Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure
Aydin Azizi,
Niloofar Malekzadeh Fard,
Hamed Mobki,
Adnène Arbi
Issue:
Volume 7, Issue 1-2, January 2018
Pages:
1-11
Received:
16 June 2017
Accepted:
19 June 2017
Published:
11 July 2017
DOI:
10.11648/j.acm.s.2018070102.11
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Abstract: This paper deals with the study of bifurcation behavior of a capacitive nano-beam considering electrostatic, Casimir and van der Waals forces. A modified mass-spring model has been implemented for analysis of the nano-beam behavior. The model has been adjusted and corrected with Euler-Bernoulli beam model, because of its less accuracy compared to distributed models. Fixed or equilibrium points of the nano-beam have been obtained, and has been shown that with variation of the applied voltage and the length of the nano-beam as control parameters the number of equilibrium points is changed. The stability of the fixed points has been investigated drawing motion trajectories in phase portraits and basins of attractions and repulsion have been illustrated. Critical values of the applied voltage and the length of the nano-beam leading to qualitative changes in the nano-beam behavior have been obtained.
Abstract: This paper deals with the study of bifurcation behavior of a capacitive nano-beam considering electrostatic, Casimir and van der Waals forces. A modified mass-spring model has been implemented for analysis of the nano-beam behavior. The model has been adjusted and corrected with Euler-Bernoulli beam model, because of its less accuracy compared to d...
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Analysis of Computer Virus Propagation Based on Compartmental Model
Pabel Shahrear,
Amit Kumar Chakraborty,
Md. Anowarul Islam,
Ummey Habiba
Issue:
Volume 7, Issue 1-2, January 2018
Pages:
12-21
Received:
25 June 2017
Accepted:
16 August 2017
Published:
6 September 2017
DOI:
10.11648/j.acm.s.2018070102.12
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Abstract: Computer viruses pose a considerable problem for users of personal computers. In order to effectively defend against a virus, this paper proposes a compartmental model SAEIQRS (Susceptible – Antidotal – Exposed - Infected – Quarantine - Recovered - Susceptible) of virus transmission in a computer network. The differential transformation method (DTM) is applied to obtain an improved solution of each compartment. We have achieved an accuracy of order O(h6) and validated the results of DTM with fourth-order Runge-Kutta (RK4) method. Based on the basic reproduction number, we analyzed the local stability of the model for virus free and endemic equilibria. Using a Lyapunov function, we demonstrated the global stability of virus free equilibria. Numerically the eigenvalues are computed using two different sets of parameter values and the corresponding dominant eigenvalues are determined by means of power method. Finally, we simulate the system in MATLAB. Based on the analysis, aspects of different compartments are investigated.
Abstract: Computer viruses pose a considerable problem for users of personal computers. In order to effectively defend against a virus, this paper proposes a compartmental model SAEIQRS (Susceptible – Antidotal – Exposed - Infected – Quarantine - Recovered - Susceptible) of virus transmission in a computer network. The differential transformation method (DTM...
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