Search results for: DARCY-WEISBACH EQUATION
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Improved model of isothermal and incompressible fluid flow in pipelines versus the Darcy–Weisbach equation and the issue of friction factor
PublicationIn this article, we consider the modelling of stationary incompressible and isothermal one-dimensional fluid flow through a long pipeline. The approximation of the average pressure in the developed model by the arithmetic mean of inlet and outlet pressures leads to the known empirical Darcy–Weisbach equation. Most importantly, we also present another improved approach that is more accurate because the average pressure is estimated...
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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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Flow of liquid in flat gaps of the satellite motor working mechanism
PublicationThe article describes the methodology and results of investigations of the flow of oil and HFA-E emulsion in flat gaps of the working mechanism of a satellite motor. The flow of liquid in those gaps is turbulent and not fully developed. The article presents two methods of modelling this flow. Method I makes use of the Darcy-Weisbach formula, while Method II bases on the assumption that in the variable-length gaps the flow is turbulent...
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Prawo Darcy w gruntach słabo przepuszczalnych.
PublicationPrawo Darcy. Badania Pane'a i Schifmana, Tavenas'a, Olsen'a. Zakres stosowalności prawa Darcy. Badania własne iłów w standardowym aparacie trójosiowego ściskania. Badania własne w prototypowym aparacie do badania przepuszczalności gruntów słabo przepuszczalnych. Liniowa zależność prędkości przepływu od spadku hydrulicznego.
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Equivariant Morse equation
PublicationThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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Dimensionally Consistent Nonlinear Muskingum Equation
PublicationAlthough the Muskingum equation was proposed nearly 75 years ago, it is still a subject of active research. Despite of its simple form, the real properties of this equation have not been comprehensively explained. This paper proposes a new interpretation of the linear McCarthy’s relation. This relation can be interpreted only together with the storage equation, whereas the Muskingum equation can be derived directly from the system...
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Newton’s Method for the McKendrick-von Foerster Equation
PublicationIn the paper we study an age-structured model which describes the dynamics of one population with growth, reproduction and mortality rates. We apply Newton’smethod to the McKendrick-von Foerster equation in the semigroup setting. We prove its first- and second-order convergence.
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Thermal ablation modeling via bioheat equation
PublicationWe consider Pennes’ bioheat equation and discuss an implicit numerical scheme which has better stability properties than other approaches. Our discussion concerns Carthesian geometry problems, however it carries over to spherical geometry models and more complicated shapes.
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Balance error generated by numerical diffusion in the solution of Muskingum equation
PublicationIn the paper the conservative properties of the lumped hydrological models with variable parameters are discussed. It is shown that in the case of the non-linear Muskingum equation the mass balance is not satisfied. The study indicates that the mass balance errors are caused by the improper form of equation and by the numerical diffusion which is generated in the solution. It has been shown that the classical way of derivation...
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Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation
PublicationTwo 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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Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublicationThe focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow...
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Computational issues of solving the 1D steady gradually varied flow equation
PublicationIn this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution....
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Straightened characteristics of McKendrick-von Foerster equation
PublicationWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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KOLMOGOROV EQUATION SOLUTION: MULTIPLE SCATTERING EXPANSION AND PHOTON STATISTICS EVOLUTION MODELING
PublicationWe consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon...
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Thermal ablation modeling via the bioheat equation and its numerical treatment
PublicationThe phenomenon of thermal ablation is described by Pennes’ bioheat equation. This model is based on Newton’s law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Open Research DataThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...
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Methods of solving the Atkins equation determine shear angle with taking into consideration a modern fracture mechanics
PublicationIn the paper are presented methods of solving nonlinear Atkins equation . The Atkins equation describe shear angle with taking into account properties of material cutting. To solve Atkins equation has been used iterative methods: Newton method and simplified method of simple iteration. Method of simple iteration is presented in the form of Java application.
