Physical Sciences and Mathematics Commons^™

Symmetry Solutions For Transient Solute Transport In Unsaturated Soils With Realistic Water Profile, Maureen Edwards, R Joel Moitsheki, Philip Broadbridge

Dr Maureen Edwards

No abstract provided.

Lie Group Symmetry Analysis Of Transport In Porous Media With Variable Transmissivity, James Hill, Maureen Edwards, A P S Selvadurai

Dr Maureen Edwards

We determine the Lie group symmetries of the coupled partial differential equations governing a novel problem for the transient flow of a fluid containing a solidifiable gel, through a hydraulically isotropic porous medium. Assuming that the permeability ($K^*$) of the porous medium is a function of the gel concentration ($c^*$), we determine a number of exact solutions corresponding to the cases where the concentration-dependent permeability is either arbitrary or has a power law variation or is a constant. Each case admits a number of distinct Lie symmetries and the solutions corresponding to the optimal systems are determined. Some typical concentration …

C*-Algebras Of Tilings With Infinite Rotational Symmetry, Michael F. Whittaker

Dr Michael Whittaker

A tiling with infinite rotational symmetry, such as the Conway– Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an etale equivalence relation is associated. A groupoid C¤-algebra for a tiling is produced and a separating dense set is exhibited in the C*-algebra which encodes the structure of the topological dynamical system. In the case of a substitution tiling, natural subsets of this separating dense set are used to define an AT-subalgebra of the C*-algebra. Finally our results are applied to the Pinwheel Tiling.

Crystal Lattice Desolvation Effects On The Magnetic Quantum Tunneling Of Single-Molecule Magnets, G Redler, Christos Lampropoulos, S Datta, C Koo, T C. Stamatatos, N E. Chakov, G Christou, S Hill

Christos Lampropoulos

High-frequency electron paramagnetic resonance (HFEPR) and alternating current (ac) susceptibility measurements are reported for a new high-symmetry Mn12 complex, [Mn12O12(O2CCH3)16(CH3OH)4]⋅CH3OH. The results are compared to those of other high-symmetry spin S=10 Mn12 single-molecule magnets (SMMs), including the original acetate, [Mn12(O2CCH3)16(H2O)4]⋅2CH3CO2H⋅4H2O, and the [Mn12O12(O2CCH2Br)16(H2O)4]⋅4CH2Cl2 and [Mn12O12(O2CCH2But)16(CH3OH)4]⋅CH3OH complexes. These comparisons reveal important insights into the factors that influence the values of the effective barrier to magnetization reversal, Ueff, deduced on the basis of ac susceptibility measurements. In particular, we find that variations in Ueff can be correlated with the degree of disorder in a crystal which can be controlled by desolvating (drying) …

Raman Spectroscopy Of Rhombohedral P4o10, Sean J. Gilliam, Scott Kirkby, Clifton N. Merrow, Daniel Zeroka, Ajit Banerjee, James O. Jensen

Scott J. Kirkby

Mathematical Aspects Of Oriental Carpets, Carol Bier

Carol Bier

The mathematical principles of pattern making according to symmetrical repetition are well-known today, but the mathematical aspects of pattern formation have been glossed over in the study of Oriental carpets, or neglected in favor of either an appreciation of color and form or a discussion of social and ethnic origins. This article seeks to address several mathematical aspects of Oriental carpets, which are both integral to their form and manifest in their visual make-up.

Measurements Of The Hyperpolarizability Tensor By Means Of Hyper-Rayleigh Scattering, Liang-Chy Chien, V. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang

Liang-Chy Chien

We describe improvements to a previously reported hyper-Rayleigh scattering technique [J. Opt. Sec. Am. B 15, 289 (1998)], for measuring all rotational invariants of the first hyperpolarizability tensor. The full hyper-Rayleigh scattering tensor is expressed in terms of its rotationally invariant components leading to a figures of merit corresponding to each of the rotationally invariant tensors. With elliptically polarized incident light, the polarization state and the intensity of the harmonic light are measured at a scattering angle of 45 degrees. A new analytical fitting method is applied to the signal for two polarization measurements to yield the invariants. We have …

Visions Of Infinity: Design And Pattern In Oriental Carpets, Carol Bier

Carol Bier

No abstract provided.

Symmetry Behavior Of The Static Taub Universe: Effect Of Curvature Anisotropy, T. C. Shen, B. L. Hu, D. J. O'Connor

T. -C. Shen

Using the static Taub universe as an example, we study the effect of curvature anisotropy on symmetry breaking of self-interacting scalar field. The one-loop effective potential of a λφ⁴ field with arbitrary coupling (ξ) is computed by ζ-function regularization. It is expressed as a perturbative series in a small anisotropy parameter α measuring the deformation from the spherical Einstein universe with radius of curvature α. This result is used for analyzing the symmetry behavior of such a system as a function of the geometric (α,α) and field (ξ,λ) parameters. The result is also used to address the question of …

Conduction Band Symmetry In Ta Chalcogenides From Ta L Edge X-Ray Absorption Spectroscopy (Xas), Juana Vivó Acrivos, S.S. P. Parkin, J. Code, J. Reynolds, K. Hathaway, H. Kurasaki, E. Marseglia

Juana Vivó Acrivos

No abstract provided.