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Wyszukujesz frazę "diffusion" wg kryterium: Temat


Wyświetlanie 1-11 z 11
Tytuł:
Inverse Model for the Solute Micro-Field Formation during Self-Propagating High Temperature Reaction
Autorzy:
Wołczyński, W.
Powiązania:
https://bibliotekanauki.pl/articles/351234.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
diffusion equation
diffusion barrier
self-propagating synthesis
Opis:
A new thermodynamic description for the self-propagating high temperature synthesis (SHS - reaction) is presented in the “inverse” version. This description is worked out for the diffusion barrier, thickness of which is at the limit, i.e. its value is infinitesimally small. The solution to the diffusion equation delivered in the description can be easily extended for the diffusion barrier of a greater thickness. The Ni/Al multi-layers system is treated as a virtual eutectic alloy solidifying with the rate equal to that involved by the self-propagating reaction. It is suggested to inverse the curves obtained for solidification in order to characterize the melting completed by the formation of the AlNi - intermetallic phase required in the self-propagating synthesis.
Źródło:
Archives of Metallurgy and Materials; 2017, 62, 1; 141-147
1733-3490
Pojawia się w:
Archives of Metallurgy and Materials
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Liquefaction of saturated soil and the diffusion equation
Autorzy:
Sawicki, A.
Sławińska, J.
Powiązania:
https://bibliotekanauki.pl/articles/178612.pdf
Data publikacji:
2015
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
liquefaction
diffusion equation
saturated soils
sea bed
Opis:
The paper deals with the diffusion equation for pore water pressures with the source term, which is widely promoted in the marine engineering literature. It is shown that such an equation cannot be derived in a consistent way from the mass balance and the Darcy law. The shortcomings of the artificial source term are pointed out, including inconsistencies with experimental data. It is concluded that liquefaction and the preceding process of pore pressure generation and the weakening of the soil skeleton should be described by constitutive equations within the well-known framework of applied mechanics. Relevant references are provided.
Źródło:
Studia Geotechnica et Mechanica; 2015, 37, 2; 39-44
0137-6365
2083-831X
Pojawia się w:
Studia Geotechnica et Mechanica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Diffusion limit for the phenomenon of random genetic drift
Autorzy:
Marciniak, Anna
Powiązania:
https://bibliotekanauki.pl/articles/1208221.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
genetic drift
telegraph equations
singularly perturbed systems
diffusion equation
random walk
Opis:
The paper deals with mathematical modelling of population genetics processes. The formulated model describes the random genetic drift. The fluctuations of gene frequency in consecutive generations are described in terms of a random walk. The position of a moving particle is interpreted as the state of the population expressed as the frequency of appearance of a specific gene. This leads to a continuous model on the microscopic level in the form of two first order differential equations (known as the telegraph equations). Applying the modified Chapman-Enskog procedure we show the transition from this system to a macroscopic model which is a diffusion type equation. Finally, the error of approximation is estimated.
Źródło:
Applicationes Mathematicae; 2000, 27, 1; 81-101
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A non integer order, state space model for one dimensional heat transfer proces
Autorzy:
Oprzedkiewicz, K.
Gawin, E.
Powiązania:
https://bibliotekanauki.pl/articles/229619.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non-integer order systems
heat transfer process
diffusion equation
infinite dimensional systems
Opis:
In the paper a new, state space, non integer order model for one dimensional heat transfer process is presented. The model is based on known semigroup model. The derivative with respect to time is described by the non integer order Caputo operator, the spatial derivative is described by integer order operator. The elementary properties of the state operator are proven. The solution of state equation is calculated with the use of Laplace transform. Results of experiments show, that the proposed model is more accurate than analogical integer order model in the sense of square cost function.
Źródło:
Archives of Control Sciences; 2016, 26, 2; 261-275
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear Interaction of Modes in a Planar Flow of a Gas with Viscous and Thermal Attenuation
Autorzy:
Perelomova, Anna
Powiązania:
https://bibliotekanauki.pl/articles/177137.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
nonlinear wave theory
nonlinear acoustics
coupling dynamic equations
Burgers equation
diffusion equation
Opis:
The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differentia form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.
Źródło:
Archives of Acoustics; 2019, 44, 3; 551-559
0137-5075
Pojawia się w:
Archives of Acoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions to Time-Fractional Diffusion-Wave Equation in Spherical Coordinates
Autorzy:
Povstenko, Y.
Powiązania:
https://bibliotekanauki.pl/articles/386572.pdf
Data publikacji:
2011
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
transformata Laplace'a
transformata Fouriera
równanie dyfuzji
Laplace transform
Fourier transform
diffusion equation
Opis:
Solutions to time-fractional diffusion-wave equation with a source term in spherical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time t, the finite Fourier transform with respect to the angular coordinate , the Legendre transform with respect to the spatial coordinate , and the Hankel transform of the order n+1/2 with respect to the radial coordinate . In the central symmetric case with one spatial coordinate the obtained results coincide with those studied earlier.
Źródło:
Acta Mechanica et Automatica; 2011, 5, 2; 108-111
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The practical stability of the discrete, fractional order, state space model of the heat transfer process
Autorzy:
Oprzędkiewicz, K.