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublicationIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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Considerations about the applicability of the Reynolds equation for analyzing high-speed near field levitation phenomena
Publicationequation 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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Impact of the Finite Element Mesh Structure on the Solution Accuracy of a Two-Dimensional Kinematic Wave Equation
PublicationThe paper presents the influence of the finite element mesh structure on the accuracy of the numerical solution of a two-dimensional linear kinematic wave equation. This equation was solved using a two-level scheme for time integration and a modified finite element method with triangular elements for space discretization. The accuracy analysis of the applied scheme was performed using a modified equation method for three different...
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Studies of Nonlinear Sound Dynamics in Fluids Based on the Caloric Equation of State
PublicationThe sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting...
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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Equation of state for Eu-doped SrSi2O2N2
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Approximated boundary conditions of the equation of difussion
PublicationProblem podejmowany w pracy dotyczy warunku brzegowego w równaniach fizyki matematycznej, opisujących procesy migracji zanieczyszczeń. W szczególności skoncentrowano się na badaniu wpływu na rozwiązanie przyjmowanych w rozwiązaniach numerycznych aproksymacji ''odpływowego'' warunku brzegowego w jednowymiarowym równaniu adwekcji - dyspersji. Rozważania teoretyczne przeprowadzono w oparciu o rozwiązania analityczne oraz numeryczne...
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The application of Monod equation to denitrification kinetics description in the moving bed biofilm reactor (MBBR)
PublicationIn this paper, the kinetic constants Vmax and KCOD occurring in the Monod equation, which describe the denitrification process in the moving bed, are determined. For this purpose, a laboratory moving bed biofilm reactor (MBBR) was used. The filling of the reactor consisted of EvU Perl carriers. The experiment was carried out with an excess of nitrate, and denitrification rate was dependent on the concentration of external organic...
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Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition
PublicationResearch on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However,...
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A Fortran-95 algorithm to solve the three-dimensional Higgs boson equation in the de Sitter space-time
Open Research DataA numerically efficient finite-difference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space-time is designed. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0,1)U(1,2], which considers a generalized potential and a time-dependent diffusion...
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Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations
PublicationVarious numerical methods were proposed for analysis of the light scattering phenomenon. Important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation (DDA). DDA uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo (MC)...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublicationIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublicationWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublicationIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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Simulating propagation of coherent light in random media using the Fredholm type integral equation
PublicationStudying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g....
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Quantum corections to SG equation solutions and applications
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Aerated grit chambers hydraulic design equation.
PublicationW pracy zaproponowano metodę wymiarowania piaskowników napowietrzanych. Jej głównymi elementami są wyznaczanie niezbędnej intensywności aeracji ścieków, pola ich prędkości oraz trajektorii cząstek zawiesiny.
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The interpretation of the parameters of the equation used for the extrapolation of apparent molar volumes of the non-electrolyte (solutes) to the infinite dilution
PublicationThe paper discusses how to interpret the parameters of the basic equation used for the extrapolation of the apparent molar volume of the solute to infinite dilution. The common misunderstandings and oversimplifications have been pointed out. We present the alternative ways of the data interpretation that can be used to eliminate these obvious but frequent mistakes.
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Some new soliton solutions to the higher dimensional Burger–Huxley and Shallow water waves equation with couple of integration architectonic
PublicationIn this paper, we retrieve some traveling wave, periodic solutions, bell shaped, rational, kink and anti-kink type and Jacobi elliptic functions of Burger’s equation and Shallow water wave equation with the aid of various integration schemes like improved -expansion scheme and Jacobi elliptic function method respectively. We also present our solutions graphically in various dimensions.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Open Research DataThe presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.
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Computationally Effcient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems
PublicationThis paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed...
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Determination of dryout localization using a five-equation model of annular flow for boiling in minichannels
PublicationDetailed studies have suggested that the critical heat flux in the form of dryout in minichannels occurs when the combined effects of entrainment, deposition, and evaporation of the film make the film flow rate go gradually and smoothly to zero. Most approaches so far used the mass balance equation for the liquid film with appropriate formulations for the rate of deposition and entrainment respectively. It must be acknowledged...
