Analytical solution of reactive hybrid cells in series (HCIS) model for pollution transport through the rivers

2020 ◽  
Vol 65 (14) ◽  
pp. 2499-2507
Author(s):  
Jafar Chabokpour ◽  
Amir Samadi
Keyword(s):  
Analytical Solution ◽  
Hybrid Cells ◽  
Pollution Transport ◽  
In Series

scholarly journals Wear of elastic tube with nonuniform coating by rigid bush

2020 ◽  
Vol 162 ◽  
pp. 02002 ◽  
Author(s):  
Kirill E. Kazakov
Keyword(s):  
Analytical Solution ◽  
Special Form ◽  
Special Functions ◽  
Contact Stresses ◽  
Elastic Tube ◽  
Analytical Representation ◽  
Standard Methods ◽  
In Series ◽  
Separate Factor ◽  
Over Time

This article is devoted to the statement and construction of analytical solution of the wearcontact problem for a rigid bush and elastic pipe with a coating in the case when the coating is nonuniform. The presence of nonuniformity leads us to the necessity of constructing a solution in a special form over special functions, since standard methods does not allow us to effectively take into account the complex properties of the coating. Analytical representation for contact stresses under the bush is presented in series with separate factor, which connect with complex properties of coating. This allows provide effective calculation even if these properties are described by rapidly changing or discontinuous functions. It is also shown that contact stresses will be negligible over time.

scholarly journals Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 335 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Muhammad Arif ◽  
Poom Kumam
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Third Order ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
In Series

In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.

ALGORITHM FOR CALCULATING SURFACES OF BIFOCAL LENS ANTENNAS

2019 ◽  
pp. 53-59
Author(s):  
Yu. S. Nikulina
Keyword(s):  
Dielectric Constant ◽  
Analytical Solution ◽  
Optical Axis ◽  
Relative Dielectric Constant ◽  
Phase Front ◽  
Systems Of Equations ◽  
Lens Antenna ◽  
Electrical Length ◽  
Lens Antennas ◽  
In Series

An algorithm is proposed that makes it possible to calculate the coefficients of power polynomials approximating the illuminated and shadow surfaces of bifocal lens antennas. The algorithm is based on providing equality of electrical lengths of rays passing from the focus points through lens body and its edge and on the assumption that the phase front is flat and is inclined at a determined angle relative to the main optical axis of the lens on the aperture of the lens antenna. For each of the rays an expression was written that determines its electrical length. The electrical length of the rays depends on the points coordinates of the illuminated and shadow surface of the lens, in which they are refracted. The analytical solution of the obtained equation is difficult. Therefore, it is proposed to determine the exact coordinate values by numerical methods. The proposed algorithm determines in series the three points lying on the illuminated and shadow surfaces. The coordinates of the points are used to form systems of equations whose solutions are the coefficients of power polynomials approximating the illuminated and shadow surfaces of the lens antenna. The algorithm does not impose restrictions on the relative dielectric constant of the material from which the lens antenna is made.

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