Search results for: euler-lagrange equations
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Finite element matrix generation on a GPU
PublicationThis paper presents an efficient technique for fast generation of sparse systems of linear equations arising in computational electromagnetics in a finite element method using higher order elements. The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly. The performance results obtained on a test platform consisting of a Fermi GPU (1x Tesla C2075) and a CPU (2x twelve-core...
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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 (),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...
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Determination of time delay between ventricles contraction using impedance measurements
PublicationThe paper presents a novel approach to assessment of ventricular dyssynchrony basing on multichannel electrical impedance measurements. Using a proper placement of electrodes, the sensitivity approach allows estimating time difference between chambers contraction from over determined nonlinear system of equations. The theoretical considerations which include Finite Element Method simulations were verified using measurements on...
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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...
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Simplified probabilistic analysis of settlement of cyclically loaded soil stratum using point estimate method
PublicationThe paper deals with the probabilistic analysis of settlement of a non-cohesive soil layer subjected to cyclic loading. Originally, the settlement assessment is based on deterministic compaction model which requires integration of a set of differential equations. However, making use of the Bessel functions the settlement of the soil stratum can be calculated by means of simplified algorithm. The compaction model parameters were...
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Vibrational excitation of acetylene by positron impact
PublicationVibrationally inelastic quantum calculations are carried out at low collision energies for the scattering of a beam of positrons off acetylene gaseous molecules. The normal mode analysis is assumed to be valid and the relative fluxes into the C–C and C–H symmetric vibrational modes are computed within a Body-Fixed (BF) formulation of the dynamics by solving the relevant vibrational Coupled Channels (VCC) equations. The clear dominance...
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Numerical tests of time-stepping schemes in the context of FEM for 6-field shell dynamics
PublicationThe paper deals with integration of dynamic equations of irregular shells performed with relatively long time steps. Numerical instability appearing often in this kind of analysis motivated the authors to present some studies based on numerical tests referring to convergence problems of finite element analysis as well the applied stability conditions. The analysis is carried out on simulations of shell dynamics with the where the...
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Modelling of heat and mass transfer through wooden buildings
PublicationThe aim of this review paper is to examine the most recent available studies dealing with theoretical, numerical and experimental aspects related to modelling of heat and mass transfer through wooden buildings. The main thermophysical, mechanical and hygrometric properties of wood are firstly discussed. Then, the basic governing equations of heat and mass transfer phenomena are presented. A detailed description of the physical...
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Fluid structure interaction study of non-Newtonian Casson fluid in a bifurcated channel having stenosis with elastic walls
PublicationFluid–structure interaction (FSI) gained a huge attention of scientists and researchers due to its applications in biomedical and mechanical engineering. One of the most important applications of FSI is to study the elastic wall behavior of stenotic arteries. Blood is the suspension of various cells characterized by shear thinning, yield stress, and viscoelastic qualities that can be assessed by using non-Newtonian models. In this...
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Activation Energy and Inclination Magnetic Dipole Influences on Carreau Nanofluid Flowing via Cylindrical Channel with an Infinite Shearing Rate
PublicationThe infinite shear viscosity model of Carreau fluid characterizes the attitude of fluid flow at a very high/very low shear rate. This model has the capacity for interpretation of fluid at both extreme levels, and an inclined magnetic dipole in fluid mechanics has its valuable applications such as magnetic drug engineering, cold treatments to destroy tumors, drug targeting, bio preservation, cryosurgery, astrophysics, reaction kinetics,...
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Modeling of medium flow processes in transportation pipelines - the synthesis of their state-space models and the analysis of the mathematical properties of the models for leak detection purposes
PublicationThe dissertation concerns the issue of modeling the pipeline flow process under incompressible and isothermal conditions, with a target application to the leak detection and isolation systems. First, an introduction to the model-based process diagnostics is provided, where its basic terminology, tools, and methods are described. In the following chapter, a review of the state of the art in the field of leak detection and isolation...