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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublicationThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...
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Journal of Applied Structural Equation Modeling
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Structural Equation Modeling: A Multidisciplinary Journal
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Modelling of FloodWave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation
PublicationA full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of...
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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublicationThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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Reduction restrictions of Darboux and Laplace transformations for the Goursat equation
PublicationZredukowane przekształcenia Darboux i Laplace`a dla równania Goursata zastosowane do rozwiązywania problemów nieliniowych i geometrycznych. Podaje się nowe rozwiązania równań KdV-MKdV w przestrzeni 2+1.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Open Research DataPresented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...
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Magdalena Brzozowska-Woś dr hab. inż.
PeopleMagdalena Brzozowska-Woś is a graduate of the Faculty of Management and Economics of the Gdańsk University of Technology (specialization: management systems). She is also a graduate of Postgraduate Studies in Advertising (Faculty of Management and Economics, GUT) and Postgraduate Studies in Public Relations (SWPS University of Humanities and Social Sciences). In the years 2000-2003, she cooperated with Panorama Internet sp. z o....
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Electronically Excited States in Solution via a Smooth Dielectric Model Combined with Equation-of-Motion Coupled Cluster Theory
PublicationWe present a method for computing excitation energies for molecules in solvent, based on the combination of a minimal parameter implicit solvent model and the equation-of-motion coupled-cluster singles and doubles method (EOM-CCSD). In this method, the solvent medium is represented by a smoothly varying dielectric function, constructed directly from the quantum mechanical electronic density using only two tunable parameters. The...
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Impact of diffusion coefficient averaging on solution accuracy of the 2D nonlinear diffusive wave equation for floodplain inundation
PublicationIn the study, the averaging technique of diffusion coefficients in the two-dimensional nonlinear diffusive wave equation applied to the floodplain inundation is presented. As a method of solution, the splitting technique and the modified finite element method with linear shape functions are used. On the stage of spatial integration, it is often assumed that diffusion coefficient is constant over element and equal to its average...
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublicationDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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Galerkin finite element analysis of Darcy–Brinkman–Forchheimer natural convective flow in conical annular enclosure with discrete heat sources
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Design Equation for Stirring Fluid by a Stream Pump in a Circulating Tank
PublicationA circulating tank is a very useful theoretical scheme for many fluid-flow objects in several branches of engineering. The motion of the fluid in such objects can be induced in different ways. A stream pump provides an especially interesting possibility; however, the quantitative description of such devices shows some shortcomings. Such a device is analogous to a jet pump, thus has similar advantages (simplicity of construction,...
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Liquid water. Analytical equation of state and acoustic parameters evaluation.
PublicationRównanie stanu dla ciekłej wody zaproponowane przez Jefferya - Austina zastosowano do obliczeń prędkości dźwięku oraz parametru nieliniowości B/A. Parametry akustyczne są porównywane z danymi doświadczalnymi.
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Mesh-free approach to Helmholtz equation on radial basis functions
PublicationMetoda radialnych funkcji bazowych (RBF) jest coraz czesciej stosowana przy rozwiazywaniu rownan rozniczkowych czastkowych oraz zagadnien wlasnych. W szczegolnosci znalazla ona zastosowanie w problemach elektrodynamiki obliczeniowej. W publikacji zastosowano RBF do rozwiazania rownania Helmholtza. Wprowadzono nowy algorytm - adaptacyjny do wyznaczania centrow interpolacyjnych. Przedstawiona metode zastosowano do wyznaczenia rozkladow...
