Search results for: Poisson's ratio

Authors: S. K. Bhullar, J. Ko, F. Ahmed, M. B. G. Jun

Abstract:

The negative Poisson’s ratios can be described in terms of models based on the geometry of the system and the way this geometry changes due to applied loads. As the Poisson’s ratio does not depend on scale hence deformation can take place at the nano to macro level the only requirement is the right combination of the geometry. Our thrust in this paper is to combine our knowledge of tailored enhanced mechanical properties of the materials having negative Poisson’s ratio with the micromachining and electrospining technology to develop a novel stent carrying a drug delivery system. Therefore, the objective of this paper includes (i) fabrication of a micromachined metal sheet tailored with structure having negative Poisson’s ratio through rotating solid squares geometry using femtosecond laser ablation; (ii) rolling fabricated structure and welding to make a tubular structure (iii) wrapping it with nanofibers of biocompatible polymer PCL (polycaprolactone) for drug delivery (iv) analysis of the functional and mechanical performance of fabricated structure analytically and experimentally. Further, as the applications concerned, tubular structures have potential in biomedical for example hollow tubes called stents are placed inside to provide mechanical support to a damaged artery or diseased region and to open a blocked esophagus thus allowing feeding capacity and improving quality of life.

Keywords: Micromachining, electrospining, auxetic materials, enhanced mechanical properties.

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Authors: Tatheer Zahra

Abstract:

Auxetic materials have counteractive properties due to re-entrant geometry that enables them to possess Negative Poisson’s Ratio (NPR). These materials have better energy absorbing and shock resistance capabilities as compared to conventional positive Poisson’s ratio materials. The re-entrant geometry can be created through 3D printing for convenient application of these materials. This paper investigates the mechanical properties of 3D printed chiral auxetic geometries of various sizes. Small scale samples were printed using an ordinary 3D printer and were tested under compression and tension to ascertain their strength and deformation characteristics. A maximum NPR of -9 was obtained under compression and tension. The re-entrant chiral cell size has been shown to affect the mechanical properties of the re-entrant chiral auxetics.

Keywords: Auxetic materials, 3D printing, Negative Poisson’s Ratio, re-entrant chiral auxetics.

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Authors: Chongyang Ye, Rong Liu

Abstract:

Compression textiles such as compression stockings (CSs) have been extensively applied for the prevention and treatment of chronic venous insufficiency of lower extremities. The involvement of multiple mechanical factors such as interface pressure, frictional force, and elastic materials make the interactions between lower limb and CSs to be complex. Determination of Poisson’s ratio and elastic moduli of CS materials are critical for constructing finite element (FE) modeling to numerically simulate a complex interactive system of CS and lower limb. In this study, a mixed approach, including an analytic model based on the orthotropic Hooke’s Law and experimental study (uniaxial tension testing and pure shear testing), has been proposed to determine Young’s modulus, Poisson’s ratio, and shear modulus of CS fabrics. The results indicated a linear relationship existing between the stress and strain properties of the studied CS samples under controlled stretch ratios (< 100%). The proposed method and the determined key mechanical properties of elastic orthotropic CS fabrics facilitate FE modeling for analyzing in-depth the effects of compression material design on their resultant biomechanical function in compression therapy.

Keywords: Elastic compression stockings, Young’s modulus, Poisson’s ratio, shear modulus, mechanical analysis.

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Authors: S. B. Mansuri

Abstract:

In this paper, at first we explain about negative hypergeometric distribution and its properties. Then we use the w-function and the Stein identity to give a result on the poisson approximation to the negative hypergeometric distribution in terms of the total variation distance between the negative hypergeometric and poisson distributions and its upper bound.

Keywords: Negative hypergeometric distribution, Poisson distribution, Poisson approximation, Stein-Chen identity, w-function.

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Authors: Sheng-Shu Cheng, Fong-Jung Yu

Abstract:

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for process control at this time. A cumulative sum (CUSUM) control chart is much better than a C control chart when a small shift will be detected. This study calculates one-sided CUSUM ARLs using a Markov chain approach to construct a CUSUM control chart with an underlying Poisson-Gamma compound distribution for the failure mechanism. Moreover, an actual data set from a wafer plant is used to demonstrate the operation of the proposed model. The results show that a CUSUM control chart realizes significantly better performance than EWMA.