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Modeling and simulation of blood flow under the influence of radioactive materials having slip with MHD and nonlinear mixed convection
PublicationRadioactive materials are widely in industry, nuclear plants and medical treatments. Scientists and workers in these fields are mostly exposed to such materials, and adverse effects on blood and temperature profiles are observed. In this regard, objective of the current study is to model and simulate blood based nanofluid with three very important radioactive materials, named as Uranium dioxide (UO2), Thorium dioxide (ThO2) and...
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Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory
PublicationIn the present investigation, a new first-order shear deformation theory (OVFSDT) on the basis of the in-plane stability of the piezo-magnetoelectric composite nanoplate (PMEN) has been developed, and its precision has been evaluated. The OVFSDT has many advantages compared to the conventional first-order shear deformation theory (FSDT) such as needless of shear correction factors, containing less number of unknowns than the existing...
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Computational analysis of power-law fluids for convective heat transfer in permeable enclosures using Darcy effects
PublicationNatural convection is a complex environmental phenomenon that typically occurs in engineering settings in porous structures. Shear thinning or shear thickening fuids are characteristics of power-law fuids, which are non-Newtonian in nature and fnd wide-ranging uses in various industrial processes. Non-Newtonian fuid fow in porous media is a difcult problem with important consequences for energy systems and heat transfer. In this...
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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...
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Generalized temperature dependence model for anammox process kinetics
PublicationTemperature is a key operational factor influencing the anammox process kinetics. In particular, at temperatures below 15 °C, the specific anammox activity (SAA) considerably decreases. This study aimed to describe the temperature dependence of the anammox process kinetics in the temperature range from 10 to 55 °C, including the specific characteristics of“cold anammox”. The commonly used Arrhenius and extended and modifiedRatkowsky...
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A Compact Basis for Reliable Fast Frequency Sweep via the Reduced-Basis Method
PublicationA reliable reduced-order model (ROM) for fast frequency sweep in time-harmonic Maxwell’s equations by means of the reduced-basis method is detailed. Taking frequency as a parameter, the electromagnetic field in microwave circuits does not arbitrarily vary as frequency changes, but evolves on a very low-dimensional manifold. Approximating this low-dimensional manifold by a low dimension subspace, namely, reduced-basis space, gives...
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Asynchronous Method of Simultaneous Object Position and Orientation Estimation with Two Transmitters
PublicationThis paper proposes an object location method for all types of applications, including the Internet of Things. The proposed method enables estimations of the position and orientation of an object on a plane or in space, especially during motion, by means of location signals transmitted simultaneously from two transmitters placed on the object at a known distance from each other. A mathematical analysis of the proposed method and...
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Energy conversion in systems-contained laser irradiated metallic nanoparticles - comparison of results from analytical solutions and numerical methods
PublicationThis work introduces the theoretical method of metallic nanoparticles’ (NPs’) heat and mass transfer where the particles are coated on a surface (base), together with considering the case wherein nanoparticles move freely in a pipe. In order to simulate the heat transfer, energy and radiative transfer equations are adjusted to the considered issue. NPs’ properties are determined following the nanofluidic theories, whereas absorption...
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Non-linear circuit model of a single doubly-fed induction machine formulated in natural axes for drive systems simulation purposes
PublicationMathematical modelling and a circuit model formulated in natural axes of a single doubly-fed induction machine, with the account of magnetic circuit nonlinearity are presented in the paper. Derivation of the model differential equations was based on Lagrange's energy method. State functions of magnetic elements in the model are non-linear and depend on all currents flowing in the machine windings and on the angle of rotor position....
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Surface finite viscoelasticity and surface anti-plane waves
PublicationWe introduce the surface viscoelasticity under finite deformations. The theory is straightforward generalization of the Gurtin–Murdoch model to materials with fading memory. Surface viscoelasticity may reflect some surface related creep/stress relaxation phenomena observed at small scales. Discussed model could also describe thin inelastic coatings or thin interfacial layers. The constitutive equations for surface stresses are...