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Analysis of the KZK equation solution for fixed pressure distributions at the piston
PublicationPraca dotyczy zagadnienia oddziaływania fal o dużej amplitudzie, generowanych przez przetwornik kołowy o gaussowskim rozkładzie ciśnienia. Model matematyczny zbudowano w oparciu o równania KZK. Do rozwiązania zagadnienia zastosowano metodę różnic skończonych. Badano zmiany ciśnienia fal różnych częstotliwości w obrębie wiązki akustycznej. Wyniki obliczeń numerycznych porównano z odpowiednimi rozwiązaniami analitycznymi
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Use of structural equation modeling in quantitative research in the field of management and economics: A bibliometric analysis in the systematic literature review
PublicationPURPOSE: This paper aims to provide a comprehensive review of scholarly research focusing on using quantitative methods and particularly structural equation modeling (SEM) in management and economics studies, as well as provide a bibliometric agenda including the time horizon of individual publications, the highest citation rate, geographic and industry areas, methodological context, and keywords. METHODOLOGY: A systematic literature...
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The use of Preston equation to determine material removal during lap-grinding with electroplated CBN tools
PublicationGrinding executed in a lapping configuration is an alternative finishing process benefiting from both grinding and free-abrasive machining, while minimizing the heat effect impact. Electroplated tools can be effectively used in different abrasive processes, including high-speed grinding, however, the assessment of machining performance over time is a key factor in their correct use to achieve satisfactory technological results....
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Mesh-free approach to Helmholtz equation based on radial basis functions.
PublicationW artykule zastosowano metodę radialnych funkcji bazowych do rozwiązania równania Helmholthza oraz zaproponowano nowy (adaptacyjny) algorytm wyznaczania centrów interpolacyjnych. W oparciu o prezentowany schemat wyznaczono długości fal odcięcia dla różnych kształtów przekrojów poprzecznych falowodów cylindrycznych.
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Thresholds of Lasing as Solutions of Characteristic Equation for a VCSEL-type Layered Structure
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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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Application of the Fröbenius method to the Schrödinger equation for a spherically symmetric potential: an anharmonic oscillator
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Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Schrodinger equation.
PublicationPrzeformułowano metodę Inglesfielda, stosowaną do obliczania własności stanów związanych równania Schrodingera, stosując formalizm operatorów całkowych Dirichleta-do-Neumanna(DtN) i Neumanna-do-Dirichleta (NtD). Wykorzystano zasady wariacyjne dla energii dopuszczające użycie funkcji próbnych nieciągłych wraz z pochodnymi. Podano metodę konstrukcji jąder operatorów DtN i NtD za pomocą rozwiązań zagadnienia własnego typu Steklova....
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Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Dirac equation
PublicationZaprezentowano uogólnienie formalizmu operatorów Dirichleta-Neumanna (DtN) i Neumanna-Dirichleta (NtD) na przypadek równania Diraca. Przedstawiono zastosowanie tego formalizmu do znajdowania poziomów energetycznych cząstki Diraca związanej w potencjale.
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MHD darcy-forchheimer nanofluid flow and entropy optimization in an odd-shaped enclosure filled with a (MWCNT-Fe3O4/water) using galerkin finite element analysis
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Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point.
PublicationW niniejszej pracy badamy problem istnienia bifurkacji w zbiorze rozwiązań równania F(x,p)=0, gdzie F jest odwzorowaniem klasy C^2z iloczynu kartezjańskiego X i R^k do Y, X i Y są przestrzeniami Banacha takimi, że X jest podprzestrzenią liniową Y. Co więcej, dany jest iloczyn skalarny w Y, ciągły względem norm w X i Y. Pokazujemy, że pod pewnymi warunkami (0,p) jest punktem bifurkacji i opisujemyzbiór rozwiązań równania F(x,p)=0...
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Asymptotic numerical solver for the linear Klein–Gordon equation with space- and time-dependent mass
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Analytical-numerical approach to solve the transport equation for steady gradually varied flow in open channel
PublicationW pracy przedstawiono metodę rozwiązania równania transportu adwekcyjno-dyfuzyjnego w przypadku ustalonego niejednostajnego przepływu w kanałach otwartych. Metoda wykorzystuje technikę dekompozycji. Do rozwiązania równania adwekcji-dyfuzji zastosowano analityczne rozwiązanie w postaci odpowiedzi impulsowej liniowego równania adwekcji-dyfuzji. Dokonano adaptacji metody dla przypadku ze zmiennymi parametrami. Do rozwiązania drugiej...
