Volume 14, Issue 2 -

In this paper, the Laplace transform Variational Iteration Method (LVIM) is employed to obtain approximate analytical solutions of the linear and nonlinear partial differential equations. This method is a combined form of the Laplace transform method and the Variational Iteration Method. The proposed scheme, finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. Some illustrative examples are presented and the numerical results show that the solutions of the LVIM are in good agreement with the exact solution.

Cyanotoxins, a kind of poisonous substances produced by cianobacteria, are responsibles for health risks in surface waters used for drinking or for recreation. As a result, anticipate its presence is a matter of importance to prevent risks. The aim of this study is to build a regression model for predicting cyanotoxin presence in the Trasona reservoir (Northern Spain). Some biological parameters related to cyanobacteria and ciantoxin by production are mesasured and the support vector machine (SVM) technique at local scale is applied with success. The results obtained are two-fold. Firstly, the significance of each kind of cyanobacteria on the cyanotoxins presence in the reservoir has been determined, showing the existence of a synergistic behaviour between two species of cyanobacteria. Finally, a predictive model able to forecast the possible presence of cyanotoxins in a short term was obtained.

An SEIR epidemic model with constant immigration and random fluctuation around the endemic equilibrium is considered. As a special case, a deterministic system discussed by Li et al. will be incorporated into the stochastic version given by us. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of the basic reproduction number ℛ 0 . By means of Lyapunov functions we give sufficient conditions for globally stochastically asymptotic stability of the unique positive endemic equilibrium. When ℛ 0  > 1, under the sufficient conditions, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average, the disease will prevail and the infected fraction persists. Numerical simulations support our analytical conclusions and show the effect of intensity of white noise on stability of the system.

A numerical and experimental analysis of sloshing phenomena (i.e. violent fluid motions inside a tank) has been conducted in shallow water regimes. A narrow tank has been used to limit three-dimensional effects and allow for an extensive study of two-dimensional waves. A large range of experimental data from small to large amplitude sway motions has been considered for five different filling heights. The numerical simulations have been performed to cover the configurations where no experiments were available and provide an exhaustive description of the shallow-water sloshing motion. Specifically, the numerical simulations have been performed through a δ -SPH model since such a scheme proved to be robust and reliable in studying violent free-surface flows.

An efficient Eulerian method for poly-dispersed particles in turbulent flows is implemented, verified and validated for a channel flow. The approach couples a mixture model with a quadrature-based moment method for the particle size distribution in a LES framework, augmented by an approximate deconvolution method to reconstructs the unfiltered velocity. The particle velocity conditioned on particle size is calculated with an equilibrium model, valid for low Stokes numbers. A population balance equation is solved with the direct quadrature method of moments, that efficiently represents the continuous particle size distribution. In this first study particulate processes are not considered and the capability of the model to properly describe particle transport is investigated for a turbulent channel flow. First, single-phase LES are validated through comparison with DNS. Then predictions for the two-phase system, with particles characterised by Stokes numbers ranging from 0.2 to 5, are compared with Lagrangian DNS in terms of particle velocity and accumulation at the walls. Since this phenomenon (turbophoresis) is driven by turbulent fluctuations and depends strongly on the particle Stokes number, the approximation of the particle size distribution, the choice of the sub-grid scale model and the use of an approximate deconvolution method are important to obtain good results. Our method can be considered as a fast and efficient alternative to classical Lagrangian methods or Eulerian multi-fluid models in which poly-dispersity is usually neglected.