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1
Content available remote An estimation of the geothermal source power
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Purpose: The purpose of the paper is to estimate the power of a geothermal source when the energy is obtained by means of a heat exchanger. It has been assumed that the temperature of the rocks at large distances from the heat exchanger is the same regardless of the direction and that the exchanger is sphere-shaped. Owing to this it is possible to estimate the power of the system without having to study the dynamics of the heat propagation in the rocks. Design/methodology/approach: The applied method is to construct a mathematical model and its analysis. The system has been analysed in steady state. Findings: The power of a geothermal source of energy depends, in steady state, on the radius of an exchanger in a linear way. Estimation the upper of the power that is attainable in a real system. Research limitations/implications: Further investigation requires an analysis of transient processes the temperature in the rock during operation of geothermal energy. Practical implications: The results presented in this paper can be used in the design of geothermal energy recovery systems. Originality/value: The model and all the calculations are the author’s results.
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Compartmental analysis has for many decades been used for the evaluation of results of mainly in vivo radiotracer experiments. However, its potential for working out similar experiments, but in non-living systems, has as yet been rather overlooked. This paper aims at reversing this situation. To this end some basic principles of compartmental analysis are given followed by examples of its use in chemistry related laboratory radiotracer studies.
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Content available Bifurcation in a nonlinear steady state system
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The steady state solutions of a nonlinear digital cellular neural network with ω neural units and a nonnegative variable parameter λ are sought. We show that λ = 1 is a critical value such that the qualitative behavior of our network changes. More specifically, when ω is odd, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ ∈ [1, ∞), steady states cannot exist; while when ω is even, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ = 1, there are no nontrivial steady states, and for λ ∈ (1, ∞), there are two fully oscillatory steady states. Furthermore, the number of existing nontrivial solutions cannot be improved. It is hoped that our results are of interest to digital neural network designers.
PL
Dokonano analizy teoretycznej statyki układu złożonego z dwóch równolegle połączonych adiabatycznych reaktorów zbiornikowych, pracujących w systemie dynamicznie otwartym lub zamkniętym recyrkulacją masy. Wykazano, iż mimo swej prostoty, system może generować bardzo skomplikowane rozwiązania stacjonarne. Stwierdzono, że struktura tych rozwiązań jest bardziej złożona, gdy nie ma recyrkulacji. Wykazano istnienie dziewięciu stanów stacjonarnych i izoli.
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Theoretical analysis of static behaviour of a set of two parallel adiabatic tank reactors with mass recycle was performed. It was proved that in spite of its simplicity, the system can generate complicated steady state solutions. It was found that the steady state solution structure is the most complicated one when there is no circulation at all. Nine steady states and isola were found in this case.
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Suitable and complete sets of stress-strain curves significantly affected by dynamic recrystallization were analyzed for 11 different iron, copper, magnesium, titanium or nickel based alloys. Using the same methodology, apparent hot deformation activation energy Qp and Qss values were calculated for each alloy based on peak stress and steady-state stress values. Linear dependence between quantities Qp and Qss was found, while Qp values are on average only about 6% higher. This should not be essential in predicting true stress of a specific material depending on the temperature-compensated strain rate and strain.
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New N-coordinated dimethyl and di-n-butyl tin hydrides containing the oxazole moiety appeared to be useful in radical cyclizations of acyclic dihalides at the steady state. Both the hydrides were prepared in three steps starting from (-)-(S)-(2-bromophenyl)- 4-isopropyl-4,5-dihydrooxazole. The advantages of the hydrides are at least twofold. First, a resolution of the radical intermediates allows generating higher stereomeric excess than in the case of commercially available hydrides. Second, tin by-products are easily removed.
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The behavior of the chemical affinity at the stage of intermediate product formation was analyzed in a three different schemes of a composite reaction involving one intermediate. It was derived expressions defining the validity of the assumption that the rate formation and the rate of decay of the intermediate are equal. These relations become a quantity criterion of the well - known Bodenstein approximation. The method by which the criterion had been derived was given and examples of application were provided. The approach has a general character and can be used with reference to any composite reaction.
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Stereoselection at the steady state is a process, which results from a complex interplay of reaction pathways that diverge and reconverge at various points. Therefore, it can be considered as a manipulation of stereocontrol mainly by reaction topography. The advantages of this process are at least twofold: First, stereoconvergence allows the system to exceed the yield of the initial stereoconvergent event, where stereomeric transition states compete. Second, a successive resolution of the reactive intermediates by chemoselective events allows the system to generate high stereomeric excess, practically without any stereoselective competition. While illustrated with radicals, the process may prove useful in other fields of chemistry.
