Search results for: Asymptotic relative efficiency

Authors: Chao Yuan, Bao Guang Tian

Abstract:

A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some degree.

Keywords: Generalized linear model, generalized relative coefficient, least eigenvalue, relative efficiency.

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Authors: Chao Yuan, Bao Guang Tian

Abstract:

A relative efficiency is defined as Ridge Estimate in the general linear model. The relative efficiency is based on the Mean square error. In this paper, we put forward a parameter of Ridge Estimate and discussions are made on the relative efficiency between the ridge estimation and the General Ridge Estimate. Eventually, this paper proves that the estimation is better than the general ridge estimate, which is based on the MSE.

Keywords: Ridge estimate, generalized ridge estimate, MSE, relative efficiency.

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Authors: Nan Chen, Baoguang Tian

Abstract:

In this paper, some relative efficiency have been discussed, including the LSE estimate with respect to BLUE in curve model. Four new kinds of relative efficiency have defined, and their upper bounds have been discussed.

Keywords: Relative efficiency, LSE estimate, BLUE estimate, Upper bound, Curve model.

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Authors: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: Hsuan-Ku Liu

Abstract:

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Tapas Kumar Sinha, Joseph Mathew

Abstract:

Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).

Keywords: KdV equation, Asymptotic Degeneracy, Solitons, Inverse Scattering

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Authors: Hsuan-Ku Liu, Ming Long Liu

Abstract:

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

Abstract:

In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.

Keywords: Hopfield neural networks, uniform asymptotic stability, global asymptotic stability, exponential stability.

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Authors: Hazem M. Al-Mofleh, John E. Daniels, Joseph W. McKean

Abstract:

In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

Keywords: Asymptotic relative efficiency, non-linear rank-based, robust, rank estimates, variogram.

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Authors: Carolina B. Baguio

Abstract:

One of the purposes of the robust method of estimation is to reduce the influence of outliers in the data, on the estimates. The outliers arise from gross errors or contamination from distributions with long tails. The trimmed mean is a robust estimate. This means that it is not sensitive to violation of distributional assumptions of the data. It is called an adaptive estimate when the trimming proportion is determined from the data rather than being fixed a “priori-. The main objective of this study is to find out the robustness properties of the adaptive trimmed means in terms of efficiency, high breakdown point and influence function. Specifically, it seeks to find out the magnitude of the trimming proportion of the adaptive trimmed mean which will yield efficient and robust estimates of the parameter for data which follow a modified Weibull distribution with parameter λ = 1/2 , where the trimming proportion is determined by a ratio of two trimmed means defined as the tail length. Secondly, the asymptotic properties of the tail length and the trimmed means are also investigated. Finally, a comparison is made on the efficiency of the adaptive trimmed means in terms of the standard deviation for the trimming proportions and when these were fixed a “priori". The asymptotic tail lengths defined as the ratio of two trimmed means and the asymptotic variances were computed by using the formulas derived. While the values of the standard deviations for the derived tail lengths for data of size 40 simulated from a Weibull distribution were computed for 100 iterations using a computer program written in Pascal language. The findings of the study revealed that the tail lengths of the Weibull distribution increase in magnitudes as the trimming proportions increase, the measure of the tail length and the adaptive trimmed mean are asymptotically independent as the number of observations n becomes very large or approaching infinity, the tail length is asymptotically distributed as the ratio of two independent normal random variables, and the asymptotic variances decrease as the trimming proportions increase. The simulation study revealed empirically that the standard error of the adaptive trimmed mean using the ratio of tail lengths is relatively smaller for different values of trimming proportions than its counterpart when the trimming proportions were fixed a 'priori'.

Keywords: Adaptive robust estimate, asymptotic efficiency, breakdown point, influence function, L-estimates, location parameter, tail length, Weibull distribution.

