Narrow Results

Dynamical systems and defects in liquid crystals (LCs) are described using topological methods. Meanwhile, the director field distribution in LC droplets is affected by many bulk and surface factors that are difficult to take into account in the topological analysis. Therefore, the structural instability of a LC droplet formed in a magnetic field has been investigated by us in the framework of the catastrophe theory. The effect of temperature on the control parameters of the cusp catastrophe, which leads to the transition from a bipolar structure with extended poles to the homogeneous or radial configuration, has been estimated. It has been established from the potential curves that the transition is induced by the variation in the LC director orientation between the potential minima related to the LC polymer anchoring energy and magnetic field. The interplay of the cusp catastrophe control parameters and anchoring parameters has been elucidated.

The Partially Averaged Navier–Stokes (PANS) method is assessed with various values of the control parameters ($f_k=0.3$–1.0, $f_{𝜀}=1.0$) by performing unsteady cavitating flows around a NACA0015 hydrofoil in a surrogate fluid of fluoroketone. Available experimental data of the cavity evolution and pressure are utilized to validate and evaluate the computational method. The results show that decreasing the control parameter $f_k$ can help to avoid the overestimations of the turbulence viscosity near the rear region of the cavity and can resolve more scales turbulence structure. The control parameter $f_k=0.4$ yields good predictions on cavitation shedding dynamics behavior and pressure distribution. Furthermore, the temperature around the hydrofoil undergoes a strong evolution that is contributed by the local evaporation and condensation processes. Interestingly, there are significant unsteady characteristics along the chordwise and spanwise directions of the hydrofoil. Finally, the thermal effect on cavitating flows is associated with the physical properties of fluid media. Evaporative cooling effects are more pronounced at high temperature and subsequently suppress the intensity of cavitation.

Kernels have become an integral part of most data classification algorithms. However, the kernel parameters are generally not optimized during learning. In this work a novel adaptive technique called Sequential Function Approximation (SFA) has been developed for classification that determines the values of the control and kernel hyper-parameters during learning. This tool constructs sparse radial basis function networks in a greedy fashion. Experiments were carried out on synthetic and real-world data sets where SFA had comparable performance to other popular classification schemes with parameters optimized by an exhaustive grid search.