Analytical solution for the lattice Boltzmann model beyond Naviers-Stokes

To understand lattice Boltzmann model capability for capturing nonequilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer

A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total $\alpha$-order variation model, which can outperform the currently popular high order regularization models. There exist several previous works using total $\alpha$-order variations for image restoration; however first no analysis is done yet and second all tested formulations, differing from each other, utilize the zero Dirichlet boundary conditions which are not realistic (while non-zero boundary conditions violate definitions of fractional-order derivatives). This paper first reviews some results of fractional-order derivatives and then analyzes the theoretical properties of the proposed total $\alpha$-order variational model rigorously. It then develops four algorithms for solving the variational problem, one based on the variational Split-Bregman idea and three based on direct solution of the discretise-optimization problem. Numerical experiments show that, in terms of restoration quality and solution efficiency, the proposed model can produce highly competitive results, for smooth images, to two established high order models: the mean curvature and the total generalized variation.Comment: 26 page

Codonopsis pilosula twines either to the left or to the right

We report the twining handedness of Codonopsis pilosula, which has either a left- or right-handed helix among different plants, among different tillers within a single plant, and among different branches within a single tiller. The handedness was randomly distributed among different plants, among the tillers within the same plants, but not among the branches within the same tillers. Moreover, the handedness of the stems can be strongly influenced by external forces, i.e. the compulsory left and right forming inclined to produce more left- and right-handed twining stems, respectively, and the reversing could make a left-handed stem to be right-handed and vice versa. We also discuss the probable mechanisms these curious cases happen