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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 S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph...
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Discussion of “Development of an Accurate Time integration Technique for the Assessment of Q-Based versus h-Based Formulations of the Diffusion Wave Equation for Flow Routing” by K. Hasanvand, M.R. Hashemi and M.J. Abedini
PublicationThe discusser read the original with great interest. It seems, however, that some aspects of the original paper need additional comments. The authors of the original paper discuss the accuracy of a numerical solution of the diffusion wave equation formulated with respect to different state variables. The analysis focuses on nonlinear equations in the form of a single transport equation with the discharge Q (volumetric flow rate)...
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Kinetics of nitrogen removal processes in constructed wetlands
PublicationThe aim of this paper is to present a state-of-the-art review of the kinetics of nitrogen removal in constructed wetlands. Biological processes of nitrogen removal from wastewater can be described using equations and kinetic models. Hence, these kinetic models which have been developed and evaluated allow for predicting the removal of nitrogen in treatment wetlands. One of the most important, first order removal model, which is...
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Smooth Particle Hydrodynamics (SPH) approach in simulating large penetration into soil
PublicationA study of Smooth Particle Hydrodynamics (SPH) approach for predicting large soil deformation is presented. Theoretical basics of SPH method, including the equations governing, discussion of the importance of smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocodes simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into soil caused...
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Predicting the viscosity and electrical conductivity of ionic liquids on the basis of theoretically calculated ionic volumes
PublicationSelected physical properties of the ionic liquids might be quantitatively predicted based on the volumes of the ions these systems are composed of. It is demonstrated that the ionic volumes calculated using relatively simple theoretical quantum chemistry methods can be utilised to estimate the viscosities and electrical conductivities of various commonly used ionic liquids. The fitting formulas of the exponential form are offered...
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A Quasi-2D MOSFET Model — 2D-to-Quasi-2D Transformation
PublicationA quasi-two-dimensional (quasi-2D) representation of the MOSFET channel is proposed in this work. The representation lays the foundations for a quasi 2D MOSFET model. The quasi 2D model is a result of a 2D into quasi 2D transformation. The basis for the transformation are an analysis of a current density vector field and such phenomena as Gradual Channel Detachment Effect (GCDE), Channel Thickness Modulation Effect (CTME), and...
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Lax-Wendroff and McCormack Schemes for Numerical Simulation of Unsteady Gradually and Rapidly Varied Open Channel Flow
PublicationTwo explicit schemes of the finite difference method are presented and analyzed in the paper. The applicability of the Lax-Wendroff and McCormack schemes for modeling unsteady rapidly and gradually varied open channel flow is investigated. For simulation of the transcritical flow the original and improved McCormack scheme is used. The schemes are used for numerical solution of one dimensional Saint-Venant equations describing free...
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Approximate models and parameter analysis of the flow process in transmission pipelines
Publicationthe paper deals with the problem of early leak detection in transmission pipelines. First we present the derivation of state-space equations of the flow process in the pipelines. This description is then aggregated in order to obtain a principal model. Next, the problem of process model parameterization is addressed, taking into account the maximization of a model stability margin. The location of the maximum is determined using...
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The behavioural model of graphene field-effect transistor
PublicationThe behavioural model of a graphene field-effect transistor (GFET) is proposed. In this approach the GFET element is treated as a “black box” with only external terminals available and without considering the physical phenomena directly. The presented circuit model was constructed to reflect steady-states characteristics taking also into account GFET capacitances. The authors’ model is defined by a relatively small number of equations...
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Numerical simulation of cold flow and combustion in a swirl stabilized combustor
PublicationA numerical simulation model was developed to investigate the cold flow and combustion using Ansys FLUENT 2021R1. The governing equations were solved using the pressure-based method, and pressure–velocity coupling was performed using the SIMPLE method. To model the turbulent process, the RSM model was used. Non-premixed model is chosen to solve the chemical kinetics between fuel and oxigen. Radiation heat transfer was calculated...
