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Search results for: MATHEMATICAL MODEL
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Some aspects of mathematical education at Gdansk University of Technology
PublicationReferat omawia wybrane zagadnienia związane z poszukiwaniem i stosowaniem nowych rozwiązań - zarówno programowych jak i organizacyjnych - w realizacji procesu kształcenia matematycznego na poziomie akademickim w Politechnice Gdańskiej.
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Mathematical Description of Sorption Isotherms of Autoclaved Aerated Concrete
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Dynamics of a simplified HPT model in relation to 24h TSH profiles
PublicationWe propose a simplified mathematical model of the hypothalamus-pituitary-thyroid (HPT) axis in an endocrine system. The considered model is a modification of the model proposed by Mukhopadhyay and Bhattacharyya in [10]. Our system of delay differential equations reconstructs the HPT axis in relation to 24h profiles of human in physiological conditions. Homeostatic control of the thyroid-pituitary axis is considered by using...
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Simulation model of IPMSM drive with rotor position estimator
PublicationThe paper presents a simulation model of electric drive consisting of: IPMSM motor, inverter and digital controller. The model was designed in Mathlab/Simulink. By modelling of the controller its discrete operation was taken into account in order to simulate precisely a specific sensorless control algorithm. A method for estimation of angular rotor position was proposed. Its mathematical algorithm was explained and errors were...
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Application of MARKAL model to optimisation of electricity generation structure in Poland in the long-term time horizon. Part II. Model and forecasts assumptions
PublicationIn this paper, the next in a series of publications on the subject, assumptions are presented of a power system development model in terms of electricity generation technology infrastructure in Poland, in the long term perspective until 2060. The model is based on the mathematical structure of the MARKAL optimization package. Among other things developed are a forecast of the final demand for electricity and heat, the current...
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Reprezentation of mechanic hysteresis in a railway track using the Preisach model
PublicationThis paper presents an implementation of the classic scalar Preisach model to describe the hysteresis phenomenon created in a railway track subjected to lateral (in the horizontal plane) displacements. The principles of the Preisach theory and the scalar mathematical model of the mechanical hysteresis that is based on statistically distributed modified hysteresis operators are briefly presented. This article presents the characteristic...
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Performance and Emission Modelling and Simulation of Marine Diesel Engines using Publicly Available Engine Data
PublicationTo analyse the behaviour of marine diesel engines in unsteady states for different purposes, for example to determine the fuel consumption or emissions level, to adjust the control strategy, to manage the maintenance, etc., a goal-based mathematical model that can be easily implemented for simulation is necessary. Such a model usually requires a wide range of operating data, measured on a test stand. This is a time-consuming process...
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Control of nonlinear and linearized model of self-balancing electric motorcycle
PublicationSelf-Balancing Electric Motorcycle (SBEM) is a dynamic and nonlinear electro-mechanical system. In this paper, the process of mathematical modelling and line-arization of SBEM is presented. The model of the control system in Matlab envi-ronment is implemented. The control system using the PID controller is designed. The operation of particular structures of the PID controller on the simulation model is compared. Due to simulation...
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Hopf bifurcation in time‐delayed gene expression model with dimers
PublicationWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive...
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A new approach to determination of the two-mass model parameters of railway current collector
PublicationThe paper presents two mathematical models of railway current collectors both with two degrees of freedom. The first one, hereinafter Pantograph Articulated Model (PAM), has one degree of freedom in rotational motion and the second degree of freedom in translational motion. The second model, called henceforth as Pantograph Reference Model (PRM), has both degrees of freedom in translational motion. Differential equations of the...
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A new approach to determination of the two-mass model parameters of railway current collector
PublicationThe paper presents two mathematical models of railway current collectors both with two degrees of freedom. The first one, hereinafter Pantograph Articulated Model (PAM), has one degree of freedom in rotational motion and the second degree of freedom in translational motion. The second model, called henceforth as Pantograph Reference Model (PRM), has both degrees of freedom in translational motion. Differential equations of the...
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Simulation of Residence Time Distribution and Mixing in Reactors with Recirculation Using 2D Approach
PublicationIn this paper, we propose a 2D approach in order to create a mathematical model for the determination of the residence time distribution for a flow reactor with recirculation. Apart from characterizing the functional residence time distribution, this model can help improve the operation of the reactor at the design stage. The mathematical model was validated by comparison with experiments carried out in a hydraulic laboratory.