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The effect of variation of physical variables on a steady flow through a porous medium with heat transfer between parallel plates is examined. The viscosity and the thermal conductivity are assumed to be temperature dependent. A constant pressure gradient is applied in the axial direction and the two plates are kept at two constant but different temperatures, while the viscous dissipation is considered in the energy equation. A numerical solution for the governing non-linear coupled equations of motion and the energy equation is determined. The effect of porosity of the medium, the variable viscosity, and the variable thermal conductivity on both the velocity and temperature distributions is reported.
PL
W pracy zbadano wpływ zmiany parametrów fizycznych na ustalony przepływ przez porowaty ośrodek przy jednoczesnym przesyle ciepła pomiędzy równoległymi płytami ograniczającym obszar ośrodka. Założono, że lepkość i współczynnik przewodnictwa cieplnego są zależne od temperatury. Do utrzymania stacjonarnego przepływu wprowadzono stały gradient ciśnienia w kierunku osiowym, a dwie płyty utrzymano w stałych, lecz różniących się temperaturach. Efekt dyssypacji wiskotycznej uwzględniono w równaniu energii. Zaprezentowano numeryczne rozwiązanie nieliniowych, sprzężonych równań ruchu oraz równania energii. Omówiono wpływ porowatości ośrodka, zmiennej lepkości i współczynnika przewodnictwa cieplnego na rozkład prędkości i temperatury w obszarze przepływu.
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This paper presents a kinetic analysis of the whole reaction course, i.e. of both the transient phase and the steady state, of open multicyclic enzyme cascade systems. Equations for fractional modifications are obtained which are valid for the whole reaction course. The steady state expressions for the fractional modifications were derived from the latter equations since they are not restricted to the condition of rapid equilibrium. Finally, the validity of our results is discussed and tested by numerical integration. Apart from the intrinsic value of knowing the kinetic behaviour of any of the species involved in any open multicyclic enzyme cascade, the kinetic analysis presented here can be the basis of future contributions concerning open multicyclic enzyme cascades which require the knowledge of their time course equations (e.g. evaluation of the time needed to reach the steady state, suggestion of kinetic data analysis, etc.), analogous to those already carried out for open bicyclic cascades.
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We analyze a single server queue with optional server vacations based on exhaustive service. Unlike other vacation policies, we assume that only at the completion of service of the last customer in the system, the server has the option to take a vacation or to remain idle in the system waiting for the next customer to arrive. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We use the supplementary variable technique and obtain explicit steady state results for the probability generating functions of the queue length, the expected number of customers in the queue and the expected waiting time of the customer. Some known results of the M/G/1 queue have been derived as a particular case.
PL
W artykule przedstawiono algorytm wykorzystujący metodę bilansu harmonicznych do znajdowania rozwiązania stanu ustalonego w maszynie synchronicznej pobudzanej momentem mechanicznym z okresową składową przemienną zależną od kąta obrotu wirnika. Problem jest skomplikowany, gdyż obecność składnika okresowego prowadzi do zagadnień nieliniowych. Opisana procedura pozwala na bezpośrednie wyznaczanie widm Fouriera najważniejszych wielkości opisujących maszynę synchroniczną. Przykładowe obliczenia wykonano dla silnika synchronicznego pracującego w stanie ustalonego synchronizmu i obciążonego momentem mechanicznym okresowo zmiennym o zadanym przebiegu.
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This paper presents an algorithm that uses the harmonic balance method for finding the steady-state solution in the moment of excited synchronous machine with periodic mechanical component of the alternating depending on the angle of rotation of the rotor. The problem is complicated because the presence of periodic component leads to problems of nonlinear. This procedure allows the direct determination of the Fourier spectra of the most important volumes describing the synchronous machine. Sample calculations were performed for a synchronous motor operating in the state of synchronism and fixed mechanical load torque varying periodicaly at a specifed course.
EN
Socio-economic factors play a key role in the development of a society, the status of which is a means to measure and assess the tendencies and the degree of economic convergence or divergence. On the whole it can be said that this is a natural and continuous process that requires permanent engagement and which, subject to certain factors, occurs at different speeds. A key factor that affects the dynamics of these processes is geographical area. This is the case for the Visegrad (V4) countries within Central Europe. The development of this region has over many years been influenced by similar economic, cultural, geopolitical, natural and ethnic interests that have been intertwined through historical developments, power interests and the strong common desire to see their economies converge with those of Western Europe. The aim of the study presented in this article is to measure and evaluate the real level of economic convergence of the Visegrad countries eleven years after joining the European Union. This is achieved by the means of β - and σ - convergence using regression analyses for the monitored periods 2004-2014, 2004-2008 and 2008-2014.