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Determination of the refractive index and wavelength‐dependent optical properties of few‐layer CrCl3 within the Fresnel formalism
PublicationBased on previous reports on the optical microscopy contrast of mechanically exfoliated few layer CrCl3 transferred on 285 nmand 270 nmSiO2 on Si(100), we focus on the experimental determination of an effective mean complex refractive index via a fitting analysis based on the Fresnel equations formalism. Accordingly, the layer and wavelength-dependent absorbance and reflectance are calculated. Layer and wavelength-dependent optical...
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Flexomagneticity in Functionally Graded Nanostructures
PublicationFunctionally graded structures have shown the perspective of materials in a higher efficient and consistent manner. This study reports a short investigation by concentrating on the flexomagnetic response of a functionally graded piezomagnetic nano-actuator, keeping in mind that the converse magnetic effect is only taken into evaluation. The rule of mixture assuming exponential composition of properties along with the thickness...
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An inclination in Thermal Energy Using Nanoparticles with Casson Liquid Past an Expanding Porous Surface
PublicationPhysical aspects of inclined MHD nanofluid towards a stretching sheet embedded in a porous medium are visualized. Two types of nanoparticles are used named as copper and alumna dioxide with water as base fluid. Similarity transformations are used to convert the partial differential equations into the set of ordinary differential equation. Closed solutions are found to examine the velocity and the temperature profiles. It is examined...
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Biomass estimation using a length-weight relationship in beetle larvae (Coleoptera: Aphodiidae, Histeridae, Hydrophilidae, Staphylinidae) obtained from cow dung
PublicationThis research enabled the relationship between length and dry body mass to be determined for 158 beetle larvaetaken from cow dung in north-eastern Poland. The larvae were divided into three morphological types, for which the power and linear function of the body length-weight relationship were determined. The linear regression equation characterizes the relationship between body weight and...
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Local mesh morphing technique for parametrized macromodels in the finite element method
PublicationThis paper presents a novel approach for enhancing the efficiency of the design process of microwave devices by means of the finite element method. It combines mesh morphing with local model order reduction (MOR) and yields parametrized macromodels that can be used to significantly reduce the number of variables in the FEM system of equations and acceleration of computer simulation. A projection basis for local reduction is generated...
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GPU-Accelerated 3D Mesh Deformation for Optimization Based on the Finite Element Method
PublicationThis paper discusses a strategy for speeding up the mesh deformation process in the design-byoptimization of high-frequency components involving electromagnetic field simulations using the 3D finite element method (FEM). The mesh deformation is assumed to be described by a linear elasticity model of a rigid body; therefore, each time the shape of the device is changed, an auxiliary elasticity finite-element problem must be solved....
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Modelling a 6-dof manipulator using Matlab software
PublicationThis paper presents an alternative approach to modelling a revolute robot. The manipulator in question is Kuka KR 16-2. The main problem in robot modelling is a kinematic analysis. The revolute robot consist of six rotary joints (6-DOF) with base, shoulder, elbow and wirst. The kinematics problem is defined as a transformation from the cartesian space to the joint space. The Denavit- Hartenberg (D-H) model of representation was...
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Approximation of Fractional Order Dynamic Systems Using Elman, GRU and LSTM Neural Networks
PublicationIn the paper, authors explore the possibility of using the recurrent neural networks (RNN) - Elman, GRU and LSTM - for an approximation of the solution of the fractional-orders differential equations. The RNN network parameters are estimated via optimisation with the second order L-BFGS algorithm. It is done based on data from four systems: simple first and second fractional order LTI systems, a system of fractional-order point...