Keywords: Nonconformities, Compound Poisson distribution, CUSUM control chart.

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Authors: N. A. Samat, S. H. Mohd Imam Ma’arof

Abstract:

Dengue disease is an infectious vector-borne viral disease that is commonly found in tropical and sub-tropical regions, especially in urban and semi-urban areas, around the world and including Malaysia. There is no currently available vaccine or chemotherapy for the prevention or treatment of dengue disease. Therefore prevention and treatment of the disease depend on vector surveillance and control measures. Disease risk mapping has been recognized as an important tool in the prevention and control strategies for diseases. The choice of statistical model used for relative risk estimation is important as a good model will subsequently produce a good disease risk map. Therefore, the aim of this study is to estimate the relative risk for dengue disease based initially on the most common statistic used in disease mapping called Standardized Morbidity Ratio (SMR) and one of the earliest applications of Bayesian methodology called Poisson-gamma model. This paper begins by providing a review of the SMR method, which we then apply to dengue data of Perak, Malaysia. We then fit an extension of the SMR method, which is the Poisson-gamma model. Both results are displayed and compared using graph, tables and maps. Results of the analysis shows that the latter method gives a better relative risk estimates compared with using the SMR. The Poisson-gamma model has been demonstrated can overcome the problem of SMR when there is no observed dengue cases in certain regions. However, covariate adjustment in this model is difficult and there is no possibility for allowing spatial correlation between risks in adjacent areas. The drawbacks of this model have motivated many researchers to propose other alternative methods for estimating the risk.

Keywords: Dengue disease, Disease mapping, Standardized Morbidity Ratio, Poisson-gamma model, Relative risk.

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Authors: Yusuke Uchiyama, Hidetoshi Konno

Abstract:

We have investigated statistical properties of the defect turbulence in 1D CGLE wherein many body interaction is involved between local depressing wave (LDW) and local standing wave (LSW). It is shown that the counting number fluctuation of LDW is subject to the sub-Poisson statistics (SUBP). The physical origin of the SUBP can be ascribed to pair extinction of LDWs based on the master equation approach. It is also shown that the probability density function (pdf) of inter-LDW distance can be identified by the hyper gamma distribution. Assuming a superstatistics of the exponential distribution (Poisson configuration), a plausible explanation is given. It is shown further that the pdf of amplitude of LDW has a fattail. The underlying mechanism of its fluctuation is examined by introducing a generalized fractional Poisson configuration.

Keywords: sub-Poisson statistics, hyper gamma distribution, fractional Poisson configuration.

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Authors: Vandna Jowaheer, Naushad A. Mamode Khan

Abstract:

Com Poisson distribution is capable of modeling the count responses irrespective of their mean variance relation and the parameters of this distribution when fitted to a simple cross sectional data can be efficiently estimated using maximum likelihood (ML) method. In the regression setup, however, ML estimation of the parameters of the Com Poisson based generalized linear model is computationally intensive. In this paper, we propose to use quasilikelihood (QL) approach to estimate the effect of the covariates on the Com Poisson counts and investigate the performance of this method with respect to the ML method. QL estimates are consistent and almost as efficient as ML estimates. The simulation studies show that the efficiency loss in the estimation of all the parameters using QL approach as compared to ML approach is quite negligible, whereas QL approach is lesser involving than ML approach.

Keywords: Com Poisson, Cross-sectional, Maximum Likelihood, Quasi likelihood

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Authors: Naushad Mamode Khan, Cheika Jahangeer, Maleika Heenaye-Mamode Khan

Abstract:

Exclusive breastfeeding is the feeding of a baby on no other milk apart from breast milk. Exclusive breastfeeding during the first 6 months of life is very important as it supports optimal growth and development during infancy and reduces the risk of obliterating diseases and problems. Moreover, it helps to reduce the incidence and/or severity of diarrhea, lower respiratory infection and urinary tract infection. In this paper, we make a survey of the factors that influence exclusive breastfeeding and use two dispersed statistical models to analyze data. The models are the Generalized Poisson regression model and the Com-Poisson regression models.

