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1
Content available remote Analytical solution of Cattaneo equation
100%
Lupa M.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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tom Vol. 6, nr 1
127-132
EN
The Cattaneo equation supplemented by adequate boundary and initial conditions is considered. The solution of this equation is found in analytic way. In the final part of the paper the computations basing on the solution presented are shown.
2
A simple trajectory model for the near and far field of a jet in a cross flow
100%
Toften T. H. , Holdo A. E. , Bullen P. R.
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2000
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tom Vol. 5, no 2
471-483
EN
Even with the present day extensive use of Computational Fluid Dynamics (CFD), simplified analytical expressions for Fluid Dynamic phenomena have their applications in highlighting significant mechanisms and aiding initial engineering estimates. The present work shows that experimental data for the trajectory of the centre line of jets exposed to a cross-flow can be found from a single expression. The expression is derived from first principles and unlike most other power law formulas the exponents are not empirically determined from measurements. In comparison with other single expressions based on dimensional analysis, which results in differing expressions for differing parts of the flow field, the equation presented here combines the asymptotic assumptions into a single expression.
3
Content available remote Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator
88%
Sweet E. , Vajravelu K. , Gorder R.
Open Physics
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2011
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tom 9
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nr 1
167-175
EN
In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.
4
Content available remote Nonlinear dispersion of a pollutant ejected into a channel flow
88%
Gorder R. , Vajravelu K.
Open Physics
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2011
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tom 9
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nr 5
1182-1194
EN
In this paper, we study the nonlinear coupled boundary value problem arising from the nonlinear dispersion of a pollutant ejected by an external source into a channel flow. We obtain exact solutions for the steady flow for some special cases and an implicit exact solution for the unsteady flow. Additionally, we obtain analytical solutions for the transient flow. From the obtained solutions, we are able to deduce the qualitative influence of the model parameters on the solutions. Furthermore, we are able to give both exact and analytical expressions for the skin friction and wall mass transfer rate as functions of the model parameters. The model considered can be useful for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water bodies.
5
Content available remote Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis
75%
Kuznetsov A.
Open Physics
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2011
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tom 9
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nr 3
662-673
EN
This paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).
6
Content available remote Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential
75%
Soylu A. , Bayrak O. , Boztosun I.
Open Physics
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2012
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tom 10
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nr 4
953-959
EN
We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ 0, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ 0 r 2, we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ 0, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.
7
Content available remote Displacement potential solution of short stiffened flat composite bars under axial loading
75%
Deb Nath S. K. , Reaz Ahmed S. , Afsar A. M.
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2006
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tom Vol. 11, no 3
557-575
EN
The present paper describes a new approach to analytical solution of two-dimensional stress problems of orthotropic composite materials. In this approach, the elastic problem is formulated in terms of a single potential function, defined in terms of the displacement components, which satisfies a single differential equation of equilibrium. The new mathematical model, namely, the displacement potential formulation is especially suitable for the solution of mixed-boundary-value elastic problems of orthotropic composite materials. This paper presents the solution of stresses and displacements at different sections of short stiffened flat composite bars under axial loading, where a number of bar aspect ratios are considered together with different materials of interest. The solutions are obtained in the form of infinite series and the results are presented mainly in the form of graphs. The results appear to be quite reasonable and accurate, and thus establish the soundness as well as reliability of the present displacement potential approach.
8
Content available remote Flow and heat transfer of a quadratic stretching sheet in a Boussinesq-Stokes suspension
75%
Sekhar G. N. , Chethan A. S.
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2011
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tom Vol. 16, no 4
1109-1128
EN
An analysis is carried out to study the flow and heat transfer in a couple stress fluid over a stretching sheet. The velocity of the sheet is taken as a quadratic polynomial of the distance from the sheet. This results in the manifestation of augmentation of flow in the direction transverse to the sheet. An analytical expression is obtained for velocity components as a function of the couple stress parameter and stretching related parameters. The heat transfer characteristic of a Boussinesq-Stokes suspension over a continuous stretching surface with internal heat generation/absorption is analyzed. Two cases are studied, namely (i) the sheet with prescribed surface temperature (PST-case) and (ii) the sheet with prescribed heat flux (PHF-case). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The resulting non-linear differential equation is solved exactly. The solution and heat transfer characteristics are obtained in terms of Kummer's functions. The results have possible technological applications in the liquid-based systems involving stretchable materials.
9
Content available remote Displacement potential approach to solution of stiffened orthotropic composite cantilever beams under combined loading
63%
Deb Nath S. K.
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2008
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tom Vol. 13, no 1
21-41
EN
In this paper, a stiffened cantilever beam of orthotropic composite materials is considered in order to analyze the elastic field due to combined loading (i.e., parabolic shear and varying axial loading at the tip). The supporting edge of the beam is rigidly fixed. Fibers are directed along the length of the beam. Following a new approach of displacement potential, the mixed-boundary-value elastic problem is formulated in terms of a single potential function, ?. The solutions are obtained in the form of infinite series. Some numerical results of different stress and displacement components at different critical sections of the beam are presented in the form of graphs. The effects of the beam aspect ratio and material orthotropy on the stresses and displacements are investigated in details. The analytical results obtained by [...] formulation at a particular section of the beam are compared to those of FEM.
10
Content available remote HOLIGILM-based simulations for a bended light guide
63%
Kocifaj M.
