We present a construction of anisotropic multiresolution and anisotropic wavelet frames based on multilevel ellipsoid covers (dilations) of R. The wavelets we construct are C∞ functions, can have any prescribed number of vanishing moments and fast decay with respect to the anisotropic quasi-distance induced by the cover. The dual wavelets are also C∞, with the same number of vanishing moments, ...

The main focus of this paper is to suggest a domain decomposition method for finite element approximations of elliptic problems with anisotropic coefficients in domains consisting of anisotropic shape rectangles. The theorems on traces of functions from Sobolev spaces play an important role in studying boundary value problems of partial differential equations. These theorems are commonly used f...

The dyadic Green’s functions (DGFs) for unbounded and layered general anisotropic media are considered in this paper. First, the DGF for unbounded problem is derived using the eigendecomposition method. Two different approaches are proposed to obtain the DGF for layered problem when the source is located inside the anisotropic region. The first approach is to apply the modified symmetrical prop...

Using the theory of electromagnetic scattering of a uniaxial anisotropic sphere, we derive the analytical expressions of the radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam. The beam's propagation direction is parallel to the primary optical axis of the anisotropic sphere. The effects of the permittivity tensor elements ε(t) and ε(z) on the axial ...

Biological rice leaf surfaces show a distinct anisotropic sliding property by means of three-level macrogrooves and micro/nanostructures, and they have many potential applications in biomimetic cell movement control, water transportation, and microfluidic devices. However, fabricating artificial threelevel biosurfaces with a controllable anisotropic sliding property by a simple and effective me...

We propose an anisotropic, patch-based adaptive mesh re nement algorithm for the nite-volume method solving partial di erential equations on Cartesian and mapped grids. For large ow gradients, such as shock waves and ame fronts, that are aligned with one grid direction, anisotropic re nement can provide a similar reduction in error using much less grid cells compared to isotropic re nement. To ...

The analysis of resonant frequency for anisotropic artificial circular dielectric resonator (CDR) encapsulated in waveguide is investigated theoretically. The anisotropic permittivity of CDR is established by taking a relative permittivity value in one direction higher than the values of other directions in cylindrical coordinate system. By deriving Maxwell time-dependent curl equations for the...

When an anisotropic material is subject to creep conditions and a complex state of stress, an anisotropic creep damage behavior is observed. Previous research has focused on the anisotropic creep damage behavior of isotropic materials but few constitutive models have been developed for anisotropic creeping solids. This paper describes the development of a new anisotropic tertiary creep damage c...

A complete theoretical presentation of the Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor (CAFFE model) is given. The CAFFE model is an application of the theory of mixtures with continuous diversity for the case of large polar ice masses in which induced anisotropy occurs. The anisotropic response of the polycrystalline ice is described by a gener...

We present a method to extract polyhedral structures from a three-dimensional set of points, even if these structures are embedded in a perturbed background. The method is based on a family of affine diagrams which is an extension of the Voronoi diagram. These diagrams, namely anisotropic diagrams, are defined by using a parameterized distance whose unit ball is an ellipsoidal one. The paramete...