Keywords: Exclusive breastfeeding, regression model, generalized poisson, com-poisson.

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Authors: Alibek Issakhov

Abstract:

In this paper developed and realized absolutely new algorithm for solving three-dimensional Poisson equation. This equation used in research of turbulent mixing, computational fluid dynamics, atmospheric front, and ocean flows and so on. Moreover in the view of rising productivity of difficult calculation there was applied the most up-to-date and the most effective parallel programming technology - MPI in combination with OpenMP direction, that allows to realize problems with very large data content. Resulted products can be used in solving of important applications and fundamental problems in mathematics and physics.

Keywords: MPI, OpenMP, three dimensional Poisson equation

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Authors: Y. N. Phang, E. F. Loh

Abstract:

The zero inflated models are usually used in modeling count data with excess zeros where the existence of the excess zeros could be structural zeros or zeros which occur by chance. These type of data are commonly found in various disciplines such as finance, insurance, biomedical, econometrical, ecology, and health sciences which involve sex and health dental epidemiology. The most popular zero inflated models used by many researchers are zero inflated Poisson and zero inflated negative binomial models. In addition, zero inflated generalized Poisson and zero inflated double Poisson models are also discussed and found in some literature. Recently zero inflated inverse trinomial model and zero inflated strict arcsine models are advocated and proven to serve as alternative models in modeling overdispersed count data caused by excessive zeros and unobserved heterogeneity. The purpose of this paper is to review some related literature and provide a variety of examples from different disciplines in the application of zero inflated models. Different model selection methods used in model comparison are discussed.

Keywords: Overdispersed count data, model selection methods, likelihood ratio, AIC, BIC.

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Authors: M. S. Gaafar, S. Y. Marzouk

Abstract:

Sodium borosilicate glasses doped with different content of NdF3 mol % have been prepared by rapid quenching method. Ultrasonic velocities (both longitudinal and shear) measurements have been carried out at room temperature and at ultrasonic frequency of 4 MHz. Elastic moduli, Debye temperature, softening temperature and Poisson's ratio have been obtained as a function of NdF3 modifier content. Results showed that the elastic moduli, Debye temperature, softening temperature and Poisson's ratio have very slight change with the change of NdF3 mol % content. Based on FTIR spectroscopy and theoretical (Bond compression) model, quantitative analysis has been carried out in order to obtain more information about the structure of these glasses. The study indicated that the structure of these glasses is mainly composed of SiO4 units with four bridging oxygens (Q4), and with three bridging and one nonbridging oxygens (Q3).

Keywords: Borosilicate glasses, ultrasonic velocity, elastic moduli, FTIR spectroscopy, bond compression model.

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Authors: Pitsanu Tongkhow, Pichet Jiraprasertwong

Abstract:

This research investigates risk factors for defective products in autoparts factories. Under a Bayesian framework, a generalized linear mixed model (GLMM) in which the dependent variable, the number of defective products, has a Poisson distribution is adopted. Its performance is compared with the Poisson GLM under a Bayesian framework. The factors considered are production process, machines, and workers. The products coded RT50 are observed. The study found that the Poisson GLMM is more appropriate than the Poisson GLM. For the production Process factor, the highest risk of producing defective products is Process 1, for the Machine factor, the highest risk is Machine 5, and for the Worker factor, the highest risk is Worker 6.

Keywords: Defective autoparts products, Bayesian framework, Generalized linear mixed model (GLMM), Risk factors.

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Authors: Ou Xie, Zhenyu Zhao

Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle

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Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

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Authors: N. Mamode Khan, V. Jowaheer

Abstract:

Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observations as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use quasi-likelihood estimation approach to estimate the parameters of the model. Under-dispersion parameter is estimated to be 2.14 justifying the appropriateness of Com-Poisson distribution in modelling under-dispersed count responses recorded in this study.

Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, quasi-likelihood estimation

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: Explicit group iterative method, finite difference, fourth order compact, Poisson equation.

