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Search results for: EQUIVARIANT FLOW
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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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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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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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On the space of equivariant local maps
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Otopy classes of equivariant maps
PublicationW artykule definiuje się stopień topologiczny niezmienniczych odwzorowań lokalnych w przypadku gradientowym i niegradientowym. Wyniki dotyczą relacji pomiędzy tymi dwoma niezmiennikami topologicznymi.
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Fixed orbit index for equivariant maps
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Degree of T-equivariant maps in R^n
PublicationW pracy przedstawiona jest konstrukcja niezmienniczego stopnia topologicznego dla odwzorowań z symetriami działających na przestrzeni euklidesowej z inwolucją. Udowodnione jest twierdzenie, że dwa dopuszczalne i gradientowe odwzorowania niezmiennicze są niezmienniczo homotopijne wtedy i tylko wtedy, gdy są one homotopijne niezmienniczo i gradientowo.
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Classification of homotopy classes of equivariant gradient maps
PublicationNiech V będzie ortogonalną reprezentacją zwartej grupy Liego Gi niech S(V),D(V) oznaczają sferę jednostkową i kulę jednostkową V.Jeżeli F jest G-niezmienniczą funkcją rzeczywistą klasy C^1 na Vto mówimy, że grad F (gradient F) jest dopuszczalny, jeżeli(grad F)(x) jest różny od zera dla x należących do S(V). Pracapoświęcona jest homotopijnej klasyfikacji dopuszczalnychG-niezmienniczych odwzorowań gradientowych.
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A Hopf type theorem for equivariant local maps
PublicationWe study otopy classes of equivariant local maps and prove a Hopf type theorem for such maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group.
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Selections and approximations of convex-valued equivariant mappings
PublicationUdowodniono szereg twierdzeń o współzmienniczych selekcjach i aproksymacjach ciągłych, mierzalnych i typu Caratheodory'ego dla odwzorowań G-współzmienniczych o wartościach wypukłych, gdzie G jest grupą zwartą Liego. Tw. typu Michaela, Celliny, Browdera, Kuratowskiego-Ryll-Nardzewskiego, Castaing itd.
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Fixed point index for $G$-equivariant multivalued maps
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The Hopf type theorem for equivariant gradient local maps
PublicationWe construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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On relations between gradient and classical equivariant homotopy groups of spheres
PublicationWe investigate relations between stable equivariant homotopy groups of spheres in classical and gradient categories. To this end, the auxiliary category of orthogonal equivariant maps, a natural enlargement of the category of gradient maps, is used. Our result allows for describing stable equivariant homotopy groups of spheres in the category of orthogonal maps in terms of classical stable equivariant groups of spheres with shifted...
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Equivariant degree of convex-valued applied to set-valued BVP
PublicationW pracy określono stopień ekwiwariantny dla odwzorowań o wartościach zwartych i wypukłych. Zastosowano go do dowodu twierdzenia o istnieniu wielunietrywialnych rozwiązań problemu brzegowego typu Dirichleta dla inkluzji różniczkowych z warunkami wzrostu typu Bernsteina-Nagumo, z dodatkowymi symetriami
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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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Equivariant degree of convex-valued maps applied to set-valued BVP
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Equivariant Conley index in Hilbert spaces and applications to strongly indefinite problems
PublicationW pracy zdefiniowano teorię indeksu Conley`a w przestrzeni Hilberta z działaniem zwartej grupy Liego. Została ona wykorzystana do szacowania z dołu ilości rozwiązań periodycznych w teorii nieliniowych autonomicznych układów Hamiltona.
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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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Flow Maps and Flow Patterns of R1233zd(E) in a Circular Minichannel at Low, Medium and High Values of Saturation Pressure
PublicationThere is a gap in knowledge regarding the flow pattern of low-boiling working fluids in the range of high saturation temperatures (above 120°C) and medium and high reduced pressures (0.5-0.9). Data are present in the literature for similar values of reduced pressures, but for lower values of saturation temperature. This is due to the existing refrigeration applications of these working fluids. At high values of reduced pressure,...
