Volume 12 (2021): Issue 1 (January 2021)

In this work, we consider a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. We propose some numerical methods to approximate the solution of the system which are based on suitable combinations of existing schemes for the single Cahn-Hilliard equation. As a verification for our experimental approach, we present some tests and a detailed description of the numerical solutions’ behaviour obtained by varying the values of the system’s characteristic parameters.

The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the interaction of an incompressible fluid described by a Leray model with a hyperelastic structure modeled as a Saint Venant-Kirchho material. We focus on a strongly coupled, partitioned fluid-structure interaction (FSI) solver in a finite volume environment, combined with an arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain. For the implementation of the Leray model, which features a nonlinear differential low-pass filter, we adopt a three-step algorithm called Evolve-Filter-Relax. We validate our approach against numerical data available in the literature for the 3D cross flow past a cantilever beam at Reynolds number 100 and 400.

Bioinformatic techniques targeting gene expression data require specific analysis pipelines with the aim of studying properties, adaptation, and disease outcomes in a sample population. Present investigation compared together results of four numerical experiments modeling survival rates from bladder cancer genetic profiles. Research showed that a sequence of two discretization phases produced remarkable results compared to a classic approach employing one discretization of gene expression data. Analysis involving two discretization phases consisted of a primary discretizer followed by refinement or pre-binning input values before the main discretization scheme. Among all tests, the best model encloses a sequence of data transformation to compensate skewness, data discretization phase with class-attribute interdependence maximization algorithm, and final classification by voting feature intervals, a classifier that also provides discrete interval optimization.