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Authors: Jung-Lo Park, Sung-Sik Kim, Sun-Young Choi, Ju-Hyung Kim, Jae-Jun Kim

Abstract:

Sub-prime mortgage crisis which began in the US is regarded as the most economic crisis since the Great Depression in the early 20th century. Especially, hidden problems on efficient operation of a business were disclosed at a time and many financial institutions went bankrupt and filed for court receivership. The collapses of physical market lead to bankruptcy of manufacturing and construction businesses. This study is to analyze dynamic efficiency of construction businesses during the five years at the turn of the global financial crisis. By discovering the trend and stability of efficiency of a construction business, this study-s objective is to improve management efficiency of a construction business in the ever-changing construction market. Variables were selected by analyzing corporate information on top 20 construction businesses in Korea and analyzed for static efficiency in 2008 and dynamic efficiency between 2006 and 2010. Unlike other studies, this study succeeded in deducing efficiency trend and stability of a construction business for five years by using the DEA/Window model. Using the analysis result, efficient and inefficient companies could be figured out. In addition, relative efficiency among DMU was measured by comparing the relationship between input and output variables of construction businesses. This study can be used as a literature to improve management efficiency for companies with low efficiency based on efficiency analysis of construction businesses.

Keywords: Construction Company, DEA, DEA/Window, Efficiency Analysis

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Authors: Abdenour Bourabaa, Mohamed Saighi, Ibrahim Belal

Abstract:

A numerical study has been conducted to investigate the influence of fin pitch and relative humidity on the heat transfer performance of the fin-and-tube heat exchangers having plain fin geometry under dehumidifying conditions. The analysis is done using the ratio between the heat transfer coefficients in totally wet conditions and those in totally dry conditions using the appropriate correlations for both dry and wet conditions. For a constant relative humidity, it is found that the heat transfer coefficient increases with the increase of the air frontal velocity. By contrast, the fin efficiency decreases when the face velocity is increased. Apparently, this phenomenon is attributed to the path of condensate drainage. For the influence of relative humidity, the results showed an increase in heat transfer performance and a decrease in wet fin efficiency when relative humidity increases. This is due to the higher amount of mass transfer encountered at higher relative humidity. However, it is found that the effect of fin pitch on the heat transfer performance depends strongly on the face velocity. At lower frontal velocity the heat transfer increases with fin pitch. Conversely, an increase in fin pitch gives lower heat transfer coefficients when air velocity is increased.

Keywords: Dehumidifying conditions, Fin efficiency, Heat andmass transfer, Heat exchangers.

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Authors: Idris A. Elfeituri

Abstract:

This paper studies the effect of ambient conditions on the performance of a 285 MW gas turbine unit using the exergy concept. Based on the available exergy balance models developed, a computer program has been constructed to investigate the performance of the power plant under varying ambient temperature and relative humidity conditions. The variations of ambient temperature range from zero to 50 ºC and the relative humidity ranges from zero to 100%, while the unit load kept constant at 100% of the design load. The exergy destruction ratio and exergy efficiency are determined for each component and for the entire plant. The results show a moderate increase in the total exergy destruction ratio of the plant from 62.05% to 65.20%, while the overall exergy efficiency decrease from 38.2% to 34.8% as the ambient temperature increases from zero to 50 ºC at all relative humidity values. Furthermore, an increase of 1 ºC in ambient temperature leads to 0.063% increase in the total exergy destruction ratio and 0.07% decrease in the overall exergy efficiency. The relative humidity has a remarkable influence at higher ambient temperature values on the exergy destruction ratio of combustion chamber and on exergy loss ratio of the exhaust gas but almost no effect on the total exergy destruction ratio and overall exergy efficiency. At 50 ºC ambient temperature, the exergy destruction ratio of the combustion chamber increases from 30% to 52% while the exergy loss ratio of the exhaust gas decreases from 28% to 8% as the relative humidity increases from zero to 100%. In addition, exergy analysis reveals that the combustion chamber and exhaust gas are the main source of irreversibility in the gas turbine unit. It is also identified that the exergy efficiency and exergy destruction ratio are considerably dependent on the variations in the ambient air temperature and relative humidity. Therefore, the incorporation of the existing gas turbine plant with inlet air cooling and humidifier technologies should be considered seriously.