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A Formal Approach to Model the Expansion of Natural Events: The Case of Infectious Diseases
PublicationA formal approach to modeling the expansion of natural events is presented in this paper. Since the mathematical, statistical or computational methods used are not relevant for development, a modular framework is carried out that guides from the external observation down to the innermost level of the variables that have to appear in the future mathematical-computational formalization. As an example we analyze the expansion of Covid-19....
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Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform
PublicationBirth–and–death models are now a common mathematical tool to describe branching patterns observed in real–world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth–and–death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the...
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TRAVELLING WAVES FOR LOW–GRADE GLIOMA GROWTH AND RESPONSE TO A CHEMOTHERAPY MODEL
PublicationLow-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the...
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Application of multi-criteria mathematical programming models for assignment of services in a hospital
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Periodic and chaotic dynamics in a map‐based neuron model
PublicationMap-based neuron models are an important tool in modeling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on continuous or hybrid dynamical systems. However, due to their discrete nature, rigorous mathematical analysis might be challenging. We study a discrete model of neuronal dynamics introduced by Chialvo in 1995. In particular, we show that its reduced one-dimensional...
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Three phase transient model of wet coal pyrolysis
PublicationA one-dimensional transient mathematical model was developed to describe the thermal and flow phenomena during coal pyrolysis in a coke oven. The model was solved numerically using partly implicit methods for gas flow and heat transfer problems. It was successfully validated with industrial-scale measurements of temperature change in the middle-plane of the coke oven chamber. The evolution of temperature and pressure, distributions...
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Polish internet mortgage market: towards fully developed fuzzy model
PublicationThe first part of the paper consists of introduction describing the Polish Internet Mortgage Market. Later there is presented the idea of the rule based model which may be used on this market. Next step consists of fuzzyfication of the model. This process begins with the initial set of variables which was used previously for the rule based model of the same market. As numerous aspects of the market cannot be presented in the crisp...
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Mathemathical model of radial passive magnetic bearing
PublicationIn the article mathematical radial model of passive magnetic bearings to ocean engineering units has been presented. The units application in underwater thrusters should increase propulsion systems durability and gives lower maintenance costs. The rotor of electric motor is hanging in magnetic field taken from radial passive magnetic bearings. However axial direction maintenance must be controlled with electromagnets and their...
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Usage of Memi-Markov Process in Operation Evaluation of Diesel Engine
PublicationIn paper, the proposition of quantitative evaluation of operation using semi-Markov processes theories has been presented. Basic assumptions, essential for creating mathematical model on example of diesel engine were shown. Special attention was given to practical aspects of using established mathematical model. Example of characteristic of analysed process - temporary distribution of probability was assigned.
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Numerical modeling of sound intensity distributions around acoustic transducer
PublicationThe aim of this research study is to measure, simulate and compare sound intensity distribution generated by the acoustic transducers of the loudspeaker. The comparison of the gathered data allows for validating the numerical model of the acoustic radiation. An accurate model of a sound source is necessary in mathematical modeling of the sound field distribution near the scattering obstacles. An example of such obstacle is a human...
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Representation of magnetic hysteresis in tape wound core using feedback Preisach model
PublicationThis paper presents a mathematical model for the hysteresis phenomenon in ferromagnetic tape wound core. The feedback scalar Preisach model of hysteresis is used to simulate magnetic behavior of the grain oriented silicon strip of ET114-27 type. Determination of B-H hysteretic curve is based on measurement of the initial magnetization curve and the main hysteresis loop. The Preisach distribution function (PDF) of ET114-27 material...
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A single and triple-objective mathematical programming models for assignment of services in a healthcare institution
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Application Isssues of the Semi-Markov Reliability Model
PublicationPredicting the reliability of marine internal combustion engines, for instance, is of particular importance, as it makes it possible to predict their future reliability states based on the information on the past states. Correct reliability prediction is a complex process which consists in processing empirical results obtained from operating practice, complemented by analytical considerations. The process of technical state changes...
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Multibody models for gait analysis
PublicationThe aim of this study was to create multibody biomechanical models to analyze a normal gait of the human. Proposed models can be used to identify joint moments of the lower limbs during normal gait in the single and double support phases. Applying Newton-Euler formulation, following planar models were developed: 1) a mathematical 6DOF model describing a gait in the sagittal plane of the body for single support phase and double...
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The process of fuzzy model development for the case of polish internet mortgage market
PublicationThe aim of the paper is to present the conceptual description of fuzzy model representing the Polish Internet mortgage market. The first part of the paper consists of assessment and verification of model variables which are important for the Polish Internet Mortgage Market. This process begins with the initial set of variables which was used previously for the rule based model of the same market. As numerous aspects of the market...
