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Introduction To Perturbation Techniques

Micro and nanoelectromechanical systems M/NEMS have been extensively investigated and exploited in the past few decades for various applications and for probing fundamental physical phenomena. Understanding the linear and nonlinear dynamical behaviors of the movable structures in these systems is crucial for their successful implementation in various novel technologies and to meet the long list of new sophisticated requirements. This paper presents a review for some of the recent topics pertaining to the dynamical behaviors, linear and nonlinear, of M/NEMS resonating structures. First, an overview is presented of the various used dynamical approaches to enhance the sensitivity of resonators for sensing applications. Then a summary is presented of the recent works on the linear and nonlinear mode coupling in M/NEMS resonator. Next, recent research is reviewed on coupled M/NEMS resonators, mechanically and electrically, leading to collective behaviors like mode localization. The final part of the paper discusses analytical approaches that have been developed to better understand and investigate the dynamical behavior of M/NEMS resonators focusing on the perturbation method the multiple time scales.

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Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Nonlinear harmonic vibration of a micro-electro-mechanical beam is investigated, and the micro-actuator, which is considered in this study, is a special kind of electrostatic symmetric actuators. A fully clamped micro-beam with a uniform thickness is modeled as an electrostatic micro-actuator with two symmetric potential walls. The nonlinear forced vibration of the micro-beam is analyzed, and the non-dimensional governing equation of motion, using the Galerkin method, is developed. Higher-order nonlinear terms in the equation of motion are taken into account for the first time, and the perturbation method is utilized regarding these terms and hence, all the resonant cases have been considered. The multiple scales method is employed to solve the nonlinear equations, and therefore, the problem does not deal with the large deformations. The primary and secondary resonance conditions are determined, and the corresponding secular terms in each case are recognized. Harmonic responses are obtained for different cases of resonance, and eventually, the stable and unstable portions of the responses are identified. A parametric sensitivity study is carried out to examine the effects of different parameters on the amplitude–frequency characteristic equations.

Primary and secondary resonance analyses of clamped–clamped micro-beams

In this paper, an automatic diagnosis system based on Neural Network for hepatitis virus is introduced. This automatic diagnosis system deals with the mixture of feature extraction and classification. The system has two stages, which are feature extraction – reduction and classification stages. In the feature extraction – diminution stage, the hepatitis features were obtained from UCI Repository of Machine Learning Databases. Missing values of the instances are adjusted using local mean method. Then, the number of these features was reduced to 6 from 19 due to relative significance of fields. In the classification stage, these reduced features are given as inputs Neural Network classifier. The classification accuracy of this ANN diagnosis system for the diagnosis of hepatitis virus was obtained, this accuracy was around 99.1% for training data and 100% for testing data. General Terms Data Mining

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PCA-ANN for Classification of Hepatitis-C Patients

In this paper, we scrutinize factors that dole out significantly to augmenting the risk of hepatitis-C virus. The dataset has been taken from the machine learning warehouse of University of California. It contains nineteen features along with a class feature having binary classification. There is a total of 15 binary attributes together with a class attribute and 5 continuous attributes. The dataset contains 155 records. In order to prevail over the missing values problem, data normalization techniques are applied. First, the dimension of the problem is trimmed down. Next binary logistic regression is applied to classify the cases by using qualitative and quantitative approaches for data reduction. The three stage procedure has produced more than 89% accurate classification. Our proposed approach has a low feature complexity with a good classification rate as it is working by using only 37% of the total fields.

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Hepatitis-C Classification using Data Mining Techniques

Hepatitis C virus (HCV) is one of the leading known causes of liver disease in the world. The HCV is a single-stranded RNA virus. The genomes of HCV display significant sequence heterogeneity and have been classified into types and subtypes. Types from 1 to 11 have so far been recognized, each type having a variable number of subtypes. It has been confirmed that 90% approximately of the isolates HCV infections in Egypt belong to a single subtype (4a) [10]. In this paper, we construct a mathematical model to study the spread of HCV-subtype 4a amongst the Egyptian population. The relation between HCV-subtype 4a and the other subtypes has also been studied. The values of reproduction numbers R01, R02 have been derived [5]. Also, threshold conditions for the value of the transmission rates k1 and k02, in terms of R01, R02 and the mutation factor μ have been determined to insure that the disease will die out. If the conditions fail to happen the disease takes off and becomes endemic.