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Alternative approach to the solution of the momentum-space Schrödinger equation for bound states of the N-dimensional Coulomb problem
PublicationW pracy rozważono zagadnienie Schrödingera-Coulomba w R^N, N>=2, w reprezentacji pędowej. Radialne równanie całkowe występujące w stowarzyszonym zagadnieniu sturmowskim rozwiązano, stosując podane przez Ossiciniego symetryczne rozwinięcie typu Poissona funkcji Legendre'a drugiego rodzaju w szereg iloczynów wielomianów Gegenbauera. Następnie wykorzystano relację pomiędzy rozwiązaniami zagadnienia sturmowskiego oraz zagadnienia własnego...
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The pollutant transport equation for a steady, gradually varied flow in an open channel network: a solution of high accuracy
PublicationW pracy przedstawiono metodę rozwiązania jednowymiarowego równania adwekcji-dyfuzji opisującego transport zanieczyszczeń w warunkach przepływu ustalonego wolnozmiennego w sieci kanałów otwartych. Zastosowano technikę dekompozycji. Zlineoryzowane równanie adwekcji-dyfuzji rozwiązano stosując całkę Duhamela, zaś równanie zacierające człon źródłowy-metodą różnic skończonych. Metoda zapewnia bardzo dużą dokładność rozwiązania nawet...
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Badania progu podwodnego na dnie piaszczystym w numerycznym kanale falowym
PublicationPodstawy modelowania wzajemnego oddziaływania falowania, przepuszczalnego progu podwodnego i piaszczystego dna z wykorzystaniem numerycznego kanału falowego CADMAS-SURF, rozbudowanego o równania przepływu Darcy z rozszerzeniem Brinkmanna-Frochheimera (DARCY-SURF).Zastosowanie modelu skonczonej cieczy lepkiej ze swobodna powierzchnia w obszarze falowania i progu.
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Wioletta Gorczewska-Langner dr inż.
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Data obtained by computation for X-ray focusing using oriented Gaussian beams
Open Research DataThe propagation of X-ray waves through an optical system consisting of several X-ray refractive lenses is considered. Gaussian beams are exact solutions of the paraxial equation. The Helmholtz equation describes the propagation of a monochromatic electromagnetic wave. Since the widths of the beams are much larger than the wavelength of X-rays, Gaussian...
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Karolina Lademann mgr
PeopleCurriculum vitae
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Michał Michna dr hab. inż.
PeopleMichal Michna received the M.Sc. and Ph.D. degrees in electrical engineering from the Gdansk University of Technology (GUT), Gdansk, Poland, in 1998 and 2005, respectively. Since 2004, he was employed at the Department of Power Electronics and Electrical Machines of the Gdańsk University of Technology (assistant, assistant professor, senior lecturer). In 2010-2015 he was a deputy of head of the Department of Power Electronics and...
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The generalized 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 generalized Suzuki fading envelope is generated using the Monte-Carlo simulation (MCS) in the LabVIEW programming environment.
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The Weibull 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 Weibull fading envelope is generated using the Monte-Carlo simulation (MCS) in the LabVIEW programming environment.
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Marta Kuc-Czarnecka dr
PeopleMarta Kuc-Czarnecka is the deputy head of the Department of Statistics and Economics at the Faculty of Management and Economics of the Gdańsk University of Technology. She also serves as the Dean's proxy for AMBA accreditation. She is a co-founder of Rethinking Economics Gdańsk and a member of the Foundation Edward Lipiński for the promotion of pluralism in economic sciences. In 2018-2022, she was Eurofound’s quality of life and...