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Model and laboratory simulation of a induction motor for diagnostic purposes
PublicationStatistics say that bearings are this part of induction motors which is most susceptible to damage. The equipment employed for bearing diagnostics usually makes use of vibrations as the criterion for technical condition of the bearings. A faulty bearing results in additional motor vibrations. They are reflected in the harmonic content of stator currents. In certain operating conditions the current signal is the sole source of information...
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Optimal state feedback controller for balancing cube
PublicationIn this paper, a nonlinear balancing cube system is considered, the concept for which is based on an inverted pendulum. The main purpose of this work was the modelling and construction of a balancing cube with the synthesis of the control system. The control objectives included swing-up and stabilization of the cube on its vertex at an unstable equilibrium. Execution of the intended purpose required, first, deriving a cognitive...
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A Combined TOPSIS and FA Based Strategic Analysis of Technical Condition of High Power Transformers
PublicationThe paper presents mathematical model { TOPSIS method, which was utilized on insulating state of distribution transformer to analyze and sensibility of individual measurements methods mutual comparison. We can uniquely determine the importance of these measurements methods with this mathematical appara- tus in these measurements methods in insulating state of transformers.
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Single Mathematical Parameter for Evaluation of the Microorganisms’ Growth as the Objective Function in the Optimization by the DOE Techniques
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Laboratory Determination of Burger's Model Parameters for Visco-elastic Analysis of Road Pavement Materials
PublicationBurger's Model is one of those models that describes performance of asphalt mixtures. Its parameters can be used in road construction analysis based on visco-elastic properties in wide variety of temperatures using dedicated programs (e.g. Veroad) or in Finite Element Method (FEM). Parameters of Burger's Model can be used for example in prediction of low temperature cracking in low winter temperatures or permanent deformation...
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Application of Multinomial Logistic Regression to Model the Impact of Rainfall Genesis on the Performance of Storm Overflows: Case Study
PublicationIn this study, a mathematical model was proposed to analyze the performance of storm overfows. The model included the infuence of rainfall genesis on the duration of storm overfow, its volume, and the maximum instantaneous fow. The multinomial logistic regression model, which has not been used so far to model objects located in a stormwater system, was proposed to simulate the duration of storm overfow. The Iman–Conover method,...
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Infiltration in a double-porosity medium: Experiments and comparison with a theoretical model
PublicationThis paper presents experimental verification of the mathematical model of unsaturated flow in double‐porosity soils developed by the asymptotic homogenization method. A series of one‐dimensional infiltration experiments was carried out in a column filled with a double‐porosity medium composed of a mixture of sand and sintered clayey spheres arranged in a periodic manner. The unsaturated hydraulic properties of each porous material...
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Prediction of manoeuvring abilities of 10000 DWT pod-driven coastal tanker
PublicationThis paper aims to present a new approach in the prediction of manoeuvring abilities of pod-driven ships. A new mathematical model of motions based on MMG methodology was developed and a new type of description of forces acting on azimuth drives is presented. Captive model tests of medium-size coastal tanker and pod open water tests were carried out in CTO S.A. (Ship Design and Research Centre S.A.) to obtain hull hydrodynamic derivatives...
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An Attempt to Create Speech Synthesis Model That Retains Lombard Effect Characteristics
PublicationThe speech with the Lombard effect has been extensively studied in the context of speech recognition or speech enhancement. However, few studies have investigated the Lombard effect in the context of speech synthesis. The aim of this paper is to create a mathematical model that allows for retaining the Lombard effect. These models could be used as a basis of a formant speech synthesizer. The proposed models are based on dividing...
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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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Calculation of motion trajectory and geometric parameters of the trawl during pelagic fishing
PublicationThis paper presents a mathematical model of the mass centre motion trajectory of the trawl, its main geometrical parameters, way of solving the model as well as its example results. It could be useful to define optimum parameters of safe, effective and environmentally friendly pelagic fishing.
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Hydrodynamic Model of the New Waterway through the Vistula Spit
PublicationThe decision to build a new waterway (strait) in the Polish part of the Vistula Spit was made in 2017. The new connection between the Gulf of Gdańsk and the Vistula Lagoon is planned as an artificial navigable channel with a lock and a small port. During storm surges and wind tides in the gulf or in the lagoon, sluicing will be re-quired for vessels to tackle the Vistula Spit. This procedure does not require significant water flow...