Gawin, E.
Powiązania:
https://bibliotekanauki.pl/articles/230065.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
discrete non-integer order system
heat transfer
diffusion equation
Grünvald-Letnikov operator
practical stability
Opis:
In the paper the practical stability problem for the discrete, non-integer order model of one dimmensional heat transfer process is discussed. The conditions associating the practical stability to sample time and maximal size of finite-dimensional approximation of heat transfer model are proposed. These conditions are formulated with the use of spectrum decoposition property and practical stability conditions for scalar, positive, fractional order systems. Results are illustrated by a numerical example.
Źródło:
Archives of Control Sciences; 2018, 28, 3; 463-482
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A numerical scheme for time-fractional fourth-order reaction-diffusion model
Autorzy:
Koç, Dilara Altan
Powiązania:
https://bibliotekanauki.pl/articles/24201500.pdf
Data publikacji:
2023
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
implicit finite difference method
fractional calculus
diffusion equation
niejawna metoda różnic skończonych
rachunek ułamkowy
równanie dyfuzji
Opis:
In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the number of iterations. The advantage of the implicit difference scheme is unconditionally stable. The stability analysis and convergency have been proven. A numerical example has been presented, and the validity of the method is supported by tables and graphics.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 15--25
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Development of the Jackson and Hunt Theory for Rapid Eutectic Growth
Autorzy:
Wołczyński, W.
Powiązania:
https://bibliotekanauki.pl/articles/353984.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Jackson and Hunt theory
diffusion equation
coupled eutectic growth
Aziz’s theory
oscillatory mode of eutectic growth
Opis:
A development of the Jackson-Hunt’s theory is delivered. Contrary to Jackson-Hunt’s theory for ideally coupled growth the current description is dealing with the coupled eutectic growth which is more realistic than an ideal course of eutectic structure formation. Thus, the undercooling of every eutectic phase is not equal to each other. A new boundary condition is introduced to solve the diffusion equation. According to this condition, the eutectic concentration is always maintained at the triple point of the solid / liquid (s/l) interface. Therefore, the solution to diffusion equation is given separately for both lamellae. The mass balance is satisfied by the current solution. Both thermodynamic equilibrium and mechanical equilibrium are assumed to be situated at the triple point of the s/l interface, only. A protrusion of the leading phase over the wetting phase is defined mathematically due to the mass balance fulfilment. The current description is associated with the asymmetrical phase diagrams. Finally, the current description is applied to interpretation of the rapid eutectic growth. Therefore, Aziz’s concept for the changes of partition ratio versus growth rate is introduced into the description. As a result, the rapid formation of the eutectic structure is described by the oscillatory mode. Interpretation of the oscillatory mode of the eutectic structure formation is illustrated in the arbitrary eutectic phase diagram. The eutectic structure, obtained through the detonation gas spraying onto the steel substrate (rapid solidification) is delivered to illustrate the present description.
Źródło:
Archives of Metallurgy and Materials; 2018, 63, 1; 65-72
1733-3490
Pojawia się w:
Archives of Metallurgy and Materials
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
General remarks on dynamic projection method
Autorzy:
Leble, S.
Powiązania:
https://bibliotekanauki.pl/articles/1938597.pdf
Data publikacji:
2016
Wydawca:
Politechnika Gdańska
Tematy:
partial differential equations
dynamical system
Cauchy problem
diffusion equation
projection operator
idempotent operators
eigen mode
mode interaction
boundary regime propagation
Opis:
A brief history and a mathematical description of the dynamic projection operators technique is presented. An example of the general Cauchy problem for evolution equations in 1+ 1 dimensions is studied in detail. A boundary regime propagation is formulated in terms of operators and illustrated by the simplest one-dimensional diffusion equation. The problem of temperature waves is discussed.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 2; 113-130
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Producibility of the ion-exchange method in manufacturing gradient refractive index in glass
Autorzy:
Rogoziński, R.
Powiązania:
https://bibliotekanauki.pl/articles/201262.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
ion exchange in glass
diffusion equation
planar gradient waveguides
effective indicies
wymiana jonowa w szkle
równanie dyfuzji
płaskie falowody gradientu
skuteczne indeksy
Opis:
This paper presents the technological aspect of application of the ion exchange method in producing gradient refractive index in glass. The possibility of predictable and repeatable producing of the changes in glass refraction with the use of this method has been presented, as well as the method of in situ control of the process of diffusion doping of glass based on the measurement of the temperature. This method is based on simultaneous (to the carried process) solving the nonlinear diffusion equation modeling the spatio-temporal changes in normalized concentration of the admixture ions in glass. For this purpose the knowledge of temperature characteristics of diffusion coefficients of exchanged ions is used. The result of such control of diffusion processes is information on the current (temporary) refractive index profile of the resulting waveguide. The presented method of control has been confirmed by experimental results, which concern modeling and measurements of planar waveguide structures of slab type. The proposed methodology can also be used to control the diffusion processes of producing another type of two- and three-dimensional gradient structures. According to the author’s knowledge the method mentioned above has not been described in literature before.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 4; 655-665
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-11 z 11

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