Keywords: Destruction, exergy, gas turbine, irreversibility, performance.

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Authors: M. Pierens, J.-P. Thermeau, T. Le Pollès, P. Duthil

Abstract:

The performances of a thermoacoustic travelling-wave refrigerator are presented. Developed in the frame of the European project called THATEA, it is designed for providing 600 W at a temperature of 233 K with an efficiency of 40 % relative to the Carnot efficiency. This paper presents the device and the results of the first measurements. For a cooling power of 210 W, a coefficient of performance relative to Carnot of 30 % is achieved when the refrigerator is coupled with an existing standing-wave engine.

Keywords: Refrigeration, sustainable energy, thermoacoustics, travelling-wave type heat pump

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Authors: A. Naamane, M. Hasnaoui

Abstract:

Numerical modeling of fluid flows, whether compressible or incompressible, laminar or turbulent presents a considerable contribution in the scientific and industrial fields. However, the development of an approximate model of a supersonic flow requires the introduction of specific and more precise techniques and methods. For this purpose, the object of this paper is modeling a supersonic flow of inviscid fluid around a dihedral airfoil. Based on the thin airfoils theory and the non-dimensional stationary Steichen equation of a two-dimensional supersonic flow in isentropic evolution, we obtained a solution for the downstream velocity potential of the oblique shock at the second order of relative thickness that characterizes a perturbation parameter. This result has been dealt with by the asymptotic analysis and characteristics method. In order to validate our model, the results are discussed in comparison with theoretical and experimental results. Indeed, firstly, the comparison of the results of our model has shown that they are quantitatively acceptable compared to the existing theoretical results. Finally, an experimental study was conducted using the AF300 supersonic wind tunnel. In this experiment, we have considered the incident upstream Mach number over a symmetrical dihedral airfoil wing. The comparison of the different Mach number downstream results of our model with those of the existing theoretical data (relative margin between 0.07% and 4%) and with experimental results (concordance for a deflection angle between 1° and 11°) support the validation of our model with accuracy.

Keywords: Asymptotic modelling, dihedral airfoil, supersonic flow, supersonic wind tunnel.

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

Abstract:

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In statistics parameter theory, usually the parameter estimations have two kinds, one is the least-square estimation (LSE), and the other is the best linear unbiased estimation (BLUE). Due to the determining theorem of minimum variance unbiased estimator (MVUE), the parameter estimation of BLUE in linear model is most ideal. But since the calculations are complicated or the covariance is not given, people are hardly to get the solution. Therefore, people prefer to use LSE rather than BLUE. And this substitution will take some losses. To quantize the losses, many scholars have presented many kinds of different relative efficiencies in different views. For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds.

Keywords: Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.

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Authors: Qianhong Zhang, Wenzhuan Zhang

Abstract:

This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.

Keywords: Difference equations, stability, unstable, global asymptotic behavior.

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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Authors: Xin Luo, Jin Huang, Pan Cheng

Abstract:

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

Keywords: Stokes problem, boundary integral equation, mechanical quadrature methods, asymptotic expansions.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: Barenten Suciu, Akio Miyamura

Abstract:

In this paper, following the study-case of an inclined plane gravitational machine, efficiency of a double-cone gravitational motor and generator is evaluated. Two types of efficiency ratios, called translational efficiency and rotational efficiency, are defined relative to the intended duty of the gravitational machine, which can be either the production of translational kinetic energy, or rotational kinetic energy. One proved that, for pure rolling movement of the double- cone, in the absence of rolling friction, the total mechanical energy is conserved. In such circumstances, as the motion of the double-cone progresses along rails, the translational efficiency decreases and the rotational efficiency increases, in such way that sum of the rotational and translational efficiencies remains unchanged and equal to 1. Results obtained allow a comparison of the gravitational machine with other types of motor-generators, in terms of the achievable efficiency.