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Potential energy curve, rovibrational energies and nuclear wave functions of 2 singlet Pi state in KLi dimer
Open Research DataThis data sets contains potential energy curve, energy levels and nuclear wave functions of rovibrational states of KLi dimer in 2 singlet Pi electronic state. Potential energy curve (PEC) for the electronic state was calculated in the Born-Oppenheimer approximation by the means of effective core potentials and MRCI method. Nuclear wave functions and...
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Mechanism of Solute and Thermal Characteristics in a Casson Hybrid Nanofluid Based with Ethylene Glycol Influenced by Soret and Dufour Effects
PublicationThis article models a system of partial differential equations (PDEs) for the thermal and solute characteristics under gradients (concentration and temperature) in the magnetohydrodynamic flow of Casson liquid in a Darcy porous medium. The modelled problems are highly non-linear with convective boundary conditions. These problems are solved numerically with a finite element approach under a tolerance of 10−8. A numerical algorithm...
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A solution of non-linear differential problem with application to selected geotechnical problems
PublicationA certain non-linear differential equation containing a power of unknown function being the solution is considered with application to selected geotechnical problems. The equation can be derived to a linear differential equation by a proper substitution and properties of the operations G and S.
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Karolina Lademann Mgr
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Flood Routing by the Non-Linear Muskingum Model: Conservation of Mass and Momentum
PublicationIn this paper, the conservative properties of the Muskingum equation, commonly applied to solve river flood routing, are analysed. The aim of this analysis is to explain the causes ofthe mass balance error, which is observed in the numerical solutions of its non-linear form. The linear Muskingum model has been considered as a semi-discrete form of the kinematic wave equation and therefore it was possible to derive its two non-linear...
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Numerical analysis of open channel steady gradually varied flow using the simplified saint-venant equations
PublicationFor one-dimensional open-channel flow modeling, the energy equation is usually used. There exist numerous approaches using the energy equation for open-channel flow computations, which resulted in the development of several very efficient methods for solving this problem applied to channel networks. However, the dynamic equation can be used for this purpose as well. This paper introduces a method for solving a system of non-linear...
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Inverse Flood Routing Using Simplified Flow Equations
PublicationThe paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve...
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DISTRIBUTION OF FLOWS IN A CHANNEL NETWORK UNDER STEADY FLOW CONDITIONS
PublicationThe article presents an algorithm for calculating the distribution of flow in a junction of open channel network under steady flow conditions. The article presents a simplified calculation algorithm used to estimate the distribution of flow in a network of channels under steady flow conditions. The presented algorithm is based on the continuity equation and a simplified energy equation. To describe the relationship between the...
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Marek Czachor prof. dr hab.
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Fluid Mechanics, L/L/E, DaPE, sem. 04, summer 21/22 (PG_00050282)
e-Learning CoursesLECTURES Introduction and basic definitions. Properties of fluids. Models of fluids. Fluids in equilibrium. Determination of hydrostatic forces. Archimedes" law. Methods of fluid flow description. General motion of fluid. Deformation of fluid element. Vortex motion of fluid. Principles of conservation of mass, momentum and energy. Balance of entropy. Navier-Stokes equation. Bernoulli equation. Similarity of flow phenomena. Potential...
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Barrett-Joyner-Halenda (BJH) and Brunauer-Emmett-Teller (BET) analysis of wood and straw based biochars
Open Research DataThis data set includes the BJH and BET analysis results for straw and wood chips-based biochars generated at 450 Celsius degrees.
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The finite difference methods of computation of X-rays propagation through a system of many lenses
PublicationThe propagation of X-ray waves through an optical system consisting of many beryllium X-ray refrac- tive lenses is considered. In order to calculate the propagation of electromagnetic in the optical sys- tem, two differential equations are considered. First equation for an electric field of a monochromatic wave and the second equation derived for complex phase of the same electric The propagation of X-ray waves through an optical system...