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Topological degree for equivariant gradient perturbations of an unbounded self-adjoint operator in Hilbert space
PublicationWe present a version of the equivariant gradient degree defined for equivariant gradient perturbations of an equivariant unbounded self-adjoint operator with purely discrete spectrum in Hilbert space. Two possible applications are discussed.
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Decolorization of organic dyes solution by atmospheric pressure glow discharge system working in a liquid flow-through mode
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Experimental Study of Flow Rate in Hydraulic Satellite Motor with the Rotating Case at a Low Constant Rotational Speed
PublicationIn this article was described the methodology for the experimental study of flows in the prototype of a satellite hydraulic motor with a rotating body. The experimental tests of the motor were carried out at a low constant rotational speed in a wide range of pressure drop in this motor. The constant rotational speed of the motor was kept by a worm gear. Based on the test results, the leakage characteristics in the flat gaps of...
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Flow boiling intensification in minichannels by means of mechanical flow turbulising inserts
PublicationThe work presents the results of experimental investigation on heat transfer in minichannels. Refrigerant R123 was used as a test fluid. Single vertical silver tubes of 380 mm length and 2.3 mm diameter were examined with two variants of turbulising inserts. A wide range of parameters was considered, namely mass flux G=534-3011 kg/(m2s), heat flux qw=28.5-68.4 kW/m2, saturation temperature Tsat=23-86 stC and the full range of vapour...
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About nutrient liquid flow between potential flow and cartilage surface in bioreactor
PublicationW niniejszej pracy wyznaczony został przepływ cieczy odżywczej o właściwościach nienewtonowskich w cienkiej warstwie granicznej w pobliżu powierzchni komórek chrząstki (chondrocytu) podczas hodowli w bioreaktorze. Ruch cieczy w warstwie granicznej jest wywołany wydatkiem przepływu dostarczanej cieczy do bioreaktora. Ponadto prędkość przepływu cieczy w warstwie granicznej wokół hodowanych komórek chrząstki stawowej jest uzależniona...
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A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern
PublicationThe paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the...
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Non-adiabatic Effects in Pressure Drop Calculations in Flow Boiling and Flow Condensation in Minichannels
PublicationConsiderations presented in the paper relate both to the case of flow boiling and flow condensation in conventional channels as well as small diameter ones. Authors devoted all the possible attention that the modeling presented is applicable to the whole range of quality variation in both cases of condensation and boiling. The form of two-phase flow multiplier, which is a major factor in modeling presented here, should be capable...
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Flow distribution and heat transfer in minigap and minichannel heat exchangers during flow boiling
PublicationThe topic of boiling heat transfer in miniscale geometries has focused the ever increasing interest of researchers in recent years. However, most of the works are related to mini- and microchannels and much less to minigaps. Meanwhile, minigaps allow for more comprehensive experimental studies, i.e. flow visualisations due to the flat, two-dimensional configuration of the flow. The results of the experimental investigations of...
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Membrane distillation with laminar flow
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Management of complexity and information flow
PublicationProblemy złożoności i zarządzania przepływem informacji. W rozdziale omówio-no podejście do modelowania systemów złożonych oraz zarządzania przepływeminformacji w takich systemach. Rozwiązania odniesiono do płaszczyzny elasty-cznego wytwarzania. Poruszono aspekty miękkiego modelowania w takich środo-wiskach.
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Flow Analysis of a Kaplan Turbine
PublicationThis monograph is a guide to a method of experimental and numerical flow investigations for Kaplan - type turbines. The numerical calculations were compared with the test results of the model Kaplan turbine. The tests were carried out on the model test rig in the Gdańsk University of Technology. The turbine has been thoroughly experimentally investigated, resulting in the identification of optimum setting combination of the stator...