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Authors: Ezzatallah Baloui Jamkhaneh, Bahram Sadeghpour-Gildeh, Gholamhossein Yari

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This purpose of this paper is to present the acceptance single sampling plan when the fraction of nonconforming items is a fuzzy number and being modeled based on the fuzzy Poisson distribution. We have shown that the operating characteristic (oc) curves of the plan is like a band having a high and low bounds whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance numbers is fixed. Finally we completed discuss opinion by a numerical example. And then we compared the oc bands of using of binomial with the oc bands of using of Poisson distribution.

Keywords: Statistical quality control, acceptance single sampling, fuzzy number.

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Authors: Dezhi Liu

Abstract:

In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.

Keywords: Impulsive, stochastic, delay, Markovian switching, Poisson jumps, mean square stability.

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Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: Ruin probability, compound Poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions.

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Authors: Abdul Wasy, Balakrishnan G., Yi Qi Wang, Atta Ur Rehman, Jung Il Song

Abstract:

Vickers indentation is used to measure the hardness of materials. In this study, numerical simulation of Vickers indentation experiment was performed for Diamond like Carbon (DLC) coated materials. DLC coatings were deposited on stainless steel 304 substrates with Chromium buffer layer using RF Magnetron and T-shape Filtered Cathodic Vacuum Arc Dual system The objective of this research is to understand the elastic plastic properties, stress strain distribution, ring and lateral crack growth and propagation, penetration depth of indenter and delamination of coating from substrate with effect of buffer layer thickness. The effect of Poisson-s ratio of DLC coating was also analyzed. Indenter penetration is more in coated materials with thin buffer layer as compared to thicker one, under same conditions. Similarly, the specimens with thinner buffer layer failed quickly due to high residual stress as compared to the coated materials with reasonable thickness of 200nm buffer layer. The simulation results suggested the optimized thickness of 200 nm among the prepared specimens for durable and long service.

Keywords: Thin film, buffer layer. Diamond like Carbon, Vickers indentation, Poisson's ratio, Finite element.

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Authors: Kevin McDaid, Simon P. Wilson

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Software developed for a specific customer under contract typically undergoes a period of testing by the customer before acceptance. This is known as user acceptance testing and the process can reveal both defects in the system and requests for changes to the product. This paper uses nonhomogeneous Poisson processes to model a real user acceptance data set from a recently developed system. In particular a split Poisson process is shown to provide an excellent fit to the data. The paper explains how this model can be used to aid the allocation of resources through the accurate prediction of occurrences both during the acceptance testing phase and before this activity begins.

Keywords: User acceptance testing. Software reliability growth modelling. Split Poisson process. Bayesian methods.

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Authors: Shan Gao

Abstract:

In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

Keywords: Poisson process, generalized Erlang risk process, Gerber-Shiu function, generating function, generalized Lundberg equation.

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Authors: Y. N. Phang, E. F. Loh

Abstract:

Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling overdispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling overdispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling overdispered medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling overdispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling overdispersed medical count data when ZIP and ZINB are inadequate.

Keywords: Zero inflated, inverse trinomial distribution, Poisson inverse Gaussian distribution, strict arcsine distribution, Pearson’s goodness of fit.

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Authors: Minh Vuong Pham, Frédéric Plourde, Son Doan Kim

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A strip domain decomposition parallel algorithm for fast direct Poisson solver is presented on a 3D Cartesian staggered grid. The parallel algorithm follows the principles of sequential algorithm for fast direct Poisson solver. Both Dirichlet and Neumann boundary conditions are addressed. Several test cases are likewise addressed in order to shed light on accuracy and efficiency in the strip domain parallelization algorithm. Actually the current implementation shows a very high efficiency when dealing with a large grid mesh up to 3.6 * 10⁹ under massive parallel approach, which explicitly demonstrates that the proposed algorithm is ready for massive parallel computing.

Keywords: Strip-decomposition, parallelization, fast directpoisson solver.

