The applicability of the method of Sobol to the non-smooth, resonant behavior of a vibrational eigen-mode of a piezoelectric element is examined. The goal is to quantify the sensitivity of the system upon variation of the piezoelectric material parameters. The randomly distributed piezoelectric material pa-rameters needed for this statistical approach are taken from a Latin hypercube sampling (LHS). For each such sampling point a frequency-domain study is performed, from which the resonance frequency of the considered eigenmode is extracted. The Sobol indices are computed from the statistical distribution of these resonance positions. A hybrid computational approach by means of the MATLAB® LiveLink™ feature is chosen. The LHS process, the COMSOL® model creation, the extraction of the resonance frequencies, and the calculation of the Sobol indices is performed in MATLAB®. COMSOL® is used for the computation of the electrical impedance of the considered block-shaped piezoceramic test spec-imen. To this end, a frequency-domain study is set up, combined with a parametric sweep with the LHS parameter combinations as input. A batch sweep is employed to speed up the computation by parallel model execution.
The applicability of the method of Sobol to the non-smooth, resonant behavior of a vibrational eigenmode of a piezoelectric element is examined. The goal is to quantify the sensitivity of the system upon variation of the piezoelectric material parameters. The randomly distributed piezoelectric material parameters needed for this statistical approach are taken from a Latin Hypercube Sampling (LHS). A hybrid computational approach is applied: The LHS process, the creation of the simulation model, the extraction of the resonance frequencies, and the calculation of the Sobol indices is performed in MATLAB®. The finite-element software COMSOL Multiphysics® is used for the computation of the electrical and mechanical properties of the considered block-shaped piezoceramic test specimen. To this end, an eigenfrequency analysis as well as a frequency domain study are set up, combined with a parametric sweep using the LHS parameter combinations as input. The convergence of the calculated Sobol indices depending on the LHS sampling size is investigated. It is shown that the Sobol analysis successfully identifies the most influential material parameters.
In a recent theoretical effort, a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar gases has been derived. Within this model, the dipolar scattering results in an anisotropic viscosity tensor. Effects of the anisotropy have been predicted to be observable in the weltering motion, i.e., the collective oscillations of a dipolar Fermi gas, as well as in its acoustic behavior. In this contribution, we approach dipolar fluids from a computational fluid dynamics (CFD) perspective. To this end, previously derived analytic expressions of the anisotropic viscosity tensor are implemented in the finite-element software COMSOL Multiphysics. This allows us to investigate a whole spectrum of fluid flow situations but now including the inherent anisotropy of dipolar scattering. We present first results of such CFD simulations with an emphasis on effects attributable to the special characteristics of the anisotropic viscosity tensor.
In a recent theoretical effort, a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar gases has been derived. Within this model, the dipolar scattering results in an anisotropic viscosity tensor. Effects of the anisotropy have been predicted to be observable in the weltering motion, i.e., the collective oscillations of a dipolar Fermi gas, as well as in its acoustic behavior. In this contribution, we approach dipolar fluids from a computational fluid dynamics (CFD) perspective. To this end, previously derived analytic expressions of the anisotropic viscosity tensor are implemented in COMSOL Multiphysics®. This allows us to investigate a whole spectrum of fluid flow situations but now including the inherent anisotropy of dipolar scattering.