Asymptotic Analysis of a Nonlinear Problem on Domain Boundaries in Convection Patterns by Homotopy Renormalization Method

2017 ◽  
Vol 72 (10) ◽  
pp. 909-913 ◽  
Author(s):  
Hua Xin
Keyword(s):  
Asymptotic Analysis ◽  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Variable Coefficient ◽  
Analytic Approximation ◽  
Domain Boundaries ◽  
Convection Patterns ◽  
Renormalization Method ◽  
Homotopy Renormalization Method ◽  
Better Than

AbstractIn this article, using the homotopy renormalization method, the asymptotic analysis to a nonlinear problem on domain boundaries in convection patterns are given. In particular, by taking a variable coefficient homotopy equation, the global asymptotic solutions satisfying boundary conditions are obtained. These results are better than the existing analytic approximation solutions.

Asymptotic analysis to free-convective boundary-layer problem by homotopy renormalization method

2019 ◽  
Vol 33 (07) ◽  
pp. 1950083 ◽  
Author(s):  
Yue Kai ◽  
Bailin Zheng
Keyword(s):  
Boundary Layer ◽  
Convective Boundary Layer ◽  
Variable Coefficient ◽  
Nonlinear Ordinary Differential Equations ◽  
Convective Boundary ◽  
Boundary Layer Problem ◽  
Renormalization Method ◽  
Fiber Manufacturing ◽  
Homotopy Renormalization Method ◽  
Layer Problem

In this paper, the homotopy renormalization (HTR) method is applied to investigate a free-convective boundary-layer problem arising from the sheet (or fiber) manufacturing, which is modeled by a system of nonlinear ordinary differential equations. By taking the inhomogeneous variable coefficient homotopy equations, the explicit asymptotic solutions satisfying the boundary conditions are given. Moreover, the comparisons with the numerical results show that our explicit function solutions have good performances in both local and large scales.

Asymptotic analysis to Von Kármán swirling-flow problem

2019 ◽  
Vol 33 (25) ◽  
pp. 1950298 ◽  
Author(s):  
Chun-Yan Wang
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
High Precision ◽  
Flow Problem ◽  
Swirling Flow ◽  
Asymptotic Solutions ◽  
Von Karman ◽  
Renormalization Method ◽  
Von Kármán ◽  
Homotopy Renormalization Method

In this paper, we consider the Von Kármán swirling-flow problem, which is described by an ordinary equations system. The explicit asymptotic solutions are given by applying the homotopy renormalization method. Furthermore, the numerical simulations verify that our asymptotic solutions have high precision and the absolute errors are less than 0.03, which means that the results obtained are truly valid and can be used practically.

scholarly journals f(T) GRAVITY FROM HOLOGRAPHIC RICCI DARK ENERGY MODEL WITH NEW BOUNDARY CONDITIONS

2013 ◽  
Vol 28 (39) ◽  
pp. 1350171 ◽  
Author(s):  
PENG HUANG ◽  
YONG-CHANG HUANG ◽  
FANG-FANG YUAN
Keyword(s):  
Dark Energy ◽  
Boundary Conditions ◽  
Dark Energy Model ◽  
Energy Model ◽  
Ricci Dark Energy ◽  
Expected Information ◽  
Better Than

Commonly used boundary conditions in reconstructing f(T) gravity from holographic Ricci dark energy (RDE) model are found to cause some problem, we therefore propose new boundary conditions in this paper. By reconstructing f(T) gravity from the RDE with these new boundary conditions, we show that the new ones are better than the present commonly used ones since they can give the physically expected information, which is lost when the commonly used ones are taken in the reconstruction, of the resulting f(T) theory. Thus, the new boundary conditions proposed here are more suitable for the reconstruction of f(T) gravity.

scholarly journals Validation of the stream function method used for reconstruction of experimental ionospheric convection patterns

2000 ◽  
Vol 18 (4) ◽  
pp. 454-460
Author(s):  
P.L. Israelevich ◽  
V. O. Papitashvili ◽  
A. I. Ershkovich
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Stream Function ◽  
Electric Fields ◽  
Electric Potential ◽  
Potential Distribution ◽  
Function Method ◽  
Polar Cap ◽  
Ionospheric Convection ◽  
Convection Patterns

