Determining Slope- and Free Air Flow Wind Profiles for WKB Prandtl Models.

During night time, when the air close to the surface cools-down and the atmosphere becomes stable, katabatic down-slope ows may occur in mountainous regions. Contrary, during day time, when the sun heats-up the air close to the surface, and the atmosphere becomes unstable, anabatic upslope ows are prevalent. Up to date, slope winds in the WKB Prandtl model are determined solely by means of specifying the height zj of the maximum turbulent jet above ground. Furthermore, depending on zj parameters K0 and h for a height-dependent eddy thermal diffusivity function KH(z) and a parameter C determining the amplitude for the Prandtl wind speeds must be specified. They are most often estimated from height-dependent wind speeds u, including slope angle α and fixed Prandtl number Pr = KM/KH with KH = KH(z) and KM the eddy viscosity. Having estimated those parameters, friction velocity u*, friction temperature θ* and sensible heat ux QH may be calculated. This article takes the reverse approach: From specified slope angle α, Pr, u*, θ*, QH and specified form of the eddy thermal diffusivity function KH(z) the corresponding WKB Prandtl model is identified. Furthermore, the relationship between u* and θ* calculated via Monin-Obukhov similarity theory for at terrain and those for the WKB Prandtl model are investigated. Using this relationship, we give hints how our new parametrization of the WKB Prandtl model may be used to determine slope ows and free air ows in a micro meteorological model of an alpine valley for pollutant dispersion calculations. We illustrate our derivations by applying our algorithms for the calculation of the WKB Prandtl model to four examples with two taken from Grisogono et al. (2015).

Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression

Edge-enhancing diffusion (EED) can reconstruct a close approximation of an original image from a small subset of its pixels. This makes it an attractive foundation for PDE based image compression. In this work, we generalize second-order EED to a fourth-order counterpart. It involves a fourth-order diffusion tensor that is constructed from the regularized image gradient in a similar way as in traditional second-order EED, permitting diffusion along edges, while applying a non-linear diffusivity function across them. We show that our fourth-order diffusion tensor formalism provides a unifying framework for all previous anisotropic fourth-order diffusion based methods, and that it provides additional flexibility. We achieve an efficient implementation using a fast semi-iterative scheme. Experimental results on natural and medical images suggest that our novel fourth-order method produces more accurate reconstructions compared to the existing second-order EED.

Perona-Malik Model with Diffusion Coefficient Depending on Fractional Gradient via Caputo-Fabrizio Derivative

The Perona-Malik (PM) model is used successfully in image processing to eliminate noise while preserving edges; however, this model has a major drawback: it tends to make the image look blocky. This work proposes to modify the PM model by introducing the Caputo-Fabrizio fractional gradient inside the diffusivity function. Experiments with natural images show that our model can suppress efficiently the blocky effect. Also, our model has good performance in visual quality, high peak signal-to-noise ratio (PSNR), and lower value of mean absolute error (MAE) and mean square error (MSE).

Numerical Investigation of the Water Vapour Diffusivity inside Homogeneous Porous Media

This work is devoted to numerical investigation of diffusivity function for water vapour interaction with homogeneous porous media. Molecular dynamics simulation is used to determine the diffusivity function. Various approximations of diffusivity are applied for numerical solution of diffusion equation.

Image Inpainting and Enhancement using Fractional Order Variational Model

<p>The intention of image inpainting is to complete or fill the corrupted or missing zones of an image by considering the knowledge from the source region. A novel fractional order variational image inpainting model in reference to Caputo definition is introduced in this article. First, the fractional differential, and its numerical methods are represented according to Caputo definition. Then, a fractional differential mask is represented in 8-directions. The complex diffusivity function is also defined to preserve the edges. Finally, the missing regions are filled by using variational model with fractional differentials of 8-directions. The simulation results and analysis display that the new model not only inpaints the missing regions, but also heightens the contrast of the image. The inpainted images have better visual quality than other fractional differential filters.</p>

The 2D Spectral Intrinsic Decomposition Method Applied to Image Analysis

We propose a new method for autoadaptive image decomposition and recomposition based on the two-dimensional version of the Spectral Intrinsic Decomposition (SID). We introduce a faster diffusivity function for the computation of the mean envelope operator which provides the components of the SID algorithm for any signal. The 2D version of SID algorithm is implemented and applied to some very known images test. We extracted relevant components and obtained promising results in images analysis applications.