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Wyniki wyszukiwania dla: RATE EQUATIONS
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Analytical method of modelling the geometric system of communication route
PublikacjaThe paper presents a new analytical approach to modelling the curvature of a communication route by making use of differential equations. The method makes it possible to identify both linear and nonlinear curvature. It enables us to join curves of the same or opposite signs of curvature. Solutions of problems for linear change of curvature and selected variants of nonlinear curvature in polynomial and trigonometric form were analyzed....
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On–line Parameter and Delay Estimation of Continuous–Time Dynamic Systems
PublikacjaThe problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous...
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Strong ellipticity conditions and infinitesimal stability within nonlinear strain gradient elasticity
PublikacjaWe discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis...
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Multi-headed chimera states in coupled pendula
PublikacjaWe discuss the occurrence of the chimera states in the network of coupled, excited by the clock’s mechanisms pendula. We find the patterns of multi-headed chimera states in which pendula clustered in different heads behave differently (oscillate with different frequencies) and create different types of synchronous states (complete or phase synchronization). The mathematical model of the network shows that the observed chimera states...
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Parameter and delay estimation of linear continuous-time systems
PublikacjaIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is usually described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous...
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Non-Wave Variations in Temperature Caused by Sound in a Chemically Reacting Gas
PublikacjaA weakly nonlinear generation of non-acoustic modes in the field of sound in a gas is considered. An exotericchemical reaction of A->B type, which takes place in a gas, may be reversible or not. Two types of sound areconsidered, low-frequency and high-frequency as compared with the characteristic time of a chemical reaction.For both these cases, the governing equations of non-acoustic modes are derived and conclusions of the efficiencyof...
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Research on the wear evenness of the tool in flat lapping
PublikacjaIn this paper, the dimensionless distribution of the material removal stock and the trajectories of abrasive grains cutting in single-sided lapping process are presented. They were numerically simulated based on the tribological model and kinematics equations. It can be observed that the trajectories geometry of single abrasive as well the velocities have a great influence on the final geometrical deviation. During machining, the...
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Nonlinear free and forced vibrations of a dielectric elastomer-based microcantilever for atomic force microscopy
PublikacjaThe majority of atomic force microcode (AFM) probes work based on piezoelectric actuation. However, some undesirable phenomena such as creep and hysteresis may appear in the piezoelectric actuators that limit their applications. This paper proposes a novel AFM probe based on dielectric elastomer actuators (DEAs). The DE is modeled via the use of a hyperelastic Cosserat model. Size effects and geometric nonlinearity are included...
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On analysis of nanocomposite conical structures
PublikacjaThis research examines the analysis of rotating truncated conical baskets reinforced by carbon nanotubes around the two independent axes. A time-dependent analysis is considered, and the nonlinear dynamic governing equations are extracted using the energy method. Carbon nanotubes (CNTs) reinforced the conical basket, and the structure's mechanical properties are determined based on the several distributions of carbon nanotubes....
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Urban flash flood hazard identification and assessment applying geospatial techniques and hydrodynamic modeling; Erbil city case study, Kurdistan Region of Iraq
PublikacjaThis dissertation aims to investigate the factors behind flash flooding in Erbil's central district, located in the Kurdistan Region of Iraq, and develop a methodology for assessing flood hazards in the city, despite limited data accessibility. In this thesis, each factor was investigated, including analyzing extreme precipitation events in the last two decades, including their spatial and temporal distribution of rainfall, intensity,...
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Natural convective heat transfer from isothermalconic
PublikacjaTheoretical considerations on convective heat transfer from isothermal upward conicalsurfaces have been presented. The physical model of this phenomenon consists of an isothermalcone of inclination angle (φ) between the cone generating line (X) and the radius (R) of the cone base. The angle is a parameter of conical surface which varied from (φ = 0−circular horizontal plate) to (φ = π/2—vertical cylinder) . Onthe basis of Navier–Stokes...