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The lemniscate knowledge flow model
PublicationKnowledge is seen as one of the main resources for organizations providing knowledge-intensive services. Therefore, sharing and reusing are the main goals of modern knowledge management (KM) approach, driven by information and communication technologies (ICT). However, one can ask for the details in order to provide means and tools to design and deploy environment able to fulfil these two goals. We observed that occurred interactions...
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High-order compact difference algorithm on half-staggered meshes for low Mach number flows
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EHD Flow Measured by 2D PIV in a Narrow Electrostatic Precipitator with Longitudinally-to-flow Wire Electrode
PublicationIn this paper, results of the electrohydrodynamic (EHD) flow patterns in two narrow ESPs with longitudinally-to-flow wire electrode are presented. The influence of the ESP geometry on the EHD flow generated in the ESP was investigated. The results obtained from 2 dimensional (2D) Particle Image Velocimetry (PIV) showed similarities and differences of the particle flow in the wire-plate and wire-cylinder type ESP.
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Comparitive study of heat transfer and pressure drop during flow boiling and flow condensation in minichannels
PublicationIn the paper a method developed earlier by authors is applied to calculations of pressure drop and heat transfer coefficient for flow boiling and also flow condensation for some recent data collected from literature for such fluids as R404a, R600a, R290, R32,R134a, R1234yf and other. The modification of interface shear stresses between flow boiling and flow condensation in annular flow structure are considered through incorporation...
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Calculation method for flow boiling and flow condensation of R134a and R1234yf in conventional and small diameter channels
PublicationThe paper presents the results of calculations performed using the authors’ model to predict the heat transfer coefficient during flow boiling for two refrigerants R134a and R1234yf. The experimental data from various past studies have been collected and the calculations have been conducted for the full range of quality variation and a wide range of mass velocity. The aim of the study was to test the sensitivity of the in-house...
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EXPERIMENTAL VERIFICATION OF THE METHOD OF FLOW BOILING AND FLOW CONDENSATION HEAT TRANSFER PREDICTION FOR SELECTED FLUIDS
PublicationIn the paper presented are the results of calculations using authors own model to predict heat transfer coefficient during flow boiling of different refrigerants. The experimental data from various research studies from literature were collected. Calculations were conducted for a full range of quality variation and a wide range of mass velocity. The aim of the study was to test the sensitivity of the in- house developed model....
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Channel Blockage and Flow Maldistribution during Unsteady Flow in a Model Microchannel Plate heat Exchanger
PublicationThis paper describes the problem of channel blockage as a result of flow maldistribution between the channels of a model mini channel plate heat exchanger consisting of one pass on each leg. Each leg of the heat exchanger contains 51 parallel and rectangular minichannels of four hydraulic diameters namely 461 μm, 571 μm, 750 μm and 823 μm. In addition, a more complex geometry has been investigated where for the sake of breaking...
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Effect of asymmetric fluid flow distribution on flow boiling in a microchannel heat sink – An experimental investigation
PublicationFlow boiling in microchannels is emerging as an exclusive cooling solution for miniaturized high-power electronic devices alongside having other high heat flux applications. Size miniaturization at microscale strangely increases heat transfer performance as well as flow boiling instabilities. Many flow boiling instabilities are interrelated and result from imperfect hydrodynamic conditions. One of such problems is flow maldistribution among...
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Application of Feed Forward Neural Networks for Modeling of Heat Transfer Coefficient During Flow Condensation for Low and High Values of Saturation Temperatur
PublicationMost of the literature models for condensation heat transfer prediction are based on specific experimental parameters and are not general in nature for applications to fluids and non-experimental thermodynamic conditions. Nearly all correlations are created to predict data in normal HVAC conditions below 40°C. High temperature heat pumps operate at much higher parameters. This paper aims to create a general model for the calculation...
