Volume 3, Issue 1

Sea levels generally oscillate with multi-decadal periodicities worldwide with up to the quasi-60 years detected in many tide gauges. Nevertheless, the most part of the literature on sea levels computes apparent rates of rise of sea levels much larger than the legitimate by using short time windows in selected locations only covering part of a valley-to-peak of this multi-decadal oscillation. It is shown in this paper that along the Pacific coast of Australia the sea levels oscillate with a frequency close to the Southern Ocean Index (SOI) oscillation of 19 years and a lower frequency of about 60 years. The rates of rise of sea levels computed by linear fitting of the data recorded since the early 1990s in selected locations of the Australian Pacific coastline and in the tropical Pacific islands are from a valley of the peak and valley oscillations and are much higher than the legitimate long term values.

In this article, the authors introduce a fractional order SIR model with constant vaccination rate. The SIR model has been used in the modeling of several epidemiological diseases, biology and medical sciences. Qualitative results show that the model has two equilibria; the disease free equilibrium and the endemic equilibrium points. The local stability of the model for fractional order time derivative is analyzed using fractional Routh-Hurwitz stability criterion. The fractional derivative is described in Caputo sense. The results obtained through numerical procedure show that the method is effective and reliable.

In this paper we find the solution of time fractional discrete Navier-Stokes equation using Adomian decomposition method. Here we discretize the space domain. The graphical representation of solution given by using Matlab software, and it compared with exact solution for alpha = 1.

The similarity solution for the steady stagnation flow towards an off-centered rotating disc is gives a systemof non-linear partial differential equations. These nonlinear differential equations are numerically solved by applyingwell known Keller-Box Method. After finding the velocity distributions, the important designing subject, entropy generation of this system has been analyzed. Graphical results are presented to investigate effects of the rotation ratio α, off-centering, Reynolds number and axial height on the radial and azimuthal velocities and entropy generation. In order to show the effectiveness of the Keller- Box method, the obtained results are compared with available solutions obtained using DTM. The obtained results demonstrate the reliability of the algorithm and the Keller- Box method is an attractive method in solving the systems of nonlinear partial differential equations, and also the entropy generation is an important parameter depends on design andwork conditions that should be in the attention of designers of these rotating systems.

In this paper, we present a numerical algorithm based on new homotopy perturbation transform method (HPTM) to solve a time-fractional nonlinear shock wave equation which describes the flow of gases. The fractional derivative is considered in the Caputo sense. The HPTM is combined form of Laplace transform, homotopy perturbation method and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient, easy to implement and computationally very attractive.

While sea levels are known to oscillate with multi-decadal periodicities worldwide up to quasi-60 years, the most part of the literature on sea levels computes apparent rates of rise of sea levels much larger than the legitimate by using short time windows covering only part of a valleyto- peak quasi-60 year multi-decadal oscillation. It is shown that along the North Atlantic coast of the United States the sea levels oscillate closely to the AMO index, and the rate of rise of sea levels computed by linear fitting of the last 30-36 years of data is much higher than the true value. It is also shown that similar minimum requirement of 60 years of recording is needed along the North Pacific coast of the US, where the longer periodicity of the oscillations is not clearly defined; possibly for the strong ENSO signal covering a quasi-60 years oscillation.