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An implementation of symbolic computation for steady state problems is proposed in the paper. A mathematical basis is derived in order to specify the quantities that the implementation will concern. An analysis is performed so that an optimal algorithm can be chosen in terms of the two chosen criteria – the operation time and memory needed to store symbolic expressions. The implementation scheme of the specialized class for symbolic computation is presented with the use of a general figure and by an example. The implementation is made in C++ but the presented idea can also be applied in other programming languages that share similar properties. A program using the proposed algorithm was studied for its efficiency in terms of calculation time and memory used by symbolic expressions. This is made by comparing the calculations made by the author’s program with those made by a script written in Mathematica.
PL
W artykule zaproponowano implementację obliczeń symbolicznych dla problemów w stanach ustalonych. Wyprowadzono podstawę matematyczną aby sprecyzować wielkości, dla których dokonana jest implementacja. Przeprowadzono analizę dzięki której dobrano optymalny algorytm pod względem wybranych kryteriów użyteczności tj. czasu wykonywania operacji oraz pamięci wymaganej do zapisu wyrażeń symbolicznych. Schemat implementacji specjalistycznej klasy do obliczeń symbolicznych przedstawiono za pomocą ogólnego schematu oraz z wykorzystaniem przykładu. Implementacji dokonano w języku C++ lecz ogólna idea przedstawiona jest w ten sposób, aby można ją było wykorzystać również w innych językach programowania o podobnych cechach. Wydajność programu wykorzystującego proponowany algorytm sprawdzono pod względem czasu wykonywania obliczeń i zajmowanej pamięci przez wyrażenia symboliczne. Dokonano tego poprzez porównanie obliczeń z autorskiego programu z wykonanymi przez skrypt napisany w programie Mathematica.
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The steady-state response of a micropolar cubic crystal due to a moving load has been studied. The eigen value approach using the Fourier transform has been employed and the transform has been inverted by using a numerical technique. The displacement and stress components in the physical domain are obtained numerically. The results of displacement and stresses have been compared for the micropolar cubic crystal and a micropolar isotropic solid. The numerical results are illustrated graphically for a particular model.
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Content available remote Effects of viscosity with moving load at micropolar boundary surface
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The steady state response at viscous fluid/micropolar elastic solid interface to a moving point load has been studied for subsonic, supersonic and transonic load velocities. The Fourier transform has been used to solve the problem. The displacement, microrotation and stress components for a micropolar elastic solid so obtained in the physical domain are computed numerically by using the numerical inversion technique. Viscosity and micropolarity effects on the resulting expressions have been presented graphically for a specific material.
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A numerical solution for the flow of fluid with dusty particles past a semi-infinite inclined plate with a constant heat flux is obtained by an implicit finite difference method, which is unconditionally stable. Gas-velocity, dust-velocity, temperature, skin friction and Nusselt number are shown graphically. It is observed that the velocity of the dusty-gas decreases with decreasing the inclination angle 'phi' to the horizontal. An increase in the mass concentration of dust also causes a fall in the gas-velocity.
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Content available remote Moving load response at thermal conducting fluid and micropolar solid interface
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The steady state response of a micropolar elastic solid with an overlying semi-infinite thermal conducting fluid subjected at the plane interface to a moving point load is determined. The analytic expressions of displacement components, force stress, couple stress and temperature distribution are obtained in the physical domain for Lord-Shulman (L-S), Green-Lindsay (G-L), coupled theory (C-T) and Green-Naghdi (G-N) theories of thermoelasticity by the use of Fourier transform technique and are shown graphically for magnesium crystal like material. The integral transform has been inverted by using a numerical technique.
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The considerable computation time of a practical application of sequential algorithms for simulating thermal and flow distribution in pipe networks is the motivating factor to study their parallei implementation. The mathematical model formulated and studied in the paper requires the solution of a set of nonlinear equations, which are solved by the Newton-Raphson method. An object-oriented solver automatically formulates the equations for networks of an arbitrary topology. The hydraulic model that is chosen as a benchmark consists of nodal flows and loop equations. A general decomposition algorithm for analysis of flow and temperature distribution in a pipe netwark is presented, and results of speedup of its parallel implementation are demonstrated.
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Reached the steady-state values, a steady-state reaction was observed. When the steady-state values were not reached, the reaction proceeded with explosive rates. The values of the explosion pressure limits established with the use of the steady-state criterion were compared with the experimental values and with the values calculated from the condition of equality of chain-branching and chain-termination rates.
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Ciśnieniowe granice wybuchu stechiometrycznej mieszaniny wodoru z tlenem oceniano z wykorzystaniem kryterium stacjonarności zbudowanego dla atomów wodoru. Jeśli stężenie atomów wodoru osiąga swoje wartości stacjonarne to reakcja przebiega spokojnie. W przeciwnym przypadku spalanie zachodzi gwałtownie, w sposób wybuchowy. Uzyskane oceny granic wybuchu porównano z wartościami doświadczalnymi granic oraz z wartościami obliczonymi z warunku równości szybkości rozgałęziania łańcuchów i szybkości ich zaniku.
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