Current Issue : January - March Volume : 2017 Issue Number : 1 Articles : 6 Articles
In this paper, the system of Burgers� equations is solved by the optimal homotopy asymptotic method\nwith Daftardar-Jafari polynomials OHAM-DJ. Two numerical examples are illustrated the efficient\nof this methods for solving the system of Burgers� equations....
The transition regimes of solitons in four-photon resonant processes in the case of two-photon absorption of the fundamental radiation are numerically investigated. The standard system of equations for the amplitudes of probability of finding the system in state with certain energy is used to derive the expression for the induced polarization in the nonlinear medium. As for the equations for the amplitudes of the optical pulses, the general case is considered in which both the amplitudes and phases are space-time dependent. We focus on the finite difference methods and the case of simultaneously propagating solitons at all frequencies of the interacting waves (simultons). The obtained results indicate that upon certain threshold conditions all interacting pulses become the solitons of Lorentzian shape. The numerical analysis has also shown that the soliton amplitudes significantly depend on the ratio between the nonlinear polarizability at the fundamental frequency Ãâ?°0 and that of combination of Ãâ?°0 and the trigger-field frequency Ãâ?°1(2Ãâ?°0 + Ãâ?°1). In the second part of the paper, we apply the method of phase planes to show that at typical values of parameters, the solitons are stable....
Effective algorithms of physical media numerical modeling problems� solution are discussed. The computation rate of such problems is limited by memory bandwidth if implemented with traditional algorithms. The numerical solution of the wave equation is considered. A finite difference scheme with a cross stencil and a high order of approximation is used. The Diamond Torre algorithm is constructed, with regard to the specifics of the GPGPU�s (general purpose graphical processing unit) memory hierarchy and parallelism. The advantages of these algorithms are a high level of data localization, as well as the property of asynchrony, which allows one to effectively utilize all levels of GPGPU parallelism. The computational intensity of the algorithm is greater than the one for the best traditional algorithms with stepwise synchronization. As a consequence, it becomes possible to overcome the above-mentioned limitation. The algorithm is implemented with CUDA. For the scheme with the second order of approximation, the calculation performance of 50 billion cells per second is achieved. This exceeds the result of the best traditional algorithm by a factor of five....
Usual applied mathematics employs three fundamental arithmetical operators: addition, multiplication, and exponentiation. However, for example, transcendental numbers are said not to be attainable via algebraic combination with these fundamental operators. At the same time, simulation and modelling frequently have to rely on expensive numerical approximations of the exact solution. The main purpose of this article is to analyze new fractional arithmetical operators, explore some of their properties, and devise ways of computing them. These new operators may bring new possibilities, for example, in approximation theory and in obtaining closed forms of those approximations and solutions. We show some simple demonstrative examples....
This study is devoted to the computational fluid dynamics (CFD) modeling of steady laminar mixed convection flow and heat transfer in lid driven cavity (10 � Re � 1000). The ratio of the height to the width of the cavity is ranged over H/L = 0.5 to 1.5. The governing equations are solved using commercial finite volume package FLUENT to visualize the nature of the flow and estimate the heat transfer inside the cavity for different aspect ratio. The simulation results are presented in terms of average Nusselt number of the hot wall, velocity profile, and temperature contours. It was found that the average Nusselt number inside the cavity is strongly governed by the aspect ratio as well as the Reynolds number. A parametric study is conducted to demonstrate the effect of aspect ratio on the flow and heat transfer characteristics. It is found that heat transfer enhancement was obtained by decreasing the aspect ratio and/or increasing the Reynolds number....
Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed\na measure for fault tolerance of the system, which is called the g-good-neighbor diagnosability\nthat restrains every fault-free node containing at least g fault-free neighbors. In 2015, Zhang et al.\nproposed a measure for fault diagnosis of the system, namely, g-extra diagnosability, which\nrestrains that every fault-free component has at least g 1 fault-free nodes. In this paper, we\nobtain some properties of the g-good-neighbor (g-extra) diagnosability of the system and give the\ng-good-neighbor (g-extra) diagnosability of some graphs under the PMC model and MM* model....
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