordinate-Partitioning Algorithm Dedicated to Frictionless Contact Constraints between Multibody System and Structure Modelled with Finite Elements
PublikacjaThe paper presents a dedicated numerical algorithm. The algorithm is advantageous during investigations of the dynamics of a hybrid multibody / finite-elements system. We focus our attention on interactions resulting from mechanical contact. Pointwise contact connects a vertex of the multibody structure and a surface of the elastic reference body. Instead of a positive value of the relative penetration factor, constraint equations...
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Fractional Order Circuit Elements Derived from Electromagnetism
PublikacjaIn 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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Asynchronous time difference of arrival (ATDOA) method
PublikacjaA new method for a location service in the asynchronous wireless sensor networks is outlined. This method, which is called asynchronous time difference of arrival (ATDOA), enables calculation of the position of a mobile node without knowledge of relative time differences (RTDs) between measuring sensors. The ATDOA method is based on the measurement of time difference of arrival between the node and the same sensor at the discrete...
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The influence of frequency separation on imaging properties in DFEIT
PublikacjaW 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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Chosen aspects of muscle biomechanics
PublikacjaConsidering a striated skeletal muscle as a different properties mechanical system, one can understand series of important phenomena happening in a real muscle phenomenon of muscle: 1) force delivery to skeletal apparatus through tendons; 2) changing of exerted muscle belly mass distribution with regards to skeletal apparatus; 3) beginning drop of muscle force. A disregard of first phenomenon causes an impossibility to explain...
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Processing of point cloud data retrieved from terrestrial laser scanning for structural modeling by Finite Element Method
PublikacjaFinite Element Method is one most popular contemporary method of strength analysis. The method is an advanced method for solving differential equations, based on discretization, which means that area is divided into finite elements. Each finite element has a solution of the equation approximated by specific functions and performing the actual calculations only for nodes of this division. Finite Element Method is widely used in...
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Testing Stability of Digital Filters Using Multimodal Particle Swarm Optimization with Phase Analysis
PublikacjaIn this paper, a novel meta-heuristic method for evaluation of digital filter stability is presented. The proposed method is very general because it allows one to evaluate stability of systems whose characteristic equations are not based on polynomials. The method combines an efficient evolutionary algorithm represented by the particle swarm optimization and the phase analysis of a complex function in the characteristic equation....
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Identification of transition curves in vehicular roads and railways
PublikacjaIn 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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Magnetoacoustic heating in a quasi-isentropic magnetic gas
PublikacjaThe nonlinear heating of a plasma which associates with the transfer of energy of magnetoacoustic waves into that of the entropy mode, is analytically studied. A plasma is uniform and motionless at equilibrium. Perturbations in a plasma are described by a system of ideal magnetohydrodynamic equations. The equilibrium straight magnetic strength and the wave vector form a constant angle which varies from 0 to π/2. There exist four...
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublikacjaIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
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Local fixed point indices of iterations of planar maps
PublikacjaW artykule podana zostaje postać indeksów iteracji dla pewnej klasy odwzorowań planarnych. Podstawowymi narzędziami stosowanym w pracy są liczba Nielsena i indeks Conleya.
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Shub’s conjecture for smooth longitudinal maps of S^m
PublikacjaLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublikacjaWe show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...
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Diagnostyka łożysk silnika indukcyjnego na podstawie prądu zasilającego przy użyciu sztucznych sieci neuronowych
PublikacjaW artykule zawarto wyniki badań dotyczące diagnostyki łożysk silnika indukcyjnego na podstawie pomiarów prądu zasilającego z wykorzystaniem sztucznych sieci neuronowych. Zaprezentowano wyniki uczenia sieci oraz rezultaty testów przeprowadzonych na danych spoza zbioru uczącego. Badania wykonane zostały na obiektach z celowo wprowadzonymi uszkodzeniami łożysk. Przedstawiona nowa koncepcja zakłada użycie zestawu sieci neuronowych...
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Nonlinear resultant theory of shells accounting for thermodiffusion
PublikacjaThe 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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Buckling analysis of a non-concentric double-walled carbon nanotube
PublikacjaOn the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient and the van der Waals interaction...
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublikacjaIn 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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Hopf bifurcation in time‐delayed gene expression model with dimers
PublikacjaWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive...
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Simulation of hybridized nanofluids flowing and heat transfer enhancement via 3-D vertical heated plate using finite element technique
PublikacjaThe present study probed the creation of heat energy and concentrating into Newtonian liquids across vertical 3D-heated plates. The role of the Soret and Dufour theories in concentrating and energy formulas is discussed. The role of hybrid nanoparticles is introduced to illustrate particle efciency in terms of solute and thermal energy. It is removed a viscous dissipation process and a changing magnetic feld. The proposed approach...
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Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow
PublikacjaThe paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. Thi smakes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a...
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Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory
PublikacjaThe 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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A Nonlinear Model of a Mesh Shell
PublikacjaFor 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
PublikacjaIn 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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Novel analysis methods of dynamic properties for vehicle pantographs
PublikacjaTransmission 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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Analytical Steady-State Model of the Pipeline Flow Process
PublikacjaThe 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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Analytical method of determining dynamic properties of thermocouples used in measurements of quick – changing temperatures of exhaust gases in marine diesel engines
PublikacjaThe 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
PublikacjaAn 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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Numerical solution of threshold problems in epidemics and population dynamics
PublikacjaA 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...