Wyniki wyszukiwania - BazTech

1

Existence and uniqueness of the solution to the optimal control problem with integral criterion over the entire domain for a nonlinear Schrödinger equation with a special gradient term

Salmanov Vuqar

Control and Cybernetics

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2020

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Vol. 49, No. 3

277--290

EN

The paper concerns the optimal control problem with the full-range integral performance criterion for the nonlinear Schrödinger equation with the specific gradient summand and the complex potential when the performance criterion is the full-range integral. In this paper, the existence and uniqueness theorems regarding the solution of the optimal control problem under consideration are proven.

2

Local stationary heat fields in fibrous composites

Baran Wojciech, Kurnik Krystian, Nawalaniec Wojciech, Shareif Albashir

Silesian Journal of Pure and Applied Mathematics

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2019

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vol. 9, iss. 1

1--8

EN

Consider a multiply connected domain D bounded by nonoverlapping circles. Introduce the complex potential u(z) = Re ϕ(z) in D where the function ϕ(z) is analytic in D except at infinity where ϕ(z) ∼ z. The function u(z) models the distribution of temperature in the domain D. The unknown function ϕ(z) is continuously differentiable in the closures of the considered domain. We solve approximately the modified Schwarz problem when u(z) = Re ϕ(z) is equal to an undetermined constant on every boundary component of D by a method of functional equations.

3

Biaxial loading of a plate containing a hole and two co-axial through cracks

Sulym H., Opanasovych V., Slobodian M., Yarema Y.

Acta Mechanica et Automatica

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2018

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Vol. 12, no. 3

237--242

EN

The paper presents the solution linear elasticity problem for an isotropic plate weakened by a hole and two co-axial cracks. The plate is exerted by uniform traction at infinity. The corresponding 2D problem is solved by the method of Kolosova-Muskhelishvili complex potentials. The method implies reduction of the problem to simultaneous singular integral equations (SIE) for the functions defined the region of the cracks and hole. For particular case the solution the SIE is obtained analytically in a closed form. A thorough analysis of the stress intensity factors (SIF) is carried out for various cases of the hole shape: penny-shaped, elliptical and rectangular.

4

Effect of polydispersity in conductivity of unidirectional cylindres

Rylko N.

Archives of Materials Science and Engineering

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2008

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Vol. 29, nr 1

45-52

EN

Purpose: Purpose of this paper is to study the effective thermal conductivity of infinite unidirectional circular cylinders arbitrary distributed in a uniform host. Design/methodology/approach: Applying the method of complex potentials we present the heat flux as a complex analytic function in the section of the fibre composite perpendicular to the direction of the cylinders. Findings: The flux is written in the form of a series. Special attention is paid to the question of polydispersity, when many cylinders of different radii are distributed in the periodicity cell. Research limitations/implications: The proposed exact formulas hold for fiber composites. Practical implications: The deduced formulas are useful in prediction and estimation of the effective thermal conductivity of fiber composites. Originality/value: The obtained formulas for the effective conductivity are new and were not known before.

5

An approximate method for estimation of fluid motion in a lake containing islands

Klonowska-Prosnak M. E., Prosnak W. J., Cześnik P. P.

Archives of Hydro-Engineering and Environmental Mechanics

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2005

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Vol. 52, nr 4

335-349

EN

The physical phenomenon considered in the paper deals with flow in a lake, which contains one or several islands. The flow is generated by rivers, their inlets and outlets being distributed on the shoreline of the lake. The problem to be solved consists in determination of the velocity field - in the domain bounded by the shorelines of the lake and the islands. In fact, it is attempted to arrive solely at an estimation of the field. Consequently, a rather simple physical model of the phenomenon, as well as its simple mathematical description has been applied. In particular, plane, irrotational and steady flow of ideal liquid has been introduced, the inlets and outlets of the rivers being simulated by sources and sinks. Hence, the problem reduces to determination of a complex function, representing the complex velocity field, which satisfies the impermeability condition on all contours representing the shorelines, the field being generated by the singularities already mentioned. Unfortunately, the so formulated problem is "overconditioned" or "too stiff", what means that the impermeability condition on the outer contour cannot be satisfied. Nevertheless, we arrived at a simple method for circumventing this obstacle, the payoff consisting in some modification of this contour. We had this particular modification in mind, applying the word "approximate" in the title of the paper. The paper contains results - in the form of streamline patterns - for lakes containing from 1 to 3 islands. In the relevant figures the distances between the given and the modified exterior contours can be seen distinctly - allowing the reader to draw conclusions, whether the errors due to the modifications are admissible or not. Of course, it depends anyway on the point of view of the user of the results.