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Viscous versus electromagnetic damping – amplification in a neighbourhood of a mechanism singular position
PublikacjaIn the paper, damping of vibrations are considered and compared in a mechanical and in a electromechanical system. In the system, a continuous beam is considered as the main vibrating element. The compared dissipations methods are based on: viscous dampers and DC generators. To increase the possible damping effectiveness, velocity amplification is proposed, i.e., a mechanism is introduced between the beam and the damping element....
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Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation
PublikacjaTwo nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It...
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An Experimental and Numerical Analysis of Water Hammer Phenomenon in Slurries
PublikacjaThe analysis of slurry transportation in pressure pipelines is important both from practical and theoretical point of view. Due to the nature of the medium, the number of problems arising in the course of design, operation, measurements and mathematical modeling is much higher compared to the cases where the flowing liquid is homogeneous. The equations describing the flow are more complex, and higher number of the parameters is...
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On Applications of Fractional Derivatives in Circuit Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited...
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Application of muscle model to the musculoskeletal modeling
PublikacjaThe purpose of this paper is to investigate new fusiform muscle models. Each of these models treats a muscle as a system composedof parts characterized by different mechanical properties. These models explain the influence of differences in the stiffness of lateral parts and the degree of muscle model discretization. Each muscle model is described by a system of differential equations and a single integro-differential equation....
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Considerations about the applicability of the Reynolds equation for analyzing high-speed near field levitation phenomena
Publikacjaequation for analyzing near field levitation (NFL) phenomena. Two separate approaches were developed, experimentally verified, and applied to meet the research objective. One was based on the Reynolds equation and the other was based on general conservation equations for fluid flow solved using computational fluid dynamic (CFD). Comparing the calculation results revealed that, for certain operating conditions, differences in the...
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublikacjaThe paper presents the neutron point kinetics and heat exchange models for the nuclear reactor. The models consist of a nonlinear system of fractional ordinary differential and algebraic equations. Two numerical algorithms are used to solve them. The first algorithm is application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. The second involves building an analog scheme in the FOMCON Toolbox...
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Wideband Macromodels in Finite Element Method
PublikacjaThis letter proposes a novel projection technique for accelerating Finite Element Method simulations. The algorithm is based on the Second-order Arnoldi Method for Passive Order Reduction (SAPOR). It involves generation of two projection bases and thanks to this it is applicable to the systems of equations, which contain the quadratic frequency-dependence in the input term, that arise when projection is applied locally in the selected...
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Homoclinic and Heteroclinic Orbits for a Class of Singular Planar Newtonian Systems
PublikacjaThe study of existence and multiplicity of solutions of differential equations possessing a variational nature is a problem of great meaning since most of them derives from mechanics and physics. In particular, this relates to Hamiltonian systems including Newtonian ones. During the past thirty years there has been a great deal of progress in the use of variational methods to find periodic, homoclinic and heteroclinic solutions...
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Explicit and implicit difefrence methods for quasilinear first order partial functional differential equations.
PublikacjaInitial boundary value problems of the Dirichlet type for quasilinear functional differential equations are considered. Explicit difference schemes of the Euler type and implicit difference methods are investigated. Suffcient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both classes...
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Hybrid, Approximate Models of Distributed-Parameter Systems
PublikacjaThe paper introduces the method of distributed-parameter systems modelling. It enables to obtain low order modal model of the system that experiences Coriolis acceleration component and gyroscopic effect. In such cases, corresponding system equations are non-self-adjoined. To solve this problem modal reduced model is built up for the system without Coriolis acceleration or gyroscopic effect terms. These phenomena are next included...
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Wideband Model Order Reduction for Macromodels in Finite Element Method
PublikacjaAbstract: This paper presents a novel algorithm for accelerating 3D Finite Element Method simulations by introducing macromodels created in local model order reduction in the selected subdomains of the computational domain. It generates the projection basis for a compact system of equations associated with a separate subdomain. Due to non-linear frequency dependency in the Right Hand Side (RHS), the standard reduction methods do...
