ON DISTRIBUTED H^(1) SHAPE GRADIENT FLOWS IN OPTIMAL SHAPE DESIGN OF STOKES FLOWS:CONVERGENCE ANALYSIS AND NUMERICAL APPLICATIONS

We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H^(1) shape gradient flows.Convergence analysis with a priori error estimates is provided under general and different regularity assumptions.We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow.Numerical comparisons in 2D and 3D show that the distributed H1 shape gradient flow is more accurate than the popular boundary type.The corresponding distributed shape gradient algorithm is more effective.

Measurement, modelling, and closed-loop control of crystal shape distribution： Literature review and future perspectives

Crystal morphology is known to be of great importance to the end-use properties of crystal products, and to affect down-stream processing such as filtration and drying. However, it has been previously regarded as too challenging to achieve automatic closed-loop control. Previous work has focused on controlling the crystal size distribution, where the size of a crystal is often defined as the diameter of a sphere that has the same volume as the crystal. This paper reviews the new advances in morphological population balance models for modelling and simulating the crystal shape distribution （CShD）, measuring and estimating crystal facet growth kinetics, and two- and three-dimensional imaging for on-line characterisation of the crystal morphology and CShD. A framework is presented that integrates the various components to achieve the ultimate objective of model-based closed-loop control of the CShD. The knowledge gaps and challenges that require further research are also identified.

User controllable anisotropic shape distribution on 3D meshes

This paper presents an automatic method for computing an anisotropic 2D shape distribution on an arbitrary 2-manifold mesh. Our method allows the user to specify the direction as well as the density of the distribution. Using a pre-computed lookup table, our method can efficiently detect collision among the shapes to be distributed on the 3D mesh. In contrast to existing approaches, which usually assume the 2D objects are isotropic and have simple geometry,our method works for complex 2D objects and can guarantee the distribution is conflict-free, which is a critical constraint in many applications. It is able to compute multi-class shape distributions in parallel.Our method does not require global parameterization of the input 3D mesh. Instead, it computes local parameterizations on the fly using geodesic polar coordinates. Thanks to a recent breakthrough in geodesic computation, the local parameterization can be computed at low cost. As a result, our method can be applied to models with complicated geometry and topology. Experimental results on a wide range of3 D models and 2D anisotropic shapes demonstrate the good performance and effectiveness of our method.

Aerosol structure and vertical distribution in a multi-source dust region

The vertical distribution of aerosols was directly observed under various atmospheric conditions in the free troposphere using surface micro-pulse lidar （MPL4） at the Zhangye Station （39.08°N, 100.27°E） in western China in the spring of 2008. The study shows that the aerosol distribution over Zhangye can be vertically classified into upper, middle and lower layers with altitudes of 4.5 to 9 km, 2.5 to 4.5 kin, and less than 2.5 km, respectively. The aerosol in the upper layer originated from the external sources at higher altitude regions, from far desert regions upwind of Zhangye or transported from higher atmospheric layers by free convection, and the altitude of this aerosol layer decreased with time; the aerosols in the middle and lower layers originated from both external and local sources. The aerosol extinction coefficients in the upper and lower layers decreased with altitude, whereas the coefficient in the middle layer changed only slightly, which suggests that aerosol mixing occurs in the middle layer. The distribution of aerosols with altitude has three features： a single peak that forms under stable atmospheric conditions, an exponential decrease with altitude that occurs under unstable atmospheric conditions, and slight change in the mixed layer. Due to the impact of the top of the atmospheric boundary layer, the diurnal variation in the aerosol extinction coefficient has a single peak, which is higher in the afternoon and lower in the morning.