Isotropy

The transversely bianisotropic uniaxial medium considered in the present article can be obtained, e.g., by mixing metal helices with an isotropic base medium in such a way that the axes of the helices are randomly oriented but perpendicular to a fixed direction in space. The medium is a generalization of the well-studied chiral medium, and is somewhat similar to the recently studied axially bianisotropic uniaxial medium, which has interesting polarization properties. Plane-wave propagation in the medium is studied and the solution for the dispersion equation is given. Numerical examples for the wave numbers corresponding to the two eigenwaves of the medium are displayed. It is seen that, unlike in the axially bianisotropic uniaxial medium, there are no optical axes in the present medium, in general. © 1993 John Wiley & Sons, Inc.

The Fresnel reflection coefficients R1, R2 for the planar interface between isotropic and generally bi-isotropic half spaces are studied in this communication. The functions (R1 + R2)/(1 + R1R2) and (R1-R2)/(1-R1R2) are seen to be simple functions of the optical material parameters of the media, as has been the case in the corresponding isotropic problem. Also pathological conditions, derived earlier elsewhere for reflection coefficients involving isotropic media, are generalized for the bi-isotropic (nonreciprocal chiral) case. Furthermore, the special cases of reflection from Pasteur or Tellegen media result from the analysis.

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.

The main aim of this study is to analyze fiber-reinforced polymer (FRP) bridge decks according to their material, cross-section, and shape geometry. Infill cell configurations of the decks (rectangular, triangular, trapezoidal, and honeycomb) were tested based on the FRP cell units available in the market. A comparison was made for each cell configuration in flat and curved bridge shapes. Another comparison was made between the material properties. Each model was computed for a composite layup material and a quasi-isotropic material. The quasi-isotropic material represents chopped fibers within a matrix. FE (finite element) analysis was performed on a total of 24 models using Abaqus software. The results show that the bridge shape geometry and infill configuration play an important role in increasing the stiffness, more so than improving the material properties. The arch shape of the bridge deck with quasi-isotropic material and chopped fibers was compared to the cross-ply laminate ...

The dose incurred in an anisotropic environment depends on the orientation of the astronaut's body relative to the direction of the radiation field. The fluctuations in exposure of specific organs due to astronaut orientation are found to be a factor of 2 or more in a typical space habitation module and typical space radiations. An approximation function is found that

The present paper concerns the formulation and the evolution of the non symmetrical growth of an avascular cancerous cell colony in an analytical mathematical fashion. Although most of the existing research considers spherical tumours, here we work in the frame of a more general case of the prolate spheroidal geometry. The tumour lies inside a host spheroidal shell which provides vital nutrients, receives the debris of the dead cells and also transmittes to the tumour the pressure imposed by the surrounding on its exterior boundary. Under the aim of studying the evolution of the exterior tumour boundary, we focus on the exterior conditions under which such a geometrical structure can be sustained. To that purpose, the corresponding nutrient concentration, the inhibitor concentration and the pressure field are calculated analytically providing the necessary data for the evolution equation to be solvable. It turns out that an avascular tumour can exhibit a prolate spheroidal growth on...

This paper presents some fundamental concepts of seismic anisotropy specifically those which have hexagonal symmetry (ordinarily called transversely isotropic in geophysics jargon). There were made calculations of phase and group angles at a planar interface separating an anisotropic media, using routines written in Matlab ® and Maple ® language. The slowness surfaces of the qP, qSV and SH wave, as well as the ray paths in these two media were also estimated. Although only the simplest situations are discussed, this paper is useful as a first step in understanding the fractured media, because it contains examples, software routines, and a reviewing of the basic concepts and formulas of wave propagation.

1Technology Cooperation Agreement: Ecopetrol SA - Instituto Colombiano del Petróleo, AA 4185 Bucaramanga, Santander, Colombia; Universidad Industrial de Santander (UIS) -Petroseismic Group, Bucaramanga, Santander, Colombia 2Geophysical Group, Research Unit, ...

1Technology Cooperation Agreement: Ecopetrol SA - Instituto Colombiano del Petróleo, AA 4185 Bucaramanga, Santander, Colombia; Universidad Industrial de Santander (UIS) -Petroseismic Group, Bucaramanga, Santander, Colombia 2Geophysical Group, Research Unit, ...

Now a days there are few areas on the surface of earth having a relatively constant BSC and can serving as radar calibration targets. Few Examples include the Amazon rain forest, the Greenland ice sheet etc. In this paper we analyse a consistent set of Ku-band radar measurements from the QuickSCAT data mission for about ten years. To study the long-term variation of observed BSC, a set of data is required from Earth's surface this band. A global survey of potential constant land targets is performed. To identify the locations of the best natural calibration targets Quantitative measurements of temporal and spatial variabilities (homogeneity) and isotropy are used. By concentrating on low variation areas, useful calibration targets for future radar missions and for inter calibration between existing radars can be identified. By focusing on regions with little spatial heterogeneity, the temporal variations on diurnal, seasonal, and also decadal scales in homogenous natural terrain types including rain forest, dry brushy areas, and ice sheets can be analysed. The Greenland ice sheet shows a significant trend in backscatter in recent years, and therefore, may not be a suitable calibration site anymore. Another location for a good stable target is a dry brushy area in the Sahara, which shows comparable stability and isotropy with those of the Amazon, Congo, and Antarctica.

We revisit the singular eigensolution to the steady state one-speed transport equation for an isotropically scattering and multiplying heterogeneous slab. It is proved that this solution is a sum of Stieltjes integrals over the resolvent set of only the operator of multiplication by the angular variable.