Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric

Influence of cross-section geometry and wire orientation on the phonon shifts in ultra-scaled Si nanowires

Engineering of the cross-section shape and size of ultra-scaled Si nanowires (SiNWs) provides an attractive way for tuning their structural properties. The acoustic and optical phonon shifts of the free-standing circular, hexagonal, square and triangular SiNWs are calculated using a Modified Valence Force Field (MVFF) model. The acoustic phonon blue shift (acoustic hardening) and the optical phonon red shift (optical softening) show a strong dependence on the cross-section shape and size of the SiNWs. The triangular SiNWs have the least structural symmetry as revealed by the splitting of the degenerate flexural phonon modes and The show the minimum acoustic hardening and the maximum optical hardening. The acoustic hardening, in all SiNWs, is attributed to the decreasing difference in the vibrational energy distribution between the inner and the surface atoms with decreasing cross-section size. The optical softening is attributed to the reduced phonon group velocity and the localization of the vibrational energy density on the inner atoms. While the acoustic phonon shift shows a strong wire orientation dependence, the optical phonon softening is independent of wire orientation.Comment: 10 figures, 4 Tables, submitted to JAP for revie

A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, $\mathrm{M}\approx 0.1$, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to a genuinely incompressible formulation. Our contributions to the state-of-the-art are twofold: Firstly, we present a high-performance discontinuous Galerkin solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures. The performance results presented in this work focus on the node-level performance and our results suggest that there is great potential for further performance improvements for current state-of-the-art discontinuous Galerkin implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows

A hybrid stabilization technique for simulating water wave - Structure interaction by incompressible Smoothed Particle Hydrodynamics (ISPH) method

The Smoothed Particle Hydrodynamics (SPH) method is emerging as a potential tool for studying water wave related problems, especially for violent free surface flow and large deformation problems. The incompressible SPH (ISPH) computations have been found not to be able to maintain the stability in certain situations and there exist some spurious oscillations in the pressure time history, which is similar to the weakly compressible SPH (WCSPH). One main cause of this problem is related to the non-uniform and clustered distribution of the moving particles. In order to improve the model performance, the paper proposed an efficient hybrid numerical technique aiming to correct the ill particle distributions. The correction approach is realized through the combination of particle shifting and pressure gradient improvement. The advantages of the proposed hybrid technique in improving ISPH calculations are demonstrated through several applications that include solitary wave impact on a slope or overtopping a seawall, and regular wave slamming on the subface of open-piled structure

A numerical method for junctions in networks of shallow-water channels

There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in networks of gas tubes, water channels and vessel networks for blood and lymph in the human circulatory system. A key point in designing numerical methods for such applications is the treatment of junctions, i.e. points at which two or more 1D domains converge and where the flow exhibits multidimensional behaviour. This paper focuses on the design of methods for networks of water channels. Our methods adopt the finite volume approach to make full use of the two-dimensional shallow water equations on the true physical domain, locally at junctions, while solving the usual one-dimensional shallow water equations away from the junctions. In addition to mass conservation, our methods enforce conservation of momentum at junctions; the latter seems to be the missing element in methods currently available. Apart from simplicity and robustness, the salient feature of the proposed methods is their ability to successfully deal with transcritical and supercritical flows at junctions, a property not enjoyed by existing published methodologies. Systematic assessment of the proposed methods for a variety of flow configurations is carried out. The methods are directly applicable to other systems, provided the multidimensional versions of the 1D equations are available