Computational Sciences and Engineering
Volume:1 Issue: 2, Summer 2021

A new version of the integrable (2+1)-dimensional Hirota–Satsuma–Ito (2D-HSI) equation is studied in the present paper. The analysis is conducted systematically by considering the bilinear form of the new integrable 2D-HSI equation and utilizing different approaches. As a consequence, a number of multiple complex and real soliton solutions to the model are formally constructed. The findings can be useful to deeply understand the dynamical features of multiple-soliton solutions in mathematical physics.

In this article, a new powerful analytical method, the Tamimi-Ansari method (TAM), has been introduced to solve some nonlinear problems that have been used in physics. This method does not require any hypothesis to counter with the nonlinear term. These results are compared with the exact solution and two other analytical methods. A few examples have been presented to show that this method is effective and reliable.

The internet of things is an emerging paradigm that will change the way we interact with objects and computers in the future. It envisions a global network of devices interacting with each other, over the internet, to perform a useful action. Firstly, we provided the overview of the internet of things and then the relevant technologies that can help in large-scale development of internet of things, then the security issues in internet of things and its challenging. Secondly, we analyzed some of the lightweight authentication protocol in internet of things based on different techniques such as RFID authentication and continuous authentication to evaluate their vulnerability. Finally, we proposed the solution for one of RFID authentication protocol by using physically unclonable functions. In this protocol, the valid authentication time period is proposed to enhance robustness of authentication between internet of things devices and used the authentication token to authenticate the message which transmits from sensor node to the gateway and at the end the security analysis is conducted to evaluate the security strength of the proposed protocol.

Presented herein is an investigation on the vibrational response of fractional viscoelastic carbon nanotubes (CNTs) conveying fluid and resting on a fractional viscoelastic foundation. The CNTs are modeled according to the Euler-Bernoulli beam theory, and the foundation is considered to be Winkler-type. Also, to incorporate the nanoscale effect into the model, Eringen’s nonlocal elasticity is applied. Derivation of governing equation is done by a variational principle together with the Kelvin-Voigt viscoelastic model. Two solution approaches are developed for obtaining the time response of embedded fluid-conveying CNTs. The first approach is on the basis of Galerkin’s method, while the GDQM and FDM are used in the second approach. Comprehensive numerical results are given to study the effects of elastic foundation, fractional order, damping, fluid, nonlocal parameter, geometrical properties and viscoelasticity coefficient on the time responses of CNTs subject to different boundary conditions.

In this paper, unsteady thermal scrutiny of radiative-convective moving fin considering the influences of magnetic field and time-dependent boundary conditions is explored via Laplace transform method. The analytical solutions obtained are employed in the investigation of the impacts of Hartmann number, Peclet number, radiative and convective parameters on the transient thermal performance and effectiveness in the moving fin. The research outcomes establish that an increase in convective and porosity terms generates a corresponding increase in the fin’s heat transfer rate. This consequently augments the fin’s efficiency. Correspondingly, an increase in increases the magnitude of temperature distribution within the fin. It is also found that increasing the results in an increase in material mobility rate. Meanwhile, the exposure period of the material to its surrounding environmental conditions diminishes while fin losses more surface heat, hence the temperature of the fin intensifies. Finally, an increase in the fin’s internal heat generation and thermal conductivity reduces heat transfer rate. Thus, the controlling terms of the fin during operation should be prudently selected to make sure that it retains its principal function of heat removal from the main surface.

The elastic modulus and Poisson’s ratio of polymer matrix nanocomposites (PMNCs) filled with graphene nanoplatelets (GNPs) are determined using an analytical micromechanical model. It is assumed that the GNPs are uniformly dispersed and randomly oriented into the polymer matrix. Due to the folded and wrinkled structure of GNPs, the effect of their flatness ratio on the elastic properties is investigated. Moreover, the micromechanical model captures the creation of interfacial region between the graphene and polymer matrix. The results show that addition of graphene particles into the polymer matrix can enhance the nanocomposite elastic modulus. Poisson’s ratio of polymer matrix increases with the increase of graphene content. It is observed that the elastic properties are decreased by the GNP non-flatness structure. Also, the material and dimensional characteristics of interfacial region affects the elastic modulus and Poisson’s ratio of GNP-reinforced PMNCs. The model predictions agree very well with the experimental data.

The developments of approximate analytical solutions to nonlinear differential equations have been achieved through the use of various approximate analytical and semi-analytical methods. These methods provide different analytical expressions which give difference values for the same input data and variables. However, under some certain conditions, the methods provide similar analytical expressions, thereby give the same values for the same input data and variables. Therefore, in this work, the conditions of similar analytical solutions by homotopy perturbation, differential transformation and Taylor series methods for linear and nonlinear differential equations are investigated. From the analysis, it is established that if some specific values or functions are assigned to the auxiliary parameters in the homotopy perturbation method, the approximate analytical solutions provided by homotopy perturbation method is entirely similar to the approximate analytical solutions given by differential transformation and Taylor series methods. Also, it is found that the results of Taylor series method when expansion is at the center, is exactly the same to the results of homotopy perturbation and differential transformation methods. It is hoped that this work will great assist and enhance the understanding of mathematical solutions providers and enthusiasts as it provides better insight into finding analytical solutions to linear and nonlinear differential equations.