Wyniki wyszukiwania - Biblioteka Nauki

1

Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid

100%

Fetecau C. , Vieru D. , Fetecau C.

Open Physics

|

2011

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tom 9

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nr 3

816-824

EN

The velocity field corresponding to the unsteady motion of a viscous fluid between two side walls perpendicular to a plate is determined by means of the Fourier transforms. The motion of the fluid is produced by the plate which after the time t = 0, applies an oscillating shear stress to the fluid. The solutions that have been obtained, presented as a sum of the steady-state and transient solutions satisfy the governing equation and all imposed initial and boundary conditions. In the absence of the side walls they are reduced to the similar solutions corresponding to the motion over an infinite plate. Finally, the influence of the side walls on the fluid motion, the required time to reach the steady-state, as well as the distance between the walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence, are established by means of graphical illustrations.

2

Exact solutions for the longitudinal flow of a generalized Maxwell fluid in a circular cylinder

100%

Siddique I.

|

2010

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tom Vol. 62, nr 4

305-317

EN

This paper deals with the longitudinal flow of a generalized Maxwell fluid in an infinite circular cylinder, due to the longitudinal variable time-dependent shear stress that is prescribed on the boundary of the cylinder. The fractional calculus approach in the constitutive relationship model of a Maxwell fluid is introduced. The velocity field and the resulting shear stress are obtained by means of the Laplace and finite Hankel transforms and satisfy all the imposed initial and boundary conditions. The solutions corresponding to ordinary Maxwell fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. Finally, the influence of the fractional coefficient on the velocity and shear stress of the fluid is analyzed by graphical illustrations.

3

Dynamics of Shallow Water Waves with Various Boussinesq Equations

100%

Kumar H. , Malik A. , Singh Gautam M. , Chand F.

Acta Physica Polonica A

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2017

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tom 131

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nr 2

275-282

EN

Attempt has been made to construct the solitary waves and shock wave solutions or domain walls (in higher dimension) for various Boussinesq equations. The method of undetermined coefficients have been used to explore the exact analytical solitary waves and shock wave solutions in terms of bell-shaped sech^p function and kink-shaped tanh^p function for the considered equations. The Boussinesq equation in the (1+1)-dimensional, the (2+1)-dimensional and the (3+1)-dimensional equations are studied and the parametric constraint conditions and uniqueness in view of both solitary waves and shock wave solutions are determined. Such solutions can be valuable and desirable for explaining some nonlinear physical phenomena in nonlinear science described by the Boussinesq equations. The effect of the varying parameters on the development of solitary waves and shock wave solutions have been demonstrated by direct numerical simulation technique.

4

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

100%

Xie Q.

Open Physics

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2014

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tom 12

|

nr 12

830-835

EN

We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing (SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable.

5

Solving nonlinear evolution equation system using two different methods

88%

Kaplan M. , Bekir A. , Ozer M. N.

Open Physics

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2015

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tom 13

|

nr 1

EN

This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

6

Exact and approximate solutions to Schrödinger’s equation with decatic potentials

75%

Brandon D. , Saad N.

Open Physics

|

2013

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tom 11

|

nr 3

279-290

EN

The one-dimensional Schrödinger’s equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential’s parameters, we show that the decatic polynomial potential V (x) = ax 10 + bx 8 + cx 6 + dx 4 + ex 2, a > 0 is exactly solvable. By examining the polynomial solutions of certain linear differential equations with polynomial coefficients, the necessary and sufficient conditions for corresponding energy-dependent polynomial solutions are given in detail. It is also shown that these polynomials satisfy a four-term recurrence relation, whose real roots are the exact energy eigenvalues. Further, it is shown that these polynomials generate the eigenfunction solutions of the corresponding Schrödinger equation. Further analysis for arbitrary values of the potential parameters using the asymptotic iteration method is also presented.

7

Exact solutions for unsteady incompressible viscous fluid flows

75%

Jamil M. , Ahmed F. , Khan N. A.

|

2007

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tom Vol. 12, no 4

975-988

EN

Two-dimensional, unsteady, laminar equations of motions of an incompressible fluid with variable viscosity are considered. The problem investigated is the flow for which the vorticity distribution is proportional to the stream function perturbed by a generalized uniform stream making an angle with the positive x-axis. Employing transformation variables, the goveming Navier-Stocks Equations (NSE) are transformed into steady state equations and then simple ordinary differential equations and a class of exact solutions are obtained. Several graphs of physical interest of streamline are also displayed and discussed.

8

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

75%

Ndlovu P. , Moitsheki R.

Open Physics

|

2013

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tom 11

|

nr 8

984-994

EN

Some new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.

9

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

75%

Schulze-Halberg A.

Open Physics

|

2005

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tom 3

|

nr 4

591-609

EN

We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

10

Exact solutions for free longitudinal vibration of bars with non-uniform Cross-sections

75%

Li Q. S.

|

2000

|

tom Vol. 5, no 3

521-541

EN

Using appropriate transformations, the differential equations of free longitudinal vibration of bars with variably distributed mass and axial stiffness are reduced to Bessel?s equations or ordinary differential equations with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of mass and axial stiffness. Exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived and used to obtain the general solution and the frequency equation of a multi-step non-uniform bar with various boundary conditions, including non-classical cases. This approach which combines the transfer matrix method and closed form solutions of one step bars leads to a single frequency equation for any number of steps.