Search

In the traditional calculations of the steady-state mode of the electrical network, the dependences of the active resistances of the overhead line wire on the ambient temperature and currents in the branches are not taken into account. However, the temperature is a function of the active power losses, the power losses are a function of the resistance and current, and the resistance is temperature dependent. Therefore, these relations should be related to the traditional equations for stationary regimes. In order to increase the accuracy of steady-state calculations, a temperature correction of the resistance of the branches is required. In this paper, we present a method based on the joint solution of nonlinear equations of the steady-state electric network regime and the thermal balance of the wires of overhead lines. The algorithm and the program of calculation of the steady-state mode of an electric network taking into account dependence of active resistances of a wire of an overhead line on ambient temperature and currents in branches have been developed. The quantitative influence of the load current, wire temperature, wind speed, solar radiation on the active resistance of the wires has been estimated, and the errors in calculating annual variable energy losses have been determined. Numerical experiments were carried out for a 6-node modified version of the IEEE test system and equivalent circuit of 110 kV. The results of the calculations of the steady-state regime on various test circuits showed that the non-account of the temperature dependence of the active resistances might cause errors in power loss for individual loaded lines up to 10 %, and for total losses of the system – up to 30 %. This is unacceptable in simulating the modes of the electric network. The results of simulation of steady-state regimes taking into account the temperature dependence of the resistance of the wires are presented on the example of 6-node and 7-node circuits.

A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE’s have been solved with a very stable and reliable numerical scheme that involves Simpson’s Rule and Successive over Relaxation method. The accuracy of the results is improved by making iterations on three different grid sizes and higher order accuracy in the results is achieved by Richardson extrapolation. This study provides realistic and differentiated results with due considerations of micropolar fluid theory. The micropolar material parameters demonstrated reduction in the bulk fluid speed, thermal distribution and skin friction coefficient but increase in local heat transfer rate and couple stress. The spin behavior of microstructures is also exhibited through microrotation vector N ( η ) .

We propose a memory-based method for the solution of a specific type of nonlinear equation systems. We observe that when the equations in a system can be separated into 2 parts, where each subset contains fewer parameters than the whole set of equations, the system can be solved faster with a preprocessing phase. We show that reduced rounds of AES produce such a system under a chosen plaintext scenario. This observation enables us to solve that system within a practically applicable complexity of 2 7 operations where a brute force approach requires 272 trials. The method can be used for the solution of other equation systems of the same structure. In the optimal case where we can divide the equations into 2, a problem that contains n binary variables can be solved at time O(n/2 x 2n/2) operations and using O(2n/2) units of memory rather than O(2n) trials of the equation system. [ABSTRACT FROM AUTHOR]

The Newton-Kantorovich theorem enjoys a special status, as it is both a fundamental result in Numerical Analysis, e.g., for providing an iterative method for computing the zeros of polynomials or of systems of nonlinear equations, and a fundamental result in Nonlinear Functional Analysis, e.g., for establishing that a nonlinear equation in an infinite-dimensional function space has a solution. Yet its detailed proof in full generality is not easy to locate in the literature. The purpose of this article, which is partly expository in nature, is to carefully revisit this theorem, by means of a two-tier approach. First, we give a detailed, and essentially self-contained, account of the classical proof of this theorem, which essentially relies on careful estimates based on the integral form of the mean value theorem for functions of class ${\mathcal{C}}^1$ with values in a Banach space, and on the so-called majorant method. Our treatment also includes a careful discussion of the often overlooked uniqueness issue. An example of a nonlinear two-point boundary value problem is also given that illustrates the power of this theorem for establishing an existence theorem when other methods of nonlinear functional analysis cannot be used. Second, we give a new version of this theorem, the assumptions of which involve only one constant instead of three constants in its classical version and the proof of which is substantially simpler as it altogether avoids the majorant method. For these reasons, this new version, which captures all the basic features of the classical version could be considered as a good alternative to the classical Newton-Kantorovich theorem. [ABSTRACT FROM AUTHOR]

A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE's have been solved with a very stable and reliable numerical scheme that involves Simpson's Rule and Successive over Relaxation method. The accuracy of the results is improved by making iterations on three different grid sizes and higher order accuracy in the results is achieved by Richardson extrapolation. This study provides realistic and differentiated results with due considerations of micropolar fluid theory. The micropolar material parameters demonstrated reduction in the bulk fluid speed, thermal distribution and skin friction coefficient but increase in local heat transfer rate and couple stress. The spin behavior of microstructures is also exhibited through microrotation vector N (η) . [ABSTRACT FROM AUTHOR]