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Search results for: NONLINEAR ADVECTION EQUATIONS
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Stability of delay induced oscillations in gene expression of Hes1 protein model
PublicationW pracy prezentowana jest matematyczna analiza modelu ekspresji genu białka Hes1. Rozważamy układ równań z dwoma opóźnieniami - w produkcji białka Hes1 oraz jego mRNA. Dowodzimy istnienia i jednoznaczności oraz nieujemności rozwiązań. Pokazujemy istnienie dokładnie jednego dodatniego stanu stacjonarnego. Wykazujemy, że stabilność stanu stacjonarnego zależy od sumy opóźnień. Podajemy warunek dostateczny na wystąpienie bifurkacji...
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublicationQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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The smoothness test for a density function
PublicationThe problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...
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On mixing in the class of quadratic stochastic operators
PublicationWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Subcritical bifurcation of free elastic shell of biological cluster
PublicationIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
PublicationWe consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions.
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Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein
PublicationWe analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop. The effect of multiple binding sites in the Hes1 promoter as well as the dimer formation process are taken into account. We consider three, possibly different, time scales connected with: (i) the process of binding to/dissolving from a binding site, (ii) formation and dissociation of dimers, (iii) production and degradation of Hes1...
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Multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets
PublicationWe construct an adaptive estimator of a density function on d dimensional unit sphere Sd (d ≥ 2), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet system, namely Daubechies, using some stereographic operators. We prove that our estimator achieves an optimal rate of convergence on some Besov type class of functions by adapting to unknown smoothness....
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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublicationStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublicationWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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An absorbing set for the Chialvo map
PublicationThe classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...
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Bifurcation of equilibrium forms of a gas column rotating with constant speed around its axis of symmetry
PublicationWe will be concerned with the problem of deformation of the lateral surface of a column that rotates with constant speed around its axis of symmetry. The column is filled by a gas and our goal is to investigate the deformation of the lateral surface depending on the pressure of the gas.
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Generalization of Kramers-Krönig relations for evaluation of causality in power-law media
PublicationClassical Kramers-Krönig (K–K) relations connect real and imaginary parts of the frequency-domain response of a system. The K–K relations also hold between the logarithm of modulus and the argument of the response, e.g. between the attenuation and the phase shift of a solution to a wave-propagation problem. For square-integrable functions of frequency, the satisfaction of classical K–K relations implies causality in the time domain....
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Simulation of influence of the air gap asymmetryon voltage waveforms of a synchronous machine
PublicationResults of simulation of a synchronous generator with the air gap asymmetry characterised by eccentricity are presented in the paper. The Lagrange's energy method has been used in derivation of the model equations. Analysis of influence of the air gap asymmetry on characteristics of self and mutual inductances of windings, as well as analysis of induced voltage waveforms as a function of the air gap asymmetry have been performed....
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Design of Microstrip UWB Balun Using Quasi-TEM Approach Aided by the Artificial Neural Network
PublicationThe design procedure for UWB balun realized in the microstrip technology is proposed in the paper. The procedure applies Artificial Neural Network which corrects the dimensions of the approximate design found by appropriate scaling of the dimensions of the prototype. The scale coefficients for longitudinal and transverse dimensions of microstrip lines are determined from electromagnetic modeling based on transmission line equations....
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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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A continual model of a damaged medium used for analyzing fatigue life of polycrystalline structural alloys under thermal–mechanical loading
PublicationThe main physical laws of thermal–plastic deformation and fatigue damage accumulation processes in polycrystalline structural alloys under various regimes of cyclic thermal–mechanical loading are considered. Within the framework of mechanics of damaged media, a mathematical model is developed that describes thermal–plastic deformation and fatigue damage accumulation processes under low-cycle loading. The model consists of three...