/pdf/modelling-the-hepatitis-c-with-different-types-of-virus-33r883puub.pdf

Modelling the hepatitis C with different types of virus genome.

This study is focused on the numerical solutions of the nonlinear Volterra-Fredholm integral equations (NV-FIEs) of the second kind, which have several applications in physical mathematics and contact problems. Herein, we develop a new technique that combines the modified Adomian decomposition method and the quadrature (trapezoidal and Weddle) rules that used when the definite integral could be extremely difficult, for approximating the solutions of the NV-FIEs of second kind with a phase lag. Foremost, Picard's method and Banach's fixed point theorem are implemented to discuss the existence and uniqueness of the solution. Furthermore, numerical examples are presented to highlight the proposed method's effectiveness, wherein the results are displayed in group of tables and figures to illustrate the applicability of the theoretical results.

Correction: Numerical solutions for nonlinear Volterra-Fredholm integral equations of the second kind with a phase lag

Abstract In this paper, we study the behaviour of the maximum ( Max.) and minimum (Min.) error for Fredholm-Volterra integral equations (F-VIEs) of the second kind using Collocation (CM) and Galerkin (GM) methods by choosing N-linearly independent functions. The approximate solution is obtained by two techniques; the first technique (1st TM) depends on representing F-VIE as a system of Fredholm integral equations (FIEs) of the second kind where the approximate (Appr.) solution is obtained as functions of x at fixed times. In the second technique (2nd TM), we represent the approximate solution as a sum of functions of x and t. Furthermore, the comparisons between the results which are obtained by two techniques in each method are devoted and the results are represented in group of figures and tables.

The behaviour of the maximum and minimum error for Fredholm-Volterra integral equations in two-dimensional space

This paper presents a simplied mathematical model for the purpose of studying the resonant responses of a nonlinear dynamical system, (micro - electro - mechanical systems (MEMS)), which represented by a Van-der Pol equation subjected to a weakly non-linear parametric and forcing excitations. Using Multiple scales method, the Van-der Pol equation is transformed to a system of second order dierential equation up to rst order of small parameter ". Three types of resonances are studied (harmonic resonance and subharmonic resonances of even order (one half and one - fourth )). The modulation equations for each resonances, steady state solutions, frequency-response equations, stability analysis are determined. Numerical analysis for frequency-response equations and stability conditions are carried out. Results are presented graphically by group of gures. Finally discussion for these gures

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Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations

Electrostatic micro-electro-mechanical system (MEMS) is a special branch with a wide range of applications in sensing and actuating devices in MEMS. In this paper the perturbation analysis of the electrostatically actuated MEMS resonant sensors which represented by a modifled Du‐ng - Van der Pol equation subjected to weakly non-linear parametric and external excitations is studied by using a perturbation technique (multiple time scales). Harmonic resonance and subharmonic resonances of order ( 1 and 1 ) are investigated. For each resonances we obtain the modulation equations in the amplitude and phase, steady state solutions, frequency-response equations and stability conditions are determined. Efiects of difierent parameters on the system behavior are investigated numerically. Results are presented graphically and discussion is provided.

/pdf/perturbation-analysis-of-an-electrostatic-micro-electro-axi7ieg5y2.pdf

Gamal A. Mosa

Papers

Modelling the hepatitis C with different types of virus genome.

Correction: Numerical solutions for nonlinear Volterra-Fredholm integral equations of the second kind with a phase lag

The behaviour of the maximum and minimum error for Fredholm-Volterra integral equations in two-dimensional space

Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations

Perturbation analysis of an electrostatic Micro-Electro-Mechanical System (MEMS) subjected to external and non-linear parametric excitations