Abstract. In this study we test a stream function method suggested by Israelevich and Ershkovich for instantaneous reconstruction of global, high-latitude ionospheric convection patterns from a limited set of experimental observations, namely, from the electric field or ion drift velocity vector measurements taken along two polar satellite orbits only. These two satellite passes subdivide the polar cap into several adjacent areas. Measured electric fields or ion drifts can be considered as boundary conditions (together with the zero electric potential condition at the low-latitude boundary) for those areas, and the entire ionospheric convection pattern can be reconstructed as a solution of the boundary value problem for the stream function without any preliminary information on ionospheric conductivities. In order to validate the stream function method, we utilized the IZMIRAN electrodynamic model (IZMEM) recently calibrated by the DMSP ionospheric electrostatic potential observations. For the sake of simplicity, we took the modeled electric fields along the noon-midnight and dawn-dusk meridians as the boundary conditions. Then, the solution(s) of the boundary value problem (i.e., a reconstructed potential distribution over the entire polar region) is compared with the original IZMEM/DMSP electric potential distribution(s), as well as with the various cross cuts of the polar cap. It is found that reconstructed convection patterns are in good agreement with the original modelled patterns in both the northern and southern polar caps. The analysis is carried out for the winter and summer conditions, as well as for a number of configurations of the interplanetary magnetic field.Key words: Ionosphere (electric fields and currents; plasma convection; modelling and forecasting)

scholarly journals Numerical and Non-Asymptotic Analysis of Elias’s and Peres’s Extractors with Finite Input Sequences

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 729 ◽  
Author(s):  
Amonrat Prasitsupparote ◽  
Norio Konno ◽  
Junji Shikata
Keyword(s):  
Asymptotic Analysis ◽  
Block Size ◽  
Input Sequence ◽  
Optimal Rate ◽  
Modern World ◽  
Random Numbers ◽  
Von Neumann ◽  
Information Theoretic ◽  
Running Time ◽  
Better Than

Many cryptographic systems require random numbers, and the use of weak random numbers leads to insecure systems. In the modern world, there are several techniques for generating random numbers, of which the most fundamental and important methods are deterministic extractors proposed by von Neumann, Elias, and Peres. Elias’s extractor achieves the optimal rate (i.e., information-theoretic upper bound) h ( p ) if the block size tends to infinity, where h ( · ) is the binary entropy function and p is the probability that each bit of input sequences occurs. Peres’s extractor achieves the optimal rate h ( p ) if the length of the input and the number of iterations tend to infinity. Previous research related to both extractors has made no reference to practical aspects including running time and memory size with finite input sequences. In this paper, based on some heuristics, we derive a lower bound on the maximum redundancy of Peres’s extractor, and we show that Elias’s extractor is better than Peres’s extractor in terms of the maximum redundancy (or the rates) if we do not pay attention to the time complexity or space complexity. In addition, we perform numerical and non-asymptotic analysis of both extractors with a finite input sequence with any biased probability under the same environments. To do so, we implemented both extractors on a general PC and simple environments. Our empirical results show that Peres’s extractor is much better than Elias’s extractor for given finite input sequences under a very similar running time. As a consequence, Peres’s extractor would be more suitable to generate uniformly random sequences in practice in applications such as cryptographic systems.

A Comparative Study of Artificial Boundary Conditions in ABAQUS

2013 ◽  
Vol 671-674 ◽  
pp. 1386-1389
Author(s):  
Yan Wei Wang ◽  
Shan You Li ◽  
Qiang Ma ◽  
Wei Li
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Element Model ◽  
The Other ◽  
Two Dimensional ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions ◽  
Dimensional Finite Element ◽  
Viscous Boundary ◽  
Better Than

Viscous boundary, viscous spring boundary, infinite boundary have been widely used during the last decades to solve the wave propagation in the infinite ground. In this paper we evaluate the performance of the three boundary conditions focusing on their solution precision. The comparison is performed on a two dimensional finite element model built by ABAQUS. The results show that viscous spring boundary outperforms the other boundary conditions, and viscous boundary is better than infinite element.

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