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Multistatyczny, Dopplerowski System określania położenia i prędkości ruchomych celów w wodzie
PublicationW omawianym w pracy multistatycznym, dopplerowskim systemie określania położenia i prędkości ruchomych celów w wodzie źródłem sygnału są dwa nadajniki emitujące sinusoidalne, akustyczne fale ciągłe o różnych częstotliwościach, które po odbiciu od ruchomego celu są obierane przez cztery hydrofony. W artykule przedstawiono analize teoretyczna efektu Dopplera, na którym oparte jest działanie systemu oraz metodę rozwiązania głównych...
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Laminated plates and shells - first ply failure analysis within 6-parameter shell theory
PublicationThis work describes Tsai-Wu and Hashin criteria modifications, dictated by nonlinear 6-parameter shell theory with asymmetric strain measures and drilling rotation. The material law is based on standard orthotropic elastic constants for a non-polar continuum, under plane state of stress. First ply failure loads of cylindrical panel subjected to pressure and flat compressed plate are estimated by means of Finite Element Analysis....
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Local buckling and initial post-buckling behaviour of channel member flange - analytical approach
PublicationThe local buckling and initial post-buckling behaviour of the cold-formed channel member flange is investigated. The governing nonlinear differential equation for axially compressed columns and beams undergoing pure bending is derived using the stationary total potential energy principle. The critical stress and initial post-buckling equilibrium path is determined by means of a perturbation approach. The results obtained allow...
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Determination of chlorine concentration using single temperature modulated semiconductor gas sensor
PublicationA periodic temperature modulation using sinusoidal heater voltage was applied to a commercial SnO2 semiconductor gas sensor. Resulting resistance response of the sensor was analyzed using a feature extraction method based on Fast Fourier Transformation (FFT). The amplitudes of the higher harmonics of the FFT from the dynamic nonlinear responses of measured gas were further utilized as an input for Artificial Neural...
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Dynamic Modeling of COVID-19 Disease with Impact of Lockdown in Pakistan and Malaysia
PublicationBeing researchers, it is an utmost responsibility to provide insight on social issues thus, this work addresses the dynamic modeling of first and most contagious disease named as COVID-19 caused by coronavirus. The first case of COVID-19 appeared in Pakistan was on 26th February 2020 and in Malaysia on 27th February 2020; both patients had foreign travel history. In the paper, the number of total affected cases and total deaths...
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Assessment of dynamic characteristics of thin cylindrical sandwich panels with magnetorheological core
PublicationBased on the equivalent single-layer linear theory for laminated shells, free and forced vibrations of thin cylindrical sandwich panels with magnetorheological core are studied. Five variants of available magnetorheological elastomers differing in their composition and physical properties are considered for smart viscoelastic core. Coupled differential equations in terms of displacements based on the generalized kinematic hypotheses...
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On the non-linear dynamics of torus-shaped and cylindrical shell structures
PublicationIn this study, the non-linear dynamic analysis of torus-shaped and cylindrical shell-like structures has been studied. The applied material is assumed as the functionally graded material (FGM). The structures are considered to be used for important machines such as wind turbines. The effects of some environmental factors on the analysis like temperature and humidity have been considered. The strain field has been calculated in...
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Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment
PublicationThis work performs a novel quasi three-dimensional (3D) bending analysis for a moderately thick functionally graded material (FGM) made of nanoceramics and metal powders, in presence of porosities due to some incorrect manufacturing processes. Such porosities can appear within the plate in two forms, namely, even and uneven distributions. The modeled system assumes a polymer matrix where both shear and transverse factors coexist....
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A chemo-mechano-thermodynamical contact theory for adhesion, friction, and (de)bonding reactions
PublicationThis work presents a self-contained continuum formulation for coupled chemical, mechanical, and thermal contact interactions. The formulation is very general and, hence, admits arbitrary geometry, deformation, and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy, and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the...