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Model of optical phantoms thermal response upon irradiation with 975 nm dermatological laser
PublicationWe have developed a numerical model describing the optical and thermal behavior of optical tissue phantoms upon laser irradiation. According to our previous studies, the phantoms can be used as substitute of real skin from the optical, as well as thermal point of view. However, the thermal parameters are not entirely similar to those of real tissues thus there is a need to develop mathematical model, describing the thermal and...
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A Multi-Fidelity Surrogate-Model-Assisted Evolutionary Algorithm for Computationally Expensive Optimization Problems
PublicationIntegrating data-driven surrogate models and simulation models of different accuracies (or fideli-ties) in a single algorithm to address computationally expensive global optimization problems has recently attracted considerable attention. However, handling discrepancies between simulation models with multiple fidelities in global optimization is a major challenge. To address it, the two major contributions of this paper include:...
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Novel method of estimation of inertial and dissipative parameters of a railway pantograph model
PublicationAn increase in electric railway vehicles service velocity requires that correct interaction between the pantograph and the catenary is ensured. This implies the need for developing mathematical models of pantographs and catenaries and determining their parameters. The article presents a method to determine parameters of mechanical joints of a railway pantograph based on analysis of pantograph subassemblies in swinging motion. The...
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Influence of Properties of Hydraulic Fluid on Pressure Peaks in Axial Piston Pumps’ Chambers
PublicationThe article concentrates on the research of the pressure peaks in a working chamber of an axial piston pump. The main focus of the article is the influence of fluid properties on the pressure peaks value. Experimental and analytical methods were used to determine the impact of the fluid density, viscosity, compressibility and aeration. The article describes the pressure peak generation process and explains the theoretical basis...
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Modeling the Effects of Slowly Biodegradable Substrate at Large WWTP in Northern Poland
PublicationThe essential study was divided into two parts: experimental investigation and mathematical modeling using special platform to computer simulations. In the first part of research an innovative measurement procedure for an indirect determination of the effect of biodegradable particulate and colloidal Xs substrate was developed and implemented. The results of laboratory tests were used futher to verify the mechanism of the hydrolysis...
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Simplified Numerical Model for Transient Flow of Slurries at Low Concentration
PublicationRapid transients are particularly dangerous in industrial hydro-transport systems, where solid-liquid mixtures are transported via long pressure pipelines. A mathematical description of such flow is difficult due to the complexity of phenomena and difficulties in determining parameters. The main aim of the study was to examine the influence of the simplified mixture density and wave celerity description on satisfactory reproduction...
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Study on effective front region thickness of PCM in thermal energy storage using a novel semi-theoretical model
PublicationThermal energy storage in mobile applications, particularly battery of electric vehicles, is currently gaining a lot of importance. In this paper, a semi-theoretical time-dependent mathematical model of the phase change in a double shell thermal energy storage module has been developed where the inner tube is a heat exchange surface. An effective front region thickness for the melting and solidification process has been studied....
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Risk of incorrect pass-fail decisions associated with assessment uncertainty
PublicationA mathematical framework for calculation teacher's and student's risks of incorrect pass-fail decisions under uncertainty of assessment, is presented. The probabilistic model of assessment process is adapted from interdisciplinary probabilistic theory of measurement.
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Monitoring of concrete curing in extradosed bridge supported by numerical simulation
PublicationThe paper describes a mathematical model of concrete curing taking into account kinetics of setting reactions. The numerical model is implemented in the author’s program that was used to monitor thermal effects recorded in the concrete bottom plate of the extradosed bridge. Numerical approach was verified by experimental measurements and used for assessment of the current compressive strength due to degree of hydration of fresh...
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The influence of water and mineral oil on volumetric losses in the displacement pump for offshore and marine applications
PublicationIn this paper volumetric losses in a positive displacement pump supplied with water and mineral oil are described and compared. The experimental tests were conducted using a prototype of a satellite pump (with a non-circular tooth working mechanism). In this paper the sources of volumetric losses in this pump are characterised. On this basis, a mathematical model of these losses has been presented. The results of the calculation...
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A Model of Thermal Energy Storage According to the Convention of Bond Graphs (BG) and State Equations (SE)
PublicationThe main advantage of the use of the Bond Graphs method and State Equations for modeling energy systems with a complex structure (marine power plants, hybrid vehicles, etc.) is the ability to model the system components of different physical nature using identical theoretical basis. The paper presents a method of modeling thermal energy storage, which is in line with basic BG theory. Critical comments have been put forward concerning...