Contact of Rough Surfaces With Asymmetric Distribution of Asperity Heights

2001 ◽  
Vol 124 (2) ◽  
pp. 367-376 ◽  
Author(s):  
Ning Yu ◽  
Andreas A. Polycarpou
Keyword(s):  
Weibull Distribution ◽  
Rough Surfaces ◽  
Closed Form Solution ◽  
Form Solution ◽  
Asymmetric Distribution ◽  
Exponential Distributions ◽  
Real Area Of Contact ◽  
Gaussian Case ◽  
Different Levels ◽  
Key Parameter

The Greenwood and Williamson (GW) statistical approach of characterizing rough surfaces is extended to include asymmetric distribution of asperity heights using the Weibull distribution. A key parameter that is used to characterize asymmetry is the skewness, and the corresponding Weibull parameters are investigated for a range of practical skewness values. The Weibull distribution is then adopted to model the asperity heights, and once normalized, is used to calculate the contact load, real area of contact and number of contacting asperities using the CEB elastic-plastic model of an equivalent rough surface in contact with a smooth plane. The effect of skewness on different levels of surface roughness, ranging from very smooth surfaces encountered in microtribological applications to rougher surfaces encountered in macrotribological applications is investigated, and also compared to the symmetric Gaussian case. Also, to allow for closed-form solution of the contact equations, simpler exponential distributions are curved-fitted to the contact side of the Weibull distribution, and the analytical results are favorably compared with the numerical results using the Weibull distribution.

Combining and Contacting of Two Rough Surfaces with Asymmetric Distribution of Asperity Heights

2004 ◽  
Vol 126 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Ning Yu ◽  
Andreas A. Polycarpou
Keyword(s):  
Standard Deviation ◽  
Weibull Distribution ◽  
Rough Surface ◽  
Rough Surfaces ◽  
Asymmetric Distribution ◽  
Magnetic Storage ◽  
Roughness Parameters ◽  
Practical Applications ◽  
Practical Engineering ◽  
Contour Plots

The statistical approach of describing rough surfaces is extended to include the contact of two rough surfaces in which their distribution of asperity heights can either be symmetric or asymmetric, and the asymmetry is modeled using the normalized Weibull distribution. In considering the contact between two rough surfaces, as in most practical applications, the contact can be approximated by an equivalent rough surface in contact with a smooth plane. The roughness parameters of the equivalent surface are obtained using the spectral moment method, and its validity is verified using realistic surface roughness measurements. This paper presents a method to obtain the equivalent rough surface with a Weibull distribution of asperity heights, in which the standard deviation and skewness parameters of asperity heights of the actual contacting surfaces are preserved. The advantages of this method are demonstrated via direct comparisons with a previously proposed method as well as with exact numerical simulation of the contact parameters of several different actual surfaces from magnetic storage and MEMS applications. For practical engineering applications, where the roughness parameters of each individual surface are known, contour plots for the skewness value of the equivalent rough surface are provided for practical ranges of combinations of standard deviation ratios and skewness values. As expected when the roughness of one of the contacting surfaces dominates, the skewness is solely determined by the rougher surface.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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