The geometric optics approximation to high frequency anisotropic wave propagation reduces the anisotropic wave equation to a static Hamilton–Jacobi equation. This equation is known as the anisotropic eikonal equation and has three different coupled wave modes as solutions. We introduce here a level set-based Eulerian approach that captures all three of these wave propagations. In particular, ou...

A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales,...

Anisotropic diffusion has widely been applied as a mechanism for intra region smoothing of images. The results of anisotropic diffusion can be used to obtain an enhanced image or as a precursor to higher-level processing such as shape description, edge detection, image segmentation and object identification and tracking, Although attractive in terms of edge localization and the ability to contr...

Anisotropic dielectric response occurs naturally due to the presence of gradation, like in functionally graded materials or graded biological cells. However, these materials with locally anisotropic dielectric responses can have macroscopically isotropic responses. In treating graded particles of anisotropic materials, traditional isotropic gradation methods need to be modified. In this work, w...

In this paper we extend anisotropic diffusion with a diffusion tensor to be applicable to data that is well modeled by linear models. We focus on its variational theory, and investigate simple discretizations and their performance on synthetic data fulfilling the underlying linear models. To this end, we first show that standard anisotropic diffusion with a diffusion tensor is directly linked t...

Singularly perturbed problems often yield solutions with strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction–diffusion pr...

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the global environmental concerns have put the light weighting of structures on the fore front of the research in transportation industry. among other light weight alloys, the transportation industry is considering magnesium intensive light body-in-white structure in automotive applications. although the research in modeling technique areas is very active, a suitable practical model mimicking t...