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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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Wykładnicze równanie Arrheniusa jako funkcja dojrzałości twardniejącego betonu
PublicationPoprawne określenie funkcji dojrzałości dla mieszanki betonowej warunkuje powodzenie szacowania wytrzymałości na ściskanie na bazie pomiarów temperatury in situ. W artykule omówiono zastosowanie równania Arrheniusa do opisu funkcji dojrzewania twardniejącego betonu. Szczególną uwagę zwrócono na zależności szybkości zachodzenia reakcji w odmiennych warunkach temperaturowych. Przedstawiono wyniki własnych badań na kostkach zaprawy...
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Fluid Mechanics and Hydraulics EE Msc sem. I r.a. 22/23
e-Learning CoursesBasic definitions. Physical properties of liquids. Forces acting on fluids. Hydrostatics - basic equations. Pressure on a flat and curved wall. Buoyancy. Archimedes' law. Balance of submerged bodies. The balance of floating bodies. Hydrodynamics. Hydrodynamic quantities. Continuity equation for the liquid stream. Bernoulli equation. Basic laws of hydrodynamics. Equation of mass behavior, preservation of the amount of motion, Bernoulli's...
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Fluid Mechanics and Hydraulics EE Msc sem. I r.a. 23/24
e-Learning CoursesBasic definitions. Physical properties of liquids. Forces acting on fluids. Hydrostatics - basic equations. Pressure on a flat and curved wall. Buoyancy. Archimedes' law. Balance of submerged bodies. The balance of floating bodies. Hydrodynamics. Hydrodynamic quantities. Continuity equation for the liquid stream. Bernoulli equation. Basic laws of hydrodynamics. Equation of mass behavior, preservation of the amount of motion, Bernoulli's...
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Torsional buckling and post-buckling of columns made of aluminium alloy
PublicationThe paper concerns torsional buckling and the initial post-buckling of axially compressed thin-walled aluminium alloy columns with bisymmetrical cross-section. It is assumed that the column material behaviour is described by the Ramberg–Osgood constitutive equation in non-linear elastic range. The stationary total energy principle is used to derive the governing non-linear differential equation. An approximate solution of the equation...
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Numerical Simulations and Tracer Studies as a Tool to Support Water Circulation Modeling in Breeding Reservoirs
PublicationThe article presents a proposal of a method for computer-aided design and analysis of breeding reservoirs in zoos and aquariums. The method applied involves the use of computer simulations of water circulation in breeding pools. A mathematical model of a pool was developed, and a tracer study was carried out. A simplified model of two-dimensional flow in the form of a biharmonic equation for the stream function (converted into...
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The finite-difference simulation of x-rays propagation through a system of lenses
PublicationThe propagation of X-ray waves through an optical system consisting of 33 aluminum X-ray refractive lenses is considered. For solving the problem, a finite-difference method is suggested and investigated. It is shown that very small steps of the difference grid are necessary for reliable computation of propagation of X-ray waves through the system of lenses. It is shown that the wave phase is a function very quickly increasing...
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Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment
PublicationWe study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k_{B}T, which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar...
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Impact of Boundary Conditions on Acoustic Excitation of EntropyPerturbations in a Bounded Volume of Newtonian Gas
PublicationExcitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoreticallyconsidered in this work. The dynamic equation for an excess density which specifies the entropy mode,has been obtained by means of the method of projections. It takes the form of the diffusion equation withan acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient isproportional...
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Acoustic heating produced in resonators filled by a newtonian fluid
PublicationAcoustic heating in resonators is studied. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in the linear part of the final equation, but preserving terms belonging to the thermal mode responsible for heating. This equation is instantaneous and includes nonlinear acoustic terms that form a...
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Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations
PublicationThe paper concerns the untypical aspect of application of the dissipative numerical methods to solve nonlinear hyperbolic partial differential equations used in open channel hydraulics. It is shown that in some cases the numerical diffusion generated by the applied method of solution produces not only inaccurate solution but as well as a balance error. This error may occur even for an equation written in the conservative form not...