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Authors: Jihad S. Daba, J. P. Dubois

Abstract:

Fading noise degrades the performance of cellular communication, most notably in femto- and pico-cells in 3G and 4G systems. When the wireless channel consists of a small number of scattering paths, the statistics of fading noise is not analytically tractable and poses a serious challenge to developing closed canonical forms that can be analysed and used in the design of efficient and optimal receivers. In this context, noise is multiplicative and is referred to as stochastically local fading. In many analytical investigation of multiplicative noise, the exponential or Gamma statistics are invoked. More recent advances by the author of this paper utilized a Poisson modulated-weighted generalized Laguerre polynomials with controlling parameters and uncorrelated noise assumptions. In this paper, we investigate the statistics of multidiversity stochastically local area fading channel when the channel consists of randomly distributed Rayleigh and Rician scattering centers with a coherent Nakagami-distributed line of sight component and an underlying doubly stochastic Poisson process driven by a lognormal intensity. These combined statistics form a unifying triply stochastic filtered marked Poisson point process model.

Keywords: Cellular communication, femto- and pico-cells, stochastically local area fading channel, triply stochastic filtered marked Poisson point process.

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Authors: Miloš Šeda, Pavel Ošmera, Jindřich Petrucha

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In the queueing theory, it is assumed that customer arrivals correspond to a Poisson process and service time has the exponential distribution. Using these assumptions, the behaviour of the queueing system can be described by means of Markov chains and it is possible to derive the characteristics of the system. In the paper, these theoretical approaches are presented on several types of systems and it is also shown how to compute the characteristics in a situation when these assumptions are not satisfied

Keywords: Queueing theory, Poisson process, Markov chains.

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Authors: N. Mamode Khan, V. Jowaheer

Abstract:

In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use the two types of quasi-likelihood estimation approaches to estimate the parameters of the model: marginal and joint generalized quasi-likelihood estimating equation approaches. Under-dispersion parameter is estimated to be around 2.14 justifying the appropriateness of Com-Poisson distribution in modelling underdispersed count responses recorded in this study.

Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, marginal quasi-likelihood estimation, joint quasi-likelihood estimation.

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Authors: Mokhtar Kouki Inès Rekik

Abstract:

This paper focuses on the assessment of the air pollution and morbidity relationship in Tunisia. Air pollution is measured by ozone air concentration and the morbidity is measured by the number of respiratory-related restricted activity days during the 2-week period prior to the interview. Socioeconomic data are also collected in order to adjust for any confounding covariates. Our sample is composed by 407 Tunisian respondents; 44.7% are women, the average age is 35.2, near 69% are living in a house built after 1980, and 27.8% have reported at least one day of respiratory-related restricted activity. The model consists on the regression of the number of respiratory-related restricted activity days on the air quality measure and the socioeconomic covariates. In order to correct for zero-inflation and heterogeneity, we estimate several models (Poisson, negative binomial, zero inflated Poisson, Poisson hurdle, negative binomial hurdle and finite mixture Poisson models). Bootstrapping and post-stratification techniques are used in order to correct for any sample bias. According to the Akaike information criteria, the hurdle negative binomial model has the greatest goodness of fit. The main result indicates that, after adjusting for socioeconomic data, the ozone concentration increases the probability of positive number of restricted activity days.

Keywords: Bootstrapping, hurdle negbin model, overdispersion, ozone concentration, respiratory-related restricted activity days.

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Authors: N. Katemee, T. Mayureesawan

Abstract:

This paper developed the c-Chart based on a Zero- Inflated Poisson (ZIP) processes that approximated by a geometric distribution with parameter p. The p estimated that fit for ZIP distribution used in calculated the mean, median, and variance of geometric distribution for constructed the c-Chart by three difference methods. For cg-Chart, developed c-Chart by used the mean and variance of the geometric distribution constructed control limits. For cmg-Chart, the mean used for constructed the control limits. The cme- Chart, developed control limits of c-Chart from median and variance values of geometric distribution. The performance of charts considered from the Average Run Length and Average Coverage Probability. We found that for an in-control process, the cg-Chart is superior for low level of mean at all level of proportion zero. For an out-of-control process, the cmg-Chart and cme-Chart are the best for mean = 2, 3 and 4 at all level of parameter.

Keywords: average coverage probability, average run length, geometric distribution, zero-inflated poisson distribution

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