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Multiple Solutions to Third-Order Differential Equations with Derivative Dependence and Deviating Arguments
PublikacjaIn this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J ⊂ [0,1] and advanced...
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SPECTRAL RESPONSE OF STATIONARY JACK-UP PLATFORMS LOADED BY SEA WAVES AND WIND USING PERTURBATION METHOD
PublikacjaThe paper addresses non-linear vibrations of offshore jack-up drilling platforms loaded by sea waves and wind in their stationary condition using the perturbation method. Non-linearity of dynamic equations of motion for fixed offshore platforms yields from two factors. The first is load excitation generating non-linear velocity coupling in a dynamic system. This coupling is inherent in the modified Morison equation, involving the...
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Genetic Algorithm Approach for Gains Selection of Induction Machine Extended Speed Observer
PublikacjaThe subject of this paper is gains selection of an extended induction machine speed observer. A high number of gains makes manual gains selection difficult and due to nonlinear equations of the observer, well-known methods of gains selection for linear systems cannot be applied. A method based on genetic algorithms has been proposed instead. Such an approach requires multiple fitness function calls; therefore, using a quality index...
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A quasi-2D small-signal MOSFET model - main results
PublikacjaDynamic properties of the MOS transistor under small-signal excitation are determined by kinetic parameters of the carriers injected into the channel, i.e., the low-field mobility, velocity saturation, mobility at the quiescent-point (Q-point), longitudinal electric field in the channel, by dynamic properties of the channel, as well as by an electrical coupling between the perturbed carrier concentration in the channel and the...
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Influence of temperature and anion type on thermophysical properties of aqueous solutions of morpholine based amino acid ionic liquids
PublikacjaDensities and sound velocities of aqueous solutions of N-butyl-N-methylmorpholine based amino acid ionic liquids (AAILs), including N-acetyl-L-alanine, N-acetyl-Lvalinate, N-acetyl-L-leucinate, and N-acetyl-L-izoleucinate anions were measured at a temperature from 293.15 to 313.15 K at 5 K intervals and atmospheric pressure. These data were used to calculate the apparent molar volumes and the apparent molar compressibilities in...
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Redundantly Actuated 3RRR Parallel Planar Manipulator - Numerical Analyses of its Dynamics Sensitivity on Modifications of its Platform’s Inertia Parameters
PublikacjaIn the paper, numerical analyses, as well as dynamics of a complex mechanism, are presented. Two objectives are crucial for the paper: inverse dynamic model is needed (dedicated to be use in the model predictive controller); an identification method is searched (some trajectory parameters are controlled, when specific trajectory is tracked under an open-loop model-based control), as selected parameters must be identified for the...
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TIME- AND FREQUENCY-DOMAIN QUASI-2D SMALL-SIGNAL MOSFET MODELS
PublikacjaA novel approach to small-signal MOSFET modeling is presented in this book. As a result, time- and frequency-domain physics-based quasi-2D NQS four-terminal small-signal MOSFET models are proposed. The time-domain model provides the background to a novel DIBL-included quasi‑2D NQS four-terminal frequency-domain small-signal MOSFET model. Parameters and electrical quantities of the frequency-domain model are described by explicit...
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Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
PublikacjaWe propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...
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Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
PublikacjaWe propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
PublikacjaWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is...
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublikacjaThis paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme...
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Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System
PublikacjaIn this paper, we study a classical two-predators-one-prey model. The classical model described by a system of three ordinary differential equations can be reduced to a one-dimensional bimodalmap. We prove that this map has at most two stable periodic orbits. Besides, we describe the bifurcation structure of the map. Finally, we describe a mechanism that leads to bistable regimes. Taking this mechanism into account, one can easily...