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Modular Approach for Modelling Warming Up Process in Water Installations with Flow-Regulating Elements
PublicationThe paper presents a new method for modelling the warming up process of a water system with elements regulating the flow in a stochastic manner. The paper presents the basic equations describing the work of typical elements which the water installation is composed of. In the proposed method, a new computational algorithm was used in the form of an iterative procedure enabling the use of boundary conditions that can be stochastically...
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Assessment of codes recommendations for the evaluation of the seismic gap of buildings founded on different soil types
PublicationSeveral equations have been proposed in the literature to evaluate the seismic gap preventing earthquake-induced structural pounding, such as the ones based on the absolute sum of the peak displacements (ABS), the square root of the sum of the squares (SRSS), the double difference method (DDC), Australian code and the approach proposed by Naderpour et al. The aim of this paper is to investigate the accuracy of these equations taking...
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Analiza następstw potencjalnej awarii wanty mostu podwieszonego w Bydgoszczy
PublicationMost Uniwersytecki został zamknięty po siedmiu latach od oddania do użytkowania. Powodem były widoczne gołym okiem objawy znacznego przeciążenia w obrębie zakotwień. Krytyczne elementy konstrukcji mostu zostały wzmocnione i przywrócono go do ruchu. W artykule przedstawiono nieliniowe analizy statyczne i dynamiczne wykonane na modelu MES, prezentujące cztery scenariusze przebiegu zachowania konstrukcji po utracie nośności mocowania...
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On Dynamic Boundary Conditions Within the Linear Steigmann-Ogden Model of Surface Elasticity and Strain Gradient Elasticity
PublicationWithin the strain gradient elasticity we discuss the dynamic boundary conditions taking into account surface stresses described by the Steigmann–Ogden model. The variational approach is applied with the use of the least action functional. The functional is represented as a sum of surface and volume integrals. The surface strain and kinetic energy densities are introduced. The Toupin–Mindlin formulation of the strain gradient elasticity...
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Parameter and delay estimation of linear continuous-time systems
PublicationIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is 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 identification...
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New Approach to Arc Fitting for Railway Track Realignment
PublicationThis article presents a new method of arc fitting for railway track realignment. The theoretical foundations are presented, along with a detailed algorithm of the iterative computational process. This method is based on solving a set of linearized pseudo-observation equations. The formulas of the functional model of the fitting problem were derived, and a special form of objective function is proposed. An iterative method for optimization...
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On dynamics of origami-inspired rod
PublicationWe discuss the dynamics of a relatively simple origami-inspired structure considering discrete and continuum models. The latter was derived as a certain limit of the discrete model. Here we analyze small in-plane deformations and related equations of infinitesimal motions. For both models, dispersion relations were derived and compared. The comparison of the dispersion relations showed that the continuum model can capture the behavior...
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Vibrational Sum-Frequency Generation Activity of a 2,4-Dinitrophenyl Phospholipid Hybrid Bilayer: Retrieving Orientational Parameters from a DFT Analysis of Experimental Data
PublicationThe vibrational nonlinear activity of films of 2,4-dinitrophenyl phospholipid (DNP) at the solid interface is measured by sum-frequency generation spectroscopy (SFG). Hybrid bilayers are formed by a LangmuirSchaefer approach in which the lipid layer is physisorbed on top of a self-assembled monolayer of dodecanethiol on Pt with the polar heads pointing out from the surface. The SFG response is investigated in two vibrational frequency...
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BADANIE EFEKTYWNOŚCI WYKRYWANIA ANOMALII PROCESOWYCH W DZIAŁANIU TURBINY PAROWEJ ELEKTROWNI JĄDROWEJ PRZY POMOCY METOD WIELOWYMIAROWEJ ANALIZY STATYSTYCZNEJ
PublicationW artykule przedstawiono analizę możliwości wykrywania anomalii procesowych w działaniu turbiny parowej elektrowni jądrowej przy pomocy metod wielowymiarowej analizy statystycznej. Zasymulowano symptomy dwóch rodzajów uszkodzeń turbiny parowej tj. uderzenie wodne oraz, wyciek pary z zaworu części niskoprężnej. Jako narzędzie diagnostyczne wykorzystano Metodę Składników Podstawowych PCA (z ang. Principal Component Analysis). Jako...