Keywords: Truncated double-cone, friction, rolling and sliding, efficiency, gravitational motor and generator.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

Abstract:

In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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Authors: Young Hee Geum

Abstract:

We propose the numerical method defined by

xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N,

and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: Asymptotic error constant, iterative method , multiple root, root-finding.

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Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

Abstract:

In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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Authors: Alessandro Barbiero

Abstract:

In this paper some procedures for building confidence intervals for the reliability in stress-strength models are discussed and empirically compared. The particular case of a bivariate normal setup is considered. The confidence intervals suggested are obtained employing approximations or asymptotic properties of maximum likelihood estimators. The coverage and the precision of these intervals are empirically checked through a simulation study. An application to real paired data is also provided.

Keywords: Approximate estimators, asymptotic theory, confidence interval, Monte Carlo simulations, stress-strength, variance estimation.

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Authors: Andrey V. Timofeev, Dmitry V. Egorov

Abstract:

The practical efficient approach is suggested for estimation of the seismoacoustic sources energy in C-OTDR monitoring systems. This approach is represents the sequential plan for confidence estimation both the seismoacoustic sources energy, as well the absorption coefficient of the soil. The sequential plan delivers the non-asymptotic guaranteed accuracy of obtained estimates in the form of non-asymptotic confidence regions with prescribed sizes. These confidence regions are valid for a finite sample size when the distributions of the observations are unknown. Thus, suggested estimates are non-asymptotic and nonparametric, and also these estimates guarantee the prescribed estimation accuracy in form of prior prescribed size of confidence regions, and prescribed confidence coefficient value.

Keywords: C-OTDR-system, guaranteed estimates, nonparametric estimation, sequential confidence estimation, multichannel monitoring systems.

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Authors: Alexander Y. Vaninsky

Abstract:

This paper presents a simplified version of Data Envelopment Analysis (DEA) - a conventional approach to evaluating the performance and ranking of competitive objects characterized by two groups of factors acting in opposite directions: inputs and outputs. DEA with a Perfect Object (DEA PO) augments the group of actual objects with a virtual Perfect Object - the one having greatest outputs and smallest inputs. It allows for obtaining an explicit analytical solution and making a step to an absolute efficiency. This paper develops this approach further and introduces a DEA model with Partially Perfect Objects. DEA PPO consecutively eliminates the smallest relative inputs or greatest relative outputs, and applies DEA PO to the reduced collections of indicators. The partial efficiency scores are combined to get the weighted efficiency score. The computational scheme remains simple, like that of DEA PO, but the advantage of the DEA PPO is taking into account all of the inputs and outputs for each actual object. Firm evaluation is considered as an example.

Keywords: Data Envelopment Analysis, Perfect object, Partially perfect object, Partial efficiency, Explicit solution, Simplified algorithm.

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Authors: Abdenour Bourabaa, Malika Fekih, Mohamed Saighi

Abstract:

A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.

Keywords: Annular fin, Dehumidification, Fin efficiency, Heat and mass transfer, Wet fin.

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Authors: Artem Nuriev, Olga Zaitseva

Abstract:

This paper is devoted to the study of a viscous incompressible flow around a circular cylinder performing harmonic oscillations, especially the steady streaming phenomenon. The research methodology is based on the asymptotic explanation method combined with the computational bifurcation analysis. The research approach develops Schlichting and Wang decomposition method. Present studies allow to identify several regimes of the secondary streaming with different flow structures. The results of the research are in good agreement with experimental and numerical simulation data.

Keywords: Oscillating cylinder, Secondary Streaming, Flow Regimes, Asymptotic and Bifurcation Analysis.

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