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Vibration of the bridge under moving singular loads - theoretical formulation and numerical solution
PublikacjaThe paper presents the results of the numerical analysis of a simple vehicle passing over a simply supported bridge span. The bridge is modelled by a Euler-Bernoulli beam. The vehicle is modelled as a linear, visco-elastic oscillator, moving at a constant speed. The system is described by a set of differential equations of motion and solved numerically using the Runge-Kutta algorithm. The results are compared with the solution...
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1D Model Callibration on the Basis on 3D calculations for Tesla Turbine
PublikacjaThe paper presents the system of equations for axisymmetriclaminar flow, after averaging, through the width of interdisk slit ofTesla turbine. Coefficients were introduced, as a result ofaveraging, that improve the efficiency of 1D model. The minimalnumber of such coefficients was determined. The 1D modelmakes it possible to attain analytical solutions to an accuracylimited by these coefficients. Calibration of 1D model depends...
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Standing Waves and Acoustic Heating (or Cooling) in Resonators Filled with Chemically Reacting Gas
PublikacjaStanding waves and acoustic heating in a one-dimensional resonator filled with chemically reacting gas, is the subject of investigation. The chemical reaction of A ! B type, which takes place in a gas, may be reversible or not. Governing equations for the sound and entropy mode which is generated in the field of sound are derived by use of a special mathematical method. Under some conditions, sound waves propagating in opposite...
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Compressed Projection Bases for Model-Order Reduction of Multiport Microwave Components Using FEM
PublikacjaThis paper presents a projection basis compression technique for generating compact reduced-order models (ROM) in the FE analysis of microwave devices. In this approach redundancy is removed from the projection basis by means of the proper orthogonal decomposition technique applied to the projected system of linear equations. Compression allows for keeping the size of a reduced-order model as small as possible without compromising...
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A Stand for Measurement and Prediction of Scattering Properties of Diffusers
PublikacjaIn this paper we present a set of solutions which may be used for prototyping and simulation of acoustic scattering devices. A system proposed is capable of measuring sound field. Also a way to use an open source solution for simulation of scattering phenomena occurring in proximity of acoustic diffusers is shown. The result of our work are measurement procedure and a prototype of the simulation script based on FEniCS - an open source...
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Design criterion for hydrodynamic vortex separators
PublikacjaTechnical objects designing involves determination of geometrical parameters that characterize a given object. When the device is described by the differential equations, an inverse problem brings difficulties, as geometrical values sought condition the solution to the problem. Vortex separators can be designed by the "criterion method'. Firstly, a critical particle is distinguished such that bigger particles are removed from...
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Modelling of Diffusing Capacity Measurement Results in Lung Microangiopathy Patients. A novel Diagnostic Suppport
PublikacjaLung microangiopathy is a little known negative influence of diabetes mellitus on the functioning of the lungs. The aim of this study is to design a supportive method for diagnosing lung microangiopathy. This will be based on routinely performed pulmonary measurements as well as on investigation process modelling and data processing. A model of the diffusion of oxygen from the alveoli to the blood has been described with a set...
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On the Nonlinea Distortions of Sound and its Coupling with Other Modes in a Gasesous Plasma with Finite Electric Conductivity in a Magnetic Field
PublikacjaNonlinear phenomena of the planar and quasi-planar magnetoacoustic waves are considered. We focus on deriving of equations which govern nonlinear excitation of the non-wave motions by the intense sound in initially static gaseous plasma. The plasma is treated as an ideal gas with finite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. This introduces dispersion of a flow. Magnetoacoustic...
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Modelling of heat and mass transfer through wooden buildings
PublikacjaThe 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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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublikacjaIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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The influence of stainless steels microstructure evolution on the mechanical properties of pressure installation elements
PublikacjaIn 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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Determination of time delay between ventricles contraction using impedance measurements
PublikacjaThe 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
PublikacjaIn 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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Finite element matrix generation on a GPU
PublikacjaThis 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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Vibrational excitation of acetylene by positron impact
PublikacjaVibrationally 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...