This paper presents a new effective radial basis function (RBF) collocation technique for the free vibration analysis of laminated composite plates using the first order shear deformation theory (FSDT). The plates, which can be rectangular or non-rectangular, are simply discretised by means of Cartesian grids. Instead of using conventional differentiated RBF networks, onedimensional integrated RBF networks (1D-IRBFN) are employed on grid lines to approximate the field variables. A number of examples concerning various thickness-to-span ratios, material properties and boundary conditions are considered. Results obtained are compared with the exact solutions and numerical results by other techniques in the literature to investigate the performance of the proposed method.

Artificial Neural Network (ANN) approaches were used to model and predict water trading prices in the Murry Irrigation area, Australia. • Prices forecast using hybrid ANN-Bayesian modelling showed greater agreement with actual water prices. • Water security allocations, cereal and meat prices were significant determinants of future water trading prices.

Turbulence and mechanical flotation cells have been the workhorse of the mining industry to process the high tonnage but low-grade ores for more than a century. However, our quantitative understanding of the effect of turbulence on flotation is still limited. Here we theoretically investigate the bubble-particle collision in flotation in homogeneous isotropic turbulence using the correlation method. We show a novel paradigm that isotropic turbulence can surpass gravity in affecting bubble-particle collision in flotation. Specifically, motions of particles of micrometer sizes and bubbles of millimeter sizes are described using the Basset-Boussinesq-Oseen equation.The drag forces on particles and bubbles are calculated using Stokes' law with a particle-size correction factor and Allen's law, respectively. The correlation method is applied to determine bubble and particle velocity variances and covariances. The collision kernel is then calculated, taking into account the effects of turbulence acceleration and shear, and gravity of the bubbleparticle system. We compare our collision model with the available models and investigate the influence of bubble and particle sizes, particle density and dissipation rate of turbulent kinetic energy on the collision kernel. The results show that the bubble-particle collision kernel increases with increasing bubble and particle sizes, and dissipation rate of turbulent kinetic energy. Importantly, turbulence can significantly enhance the collision efficiency, exceeding the ideal rate of collision by gravity and leading to the turbulence collision efficiency greater than unity.

A control volume scheme using compact integrated radial basis function stencils for solving the Richards equation,

This paper presents improved ways of constructing compact integrated radial basis function (CIRBF) stencils, based on extended precision, definite integrals, higher-order IRBFs and minimum number of derivative equations, to enhance their performance over large values of the RBF width. The proposed approaches are numerically verified through secondorder linear differential equations in one and two variables. Significant improvements in the matrix condition number, solution accuracy and convergence rate with grid refinement over the usual approaches are achieved.

Centre manifold method is an accurate approach for analytically constructing an advection-diffusion equation (and even more accurate equations involving higher-order derivatives) for the depth-averaged concentration of substances in channels. This paper presents a direct numerical verification of converge to each other, with their velocities becoming practically equal. The obtained numerical results also demonstrate that the longitudinal diffusion can be neglected compared to the advection.

In this article, integrated radial basis functions (IRBFs) are used for Hermite interpolation in the solution of differential equations, resulting in a new meshless symmetric RBF method. Both global and local approximation‐based schemes are derived. For the latter, the focus is on the construction of compact approximation stencils, where a sparse system matrix and a high‐order accuracy can be achieved together. Cartesian‐grid‐based stencils are possible for problems defined on nonrectangular domains. Furthermore, the effects of the RBF width on the solution accuracy for a given grid size are fully explored with a reasonable computational cost. The proposed schemes are numerically verified in some elliptic boundary‐value problems governed by the Poisson and convection‐diffusion equations. High levels of the solution accuracy are obtained using relatively coarse discretisations.

This paper presents a local moving least square -one-dimensional integrated radial basis function networks (LMLS-1D-IRBFN) method for solving incompressible viscous flow problems using stream function-vorticity formulation. In this method, the partition of unity method is employed as a framework to incorporate the moving least square (MLS) and one-dimensional integrated radial basis function networks (1D-IRBFN) techniques. The major advantages of the proposed method include: (i) a banded sparse system matrix which helps reduce the computational cost; (ii) the Kronecker-δ property of the constructed shape function which helps impose the essential boundary condition in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of integration instead of conventional differentiation to construct the local RBF approximations. Several examples including two-dimensional Poisson problems, lid-driven cavity flow and flow past a circular cylinder are considered and the present results are compared with the exact solutions and numerical results from other methods in the literature to demonstrate the attractiveness of the proposed method.