Through a series of papers in the 1980’s, Bouchet introduced isotropic systems and the Tutte-Martin polynomial of an isotropic system. Then, Arratia, Bollobás, and Sorkin developed the interlace polynomial of a graph in [ABS00] in response to a DNA sequencing application. The interlace polynomial has generated considerable recent attention, with new results including realizing the original inte...

Based upon the fundamental solution to a single straight dislocation segment, a complete set of exact closed-form solutions is presented in a unified manner for elastic displacements and strains due to general polygonal dislocations in a transversely isotropic half-space. These solutions are systematically composed of two parts: one representing the solution in an infinite transversely isotropi...

[1] There is a potential for isotropic tomographic models to be biased by ignored anisotropy; anisotropy could be mapped as artificial isotropic velocity perturbations. We investigate the distribution and strength of this potential bias for three tomographic S velocity models based on regional S and Rayleigh waveforms. We use observed SKS delay times and fast-axis orientations to compute equiva...

We consider the role of array geometry on the Direction of Arrival (DOA) estimating performance of the array where the impinging signal is wideband. We concentrate on arrays that have isotropic performance. An isotropic array is one whose Cramér Rao bound (CRB) on the DOA of a single source is uniform for all angles. We derive the necessary and sufficient conditions on the location of array ele...

We construct a phenomenological Landau-de Gennes theory for hard colloidal rods by performing an order parameter expansion of the chemical-potential dependent grand potential. By fitting the coefficients to known results of Onsager theory, we are not only able to describe the isotropic-nematic phase transition as function of density, including the well-known density jump, but also the isotropic...

Several properties of the isotropic matroid of a looped simple graph are presented. Results include a characterization of the multimatroids that are associated with isotropic matroids and several ways in which the isotropic matroid of G incorporates information about graphs locally equivalent to G. Specific results of the latter type include a characterization of graphs that are locally equival...

It is common to assume that a Hookean solid is isotropic. For a generally anisotropic elasticity tensor, it is possible to obtain its isotropic counterparts. Such a counterpart is obtained in accordance with a given norm. Herein, we examine the effect of three norms: the Frobenius 36-component norm, the Frobenius 21-component norm and the operator norm on a general Hookean solid. We find that b...

Light-scattering measurements of the correlation length in the isotropic phase of a nematic liquid crystal reveal a temperature dependence following Landau-de Gennes theory for the isotropic phase with a bare correlation length smaller than has been measured in other liquid crystals. Similar measurements in a cholesteric liquid crystal demonstrate that the correlation length in the isotropic ph...

We present the first quantitative assessment of the maximum amount of nanotubes that can exist in the isotropic phase () of single-walled carbon nanotubes (SWNTs) in Brønsted-Lowry acids. We employ a centrifugation technique in conjunction with UV-vis-nIR spectroscopy to quantify , which is also the critical concentration of the isotropic-nematic transition of SWNTs in strong acids. Centrifugat...

The uniaxial compressive strength (UCS) of intact rocks is one of the key parameters in the course of site characterizations. The isotropy/anisotropy condition of the UCS of intact rocks is dependent on the internal structure of the rocks. The rocks with a random grain structure exhibit an isotropic behavior. However, the rocks with a linear/planar grain structure generally behave transversely-...