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THE COMPOSITION MODULATION EFFECT IN GaInPAs SOLID SOLUTIONS AS A MANIFESTATION OF ENERGY RESONANCE AFTER MATERIAL'S SPINODAL DECOMPOSITION
PublicationThe Cahn-Hilliard model concepts are extended to describe the spinodal decomposition of Ga$_x$In$_{1-x}$P$_y$As$_{1-y}$ solid solutions grown on the InP substrate. The energy of elastic deformation of the thin layer of a solid solution was calculated on the assumption of its coherent conjugation with the massive InP substrate. The excess energy of component mixing in the solid phase was modeled in accordance with the simple solution...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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Analog modelling in qualitative analysis of vibration propagation
PublicationThe theory of dynamic systems is usually used to model the real systems. The models are based on solving ordinary differential equations, partial or difference, which enable obtaining the relation between input signal and the system response (output signal). The analogy between those models and generalized dynamic systems or control systems can be practically used. Vibration propagation can be described in a similar way as the...
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The application of nonlinear curvature sections in the turnout diverging track
PublicationThe paper presents the analytical method of modelling the diverging track of railway turnout with nonlinear curvature sections. These sections were used for smoothing the graph of curvature in the extreme areas of turnout. The problem of the curvature distribution was identified with the use of differential equations. The resulting solutions are of universal nature for example the ability of assuming any values of curvature at...
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The Suzuki model of the multipath fading channel
Open Research DataThe dataset contains the results of simulations that are part of the research on modelling the multipath fading in the communication channel. The Suzuki fading envelope is generated using the Monte-Carlo simulation (MCS) in the LabVIEW programming environment.
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Finite element modeling of plastic hinges based on ductility demand-capacity method using nonlinear material for dynamic analysis
PublicationThe article discusses modeling plastic hinges in reinforced concrete interme-diate supports using finite elements methods. The ductility demand-capacitymethod was used to determine the geometrical parameters of cross-section plas-ticization zones, their ability to move and rotate, as well as their ductility. Dueto the varied geometry and stiffness of the supports and their nonlinear behav-ior under dynamic load, this method was...
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Stability by linear approximation for time scale dynamical systems
PublicationWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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Maximum transportation growth in energy and solute particles in Prandtl martial across a vertical 3D-heated surface: Simulations achieved using by finite element approach
PublicationThe goal of this study is to determine the maximum energy and solute particles' transportation growth in a 3D-heated region of Prandtl martial through a dynamic magnetic field. The effects of this field on the properties of solvent molecules and heat conduction are studied. A correctly stated functional method and a finite element approach are comparable to a certain type of differential equations. In order demonstrate the effects...
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Effect of Sinusoidal Corrugated Geometries on the Vibrational Response of Viscoelastic Nanoplates
PublicationThe vibrational behavior of viscoelastic nanoplates with a corrugated geometry is a key topic of practical interest. This problem is addressed here for wrinkled nanoplates with small corrugations related to incorrect manufacturing. To this end, a new One-Variable First-order Shear Deformation plate Theory (OVFSDT) is proposed in a combined form with a non-local strain gradient theory. The Kelvin–Voigt model is employed to describe...
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Novel Analytic-Numerical Model of Free Convection: with Leading Edge Considered
PublicationA novel solution of the free convection boundary problem is represented in analytical form for velocity and temperature for an isothermal vertical plate, as an example. These fields are built as a Taylor Series in the x coordinate with coefficients as functions of the vertical coordinate (y). We restrict ourselves by cubic approximation for both functions. The basic Navier-Stokes and Fourier-Kirchhoff equations and boundary conditions...
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Simulation of the remanence influence on the transient states in a single-phase multiwinding transformer
PublicationThis paper presents the mathematical model of a single-phase multi-winding core type transformer taking into account magnetic hysteresis phenomenon based on the feedback Preisach model (FPM). The set of loop differential equations was developed for a K-th winding transformer model where the flux linkages of each winding includes flux Φ common to all windings as a function of magneto motive force Θ of all windings. The first purpose...