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2010
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tom R. 86, nr 10
218-221
EN
Hollow light guides became very attractive in last decades, due to a globally recognized need for alternative light sources with low energy requirements. Light guides transport the daylight from exterior to an interior space thus making the visual conditions in more acceptable. Recent numerical tools based on flux methods enable to evaluate performance of the light guides, but these tools are inaccurate in determining the light conditions below non-lambertian diffusers. In addition, the flux methods are inapplicable for modelling the directional characteristics of light beams propagating through transparent or semi-transparent optical interfaces (usually supplying the traditional diffusers). To overcome these problems, the analytical HOLIGILM solution was originally developed for straight light pipes and now it is applied to bended pipes. The solution accepts the skylight patterns (including the sun) and after complex transformations in the bended light pipe it provides an angular distribution of light at the bottom interface of the pipe. The demonstrative results of numerical calculations based on HOLIGILM solution are presented and discussed.
PL
Światłowody tubularne stały sie bardzo atrakcyjne w ostatniej dekadzie z powodu globalnego poszukiwania alternatywnych, energooszczędnych źródeł światła. Światłowody umożliwiają wprowadzanie światła dziennego do wnętrz zapewniając pożądane warunki oświetleniowe. Stosowane dotychczas narzędzia numeryczne oparte na metodach strumieniowych umożliwiają ocenę właściwości światłowodów, nie dając jednak dokładnych wyników w zakresie warunków oświetleniowych pod światłowodem o rozsyle lambertowskim. Co więcej, metody strumieniowe nie umożliwiają modelowania charakterystyk kierunkowych strumienia świetlnego w przezroczystym lub półprzezroczystym interfejsie optycznym (zwykle wykorzystującym tradycyjny element rozpraszający światło). Rozwiązaniem tego problemu jest zastosowanie, w badaniach światłowodów ugiętych, programu HOLIGILM, który początkowo wykorzystywano do badania prostych rur światłowodzących. Narzędzie uwzględnia nieboskłon bezchmurny (włączając bezpośrednie promieniowanie słoneczne), a po kompleksowych transformacjach promieni świetlnych w światłowodzie ugiętym umożliwia przedstawienie przestrzennego rozkładu oświetlenia w dolnym interfejsie rury. Zademonstrowano i przedyskutowano wyniki obliczeń numerycznych oparte na narzędziu HOLIGILM.
11
Content available remote 2D analytical solution of magnetic field in linear permanent magnet synchronous machine; comparison of analytical and numerical solution of magnetic field by permanent magnets
63%
Virtic P. , Stumberger B.
|
2007
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tom R. 83, nr 7-8
139-142
EN
The comparison between analytical and numerical (finite element method (FEM)) solution of magnetic field by permanent magnets (PMs) excitation in linear permanent magnet synchronous machine (LPMSM) is presented. Both analytical and numerical solutions are obtained from 2D analysis via magnetic vector potential. It is shown that good agreement between both is obtained.
PL
Przeprowadzono porównanie rozkładów pola magnetycznego uzyskanego metodą analityczną i numeryczną (metoda elementów skończonych) i generowanego w liniowym silniku synchronicznym z magnesami trwałymi. Oba rozwiązania zostały uzyskane w modelu dwuwymiarowym przy użyciu magnetycznego potencjału wektorowego. Analiza porównawcza wykazała dobrą zgodność obu rozwiązań.
12
Content available remote The transformational analytical solution for nonlinear convection in the presence of two-way rotation
51%
El-Kholy S. A. , Ismail I. A.
|
2004
|
tom Vol. 7, nr 1
119-130
EN
Steady two-dimensional finite amplitude solutions are obtained for the problem of convection in a horizontal fluid layer heated from below and rotated about its vertical axis. The flow is assumed to be laminar and two-dimensional. The density variation is taken into account by the Boussinesq approximation. Different boundaries with prescribed constant temperature are assumed and the solutions are obtained. The transform for summing the variables, which reduce the nonlinear partial differential equation into ordinary differential equation of the high order, is used. The existence of steady subcritical finite amplitude solutions is demonstrated for different Prandtl numbers. A strong reduction in the domain of stable rolls that occurs as the rotation rate is increasing. Convection driven by thermal buoyancy in the presence of the Coriolis force occurs in planetary atmospheres and interiors. Asymptotic expressions for the onset of convection in a horizontal fluid layer of finite extent heated from below and rotating about a vertical axis are derived in the limit of large rotation rates in the case of stress-free upper and lower boundaries. In the presence of the vertical sidewalls the critical Rayleigh number R is much lower than the classical value of the infinity extended layer.
13
Content available remote Buckling resistance assessment of a slender cylindrical shell axially compressed
51%
Marcinkowski J.
|
2010
|
tom Vol. 14, nr 2
309-316
EN
The paper deals with some considerations focused on resistance assessment of slender cylindrical shells subjected to the axial compression. The load carrying capacity of such shells is determined by stability criterion. It is not enough to determine the critical load in order to assess the load carrying capacity. It is necessary to apply the whole procedure recommended by designing codes and other design recommendations. Details of this procedure were presented in the paper. The correctness of the resistance assessment was verified experimentally on segments of cylindrical shells made of stainless steel.
14
Content available remote Effect of the ion slip on the MHD flow of a dusty fluid with heat transfer under exponential decaying pressure gradient
51%
Attia H.
Open Physics
|
2005
|
tom 3
|
nr 4
484-507
EN
In the present study, the unsteady Hartmann flow with heat transfer of a dusty viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied without neglecting the ion slip. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions.
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