A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the thicknesses of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee [J. Comput. Phys. 86, 187] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin [J. Comput. Phys. 163, 216] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving and the statistical average of this method is shown to significantly delay the onset of pinning

Dimensionality Reduction Approach using Attributes Extraction and Attributes Selection in Gene Expression Databases

The gene expression databases are formed by a high number of attributes. To deal with this amount, data dimensionality reduction is used in order to minimize the volume of data to be treated regarding the number of attributes, and to increase the generalization capability of learning methods by eliminating irrelevant and/or redundant data. This paper proposes an approach to means of dimensionality reduction, which joins attribute extraction and attributes selection. For this, we used the Random Projection method and the filter and wrapper approaches for the attribute selection. The experiments are realized in five gene expression microarray databases. The results of the experiments showed that join of those approaches can provide promising results