Quantum spins and quasiperiodicity: a real space renormalization group approach

We study the antiferromagnetic spin-1/2 Heisenberg model on a two-dimensional bipartite quasiperiodic structure, the octagonal tiling, the aperiodic equivalent of the square lattice for periodic systems. An approximate block spin renormalization scheme is described for this problem. The ground state energy and local staggered magnetizations for this system are calculated and compared with the results of a recent quantum Monte Carlo calculation for the tiling. It is conjectured that the ground state energy is exactly equal to that of the quantum antiferromagnet on the square lattice.     

Mechanistic modeling of destratification in cryogenic storage tanks using ultrasonics

Stratification is one of the main causes for vaporization of cryogens and increase of tank pressure during cryogenic storage. This leads subsequent problems such as cavitation in cryo-pumps, reduced length of storage time. Hence, it is vital to prevent stratification to improve the cost efficiency of storage systems. If stratified layers exist inside the tank, they have to be removed by suitable methods without venting the vapor. Sonication is one such method capable of keeping fluid layers