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Interaction Between Storm Water Conduit Flow and Overland Flow for Numerical Modelling of Urban Area Inundation
PublicationNowadays we can observe increasing frequency of inundations in cities. This makes accurate predicting of inundations more important than ever. Numerical modeling of this issue requires complex approach with simultaneous calculations of pipe flow and surface flow. In this paper, after a short review of known methods used for solving pipe and surface flow, we will try to answer the question if presented methods would be sufficiently...
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Experimental validation of pressure drop models during flow boiling of R134a – effect of flow acceleration and entrainment
PublicationA crucial step to assure proficient work of power and process apparatus is their proper design. A wide array of those devices operates within boiling or condensation of the working fluid to benefit from high heat transfer rates. Two-phase flows are associated with high heat transfer coefficients because of the latent heat of evaporation and high turbulence level between the liquid and the solid surface. Predicting heat transfer...
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Modelling of dryout process in an annular flow
PublicationW pracy pokazano teoretyczny model kryzysu wrzenia przy wysokich stopniach suchości, który jest modyfikacją modelu proponowanego wcześniej przez Sedlera i Mikielewicza. Model wysychania filmu cieczowego w przepływie pierścieniowym składa się z różniczkowych równań bilansu masy zapisanych dla filmu na ściance i kropel w rdzeniu przepływu. Rozwiązanie układu równań wymaga znajomości gęstości strumienia masy kropel wytrącających się...
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Practical aspects of Flow Thinning optimization
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Complexity of a classical flow restoration problem
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Isotropic damage in viscoplastic flow conditions
PublicationMechanika zniszczenia jest obecnie jedną z ważniejszych gałęzi mechaniki ciał stałych. Jest cały czas rozwijającą się dziedziną nauki, która znalazła swoje zastosowania w problemach inżynierskich. W artykule zaprezentowano podstawowe informacje na temat lepkoplastyczności i jej zastosowania, koncepcję mechanicznej reprezentacji zniszczenia przez zmienną D, koncepcję naprężeń efektywnych, równania opisujące zniszczenie oraz lepkoplastyczny...
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The wastewater flow through trickling filters.
PublicationFiltry zraszane projektowane są głównie w oparciu o wytyczne techniczne. W pracy zaproponowano metodę o charakterze strukturalnym. Pokazano sposób określania miarodajnego czasu przebywania cieczy w układzie i powiązania go z kinetyczną charakterystyką procesu oczyszczania ścieków.
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Flow Control Algorithm for UMTS HSDPA
PublicationHSDPA (High Speed Downlink Packet Access) jest istotnym etapem ewolucji systemu UMTS. Pozwala na transmisję do użytkownika z prędkością dochodzącą do 14.4 Mbit/s; aby to umożliwić, wprowadzono w wersji 5 UMTS szereg nowych mechanizmów w warstwie fizycznej oraz MAC. W tej pracy przedstawiono szczegółową analizę jednego z nowych mechanizmów - algorytmu kontroli natężenia ruchu między MAC-hs i MAC-d. Zaproponowano nowy, efektywny...
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Some solutions of unsteady flow in bioreactor.
PublicationCzas regeneracji chrząstki stawowej po urazie jest długotrwały. Czasem tkanka nie regeneruje się. Dlatego też przeszczepy odgrywają bardzo ważną rolę. Najlepsze efekty hodowli tkanek zaobserwowano w bioreaktorach wykonujących ruch obrotowy i zapewniających nieustalony charakter przepływu ciecy odżywczej. Dlatego tematem niniejszego artykułu są pewne metody i rozwiązania nieustalonego przepływu cieczy w warstwie przyściennej hodowanej...
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MODELLING OF TRANSIENT FLOW IN STORM SEWERS
PublicationThe paper focuses on the assessment of second-order explicit numerical scheme for unsteady flows in sewers. In order to simulate the pressurized flow the 'Preissmann slot' concept is implemented. For simulation of the transcritical flow the original and improved McCormack scheme is used. The calculated results are compared with numerical solutions and laboratory measurements published in the technical literature. Moreover, the...