9,297 research outputs found
Marangoni convection of a viscous fluid over a vibrating plate
No full textThis research presents a new insight into Marangoni convection through investigating, both numerically and analytically, the surface tension driven instability activated by a coupled effect of a vibrating plate and viscous dissipation. A horizontal, thin fluid layer is bounded from below by an impermeable, adiabatic plate that vibrates in the horizontal direction. The upper boundary is modelled by a free surface subject to a thermal boundary condition of the third kind (Robin). The internal heat generation due to viscous dissipation yields a vertical, potentially unstable temperature gradient. The linear stability analysis of the stationary terms of the basic state is performed. The perturbed flow, in the form of plane waves, is superimposed onto the basic state. The obtained system of ordinary differential equations is solved numerically by means of the Runge-Kutta method coupled with the shooting method. For the two limiting cases, the isothermal upper boundary and adiabatic upper boundary, the analytical solutions of the eigenvalue problem are obtained. The values of the critical parameter, which identifies the threshold for the onset of Marangoni convection, are presented
Algorithms for determining residues modulo in a complex numerical domain
No full textAn important aspect of improving modern computer systems and their components is an increasing the speed of arithmetic calculations, including due to the use of new mathematical models and methods based on non-positional residue number systems. The increase in the volume of processed data in modern computer systems leads to the additional risks and threats of unintentional failures and denials of service. This is especially important when building fault-tolerant critical information systems in which failure or denial of service can lead to catastrophic consequences. The article discusses arithmetic operations in the ring of residue classes. These techniques make it possible to implement fast and fault-tolerant computing for modern computer systems and telecommunication networks. We propose an algorithm for calculating the residues of integer data in a complex numerical domain. The algorithm is based on the use of the first fundamental Gauss theorem, which establishes an isomorphism between complex and real residues. Examples of determining the residues of integer data in a complex numerical domain are presented, which clearly demonstrate the constructiveness of the proposed techniques
Simplified algorithm for numerical solution of liquid flow equations
No full textKuznetsov V. A. Simplified algorithm for numerical solution of liquid flow equations / V. A. Kuznetsov // Journal of Engineering Physics and Thermophysics. - 2018. - Vol.91, No3. - P. 648-654.An algorithm is suggested for numerical solution of differential equations for velocity and pressure on a staggered grid. The algorithm ensures unconditional convergence of iterations for a correction to pressure and without it
Transverse heterogeneity effects in the dissipation-induced instability of a horizontal porous layer
No full textThe linear stability of a parallel flow in a heterogeneous porous channel is analyzed by means of the Darcy law and the Oberbeck–Boussinesq approximation. The basic velocity and temperature distributions are influenced by the effect of the viscous dissipation, as well as, by the boundary conditions. A horizontal porous layer bounded by impermeable and infinitely wide walls is considered. The lower boundary is assumed to be thermally insulated, while the upper boundary is assumed to be isothermal. A transverse heterogeneity for the permeability and for the thermal conductivity is taken into account. The main task of this work is to investigate the role of this heterogeneity in changing the threshold for the onset of instability. A linear stability analysis by means of the normal modes method is performed. The onset of instability against oblique rolls is studied. The eigenvalue problem is solved numerically
Heterogeneity and onset of instability in Darcy's flow with a prescribed horizontal temperature gradient
No full textThe aim of this study is the analysis of the onset conditions for the thermal instability in a fluid saturated porous medium. The investigation refers to an infinitely wide horizontal porous layer with vertical heterogeneity, such that the lower plane boundary is impermeable and thermally insulated (adiabatic). The temperature distribution on the upper plane boundary is assumed to be prescribed and linearly varying in the horizontal direction. It is shown that these boundary conditions are compatible with a buoyancy-induced parallel-flow solution such that the temperature gradient is inclined with respect to the verticaldirection. The basic parallel flow is perturbed by small–amplitude roll disturbances, so that a linear analysis of the neutral stability is carried out. The local balance equations for the disturbances are solved numerically. The critical conditions for the onset of convection are determined
Solving the Shortest Path Problem Using Integer Residual Arithmetic
No full textThe report considers solution to the problem of routing, the essence of which is to determine the shortest path length between any pair of computer network subscribers represented as an undirected graph, as one of the possible methods to increase the speed and performance of computer systems (CS). To carry out calculations and comparative analysis of the speed and productivity of CS in a positional binary number system (PNS) and in a non-positional number system in residual classes (residual number system-RNS), we consider one practical problem. Task is the routing problem, the essence of which is to determine the shortest path length, that is, to find the optimal data transmission route in the computer network
Method of diagnostic of non-positional code structures in the system of residue classes basing on the usage of an alternative number set informativeness
No full textA method of diagnosis of data represented in the system of residue classes (SRC) is suggested in the article. It is shown, that the main disadvantage of existing methods of diagnosis data in SRC is a significant time of data diagnosis while the necessity of entering heavy informational redundancy to non-positional code structure (NCS) in SRC. The considered in the article method of diagnosis data in SRC allows increasing operability of a diagnosis procedure while entering minimal informational redundancy. The time of data diagnostic, compared to known methods, is decreasing firstly due to excluding the procedure of transforming numbers in SRC to positional notation as in known methods, i. e. eliminating a positional operation of numbers comparing. Secondly, the time of data diagnostic is decreased by reducing the quantity of SRC bases, which are giving the possibility of mistakes. Thirdly, the time of data diagnostic is decreased due to the usage of tabular sample value of an alternative set (AS) of numbers in SRC in one beat. The quantity of additionally entered informational redundancy is decrease by effective usage of inner informational redundancy existing in NCS. A specific example of the usage of the suggested method of diagnosis data in SRC is given. Therefore, the suggested method allows reducing the time of diagnosis of data errors in NCS, represented in SRC, which is increasing the diagnostic operability while entering minimal informational redundancy
The data errors control in the modular number system based on the nullification procedure
No full textA method for error control in the modular number system (MNS) based on the use of the zeroing procedure is proposed. Error control in the MNS is a non-positional operation and requires the development of special methods, designed to increase the efficiency of this procedure. This method is designed to verify the correct implementation of the computing process of computer systems and components. It is assumed that the error in one module remainder does not affect the residual values corresponding to other modules (bases) of the MNS. The essence of the proposed method is that, when performing the procedure of zeroing in the MNS, the operation of determining is combined in time, in accordance with the digits ai(i-1) and an(i - i1) +1 of the number A(i-1), the zeroing constant ZC(i) and the calculation operation for the values of ai(i -1) and an(i - - i1) +1 of the following digits ai(+ i)1 and an(i-)i of the number A(i). This makes it possible to increase the efficiency of information control, presented in the modular number system
The Procedure for Implementing the Operation of Multiplying Two Matrices Using the Residual Number System
No full textThe report considers solution to the problem of improving the speed implementation of the operation of multiplying two square matrices of the same dimension. To carry out calculations and comparative analysis of the speed of the multiplication operation, we consider a computer system (CS) in the positional binary number system (PNS) and in the non-positional number system in the residual classes (the residual number system - RNS). A comparative analysis of the performance of the CS was carried out with the same characteristics of the computing system: equal lengths of bit grids, the same command systems, the same methods of addressing operands and instructions, the same clock speed of the processor, the equal number of program commands, etc. When calculating the speed of the matrix multiplication operation, the fastest data processing method in RNS was used, based on the tabular principle
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