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Determination of equivalent circuit parameters of an induction motor using field calculation software
PublicationSimulation of the drive system comprising a power electronic converter and an induction motor requires that the equivalent circuit parameters of the motor are known. These parameters can be either measured or calculated. A method of calculation of self and mutual inductances that are parameters of a polyphase model of the motor is presented in the paper. All self-inductances and mutual inductances have been calculated using the...
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Parameter and delay estimation of linear continuous-time systems
PublicationIn 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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On–line Parameter and Delay Estimation of Continuous–Time Dynamic Systems
PublicationThe 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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Multi-headed chimera states in coupled pendula
PublicationWe 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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Research on the wear evenness of the tool in flat lapping
PublicationIn 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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EMC disturbances in connection of driving system
PublicationIt is known the steep voltage changes caused by IGBT frequency inverters may cause some electromagnetic problems in driving system. Special dU/dt type as well as sinusoidal filters are used in order to limit the level of the disturbances. The paper presents investigation results of EMC disturbances in inverter supplied induction motor. Experiments have proved that disturbances in current connection differ essentially. Important...
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Numerical and experimental investigation of rotational stiffness of zed-purlins connection with sandwich panels
PublicationA rotational resistant stiffness of the zed-purlins connection with sandwich panels is investigated. A simple finite element method model of the connection is proposed. The numerical analysis of the model performed by ABAQUS software, in physically linear and geometrically nonlinear ranges, leads to the rotational resistant stiffness sought. The numerical solution obtained is verified experimentally. Two variants of distribution...
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RADIATION OF HIGH INTENSITY SOUND BY CIRCULAR DISC BY MEANS OF THE NUMERICAL METHOD
PublicationThe main goal of this paper is to find sound pressure distribution radiated by the circular piezoelectric disc that vibrates with the finite amplitude. There has been presented the pressure distribution close to the radiating surface. Also it is shown the sound pressure distribution in the 3D form. The mathematic modeling was carried out on the base of the nonlinear acoustic equation with the proper boundary condition. The axial...
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SHM System of the Roof Structure of Sports Arena “Olivia”
PublicationThe paper presents a structural health monitoring system of the Sports Arena “Olivia” in Gdansk, Poland. The system was installed because of doubts about the roof stability due to observed buckling of the steel truss members. The SHM system was based on nonlinear FEM models used for detection of type of near failure modes of the roof. The application of detailed FEM model in current state updated on data from in situ loading testes...
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Model Order Reduction for Problems With Dispersive Surface Boundary Conditions
PublicationThis letter proposes a new scheme for reduced-order finite-element modeling of electromagnetic structures with nonlinear, dispersive surface boundary conditions, which optimally exploits the numerically stable and efficient MOR framework for second-order systems provided by SAPOR method. The presented results of numerical experiments for an example of a waveguide filter demonstrate the superior accuracy of the resulting reduced models...
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Curves of thermodynamic states in some fluids with dispersion
Publicationvariations in the thermodynamic state of a dispersive medium, caused by sound, are studied. A bubbly liquid and a Maxwell fluid are considered as examples. Curves in the plane of thermodynamic states are plotted. They are in fact pictorial images of linear relations of excess pressure and excess density in the acoustic wave which reflect irreversible attenuation of the sound energy. The curves account for the nonlinear generation...
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Natural convective heat transfer from isothermalconic
PublicationTheoretical 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
PublicationIn 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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An Experimental and Numerical Analysis of Water Hammer Phenomenon in Slurries
PublicationThe 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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Urban flash flood hazard identification and assessment applying geospatial techniques and hydrodynamic modeling; Erbil city case study, Kurdistan Region of Iraq
PublicationThis 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,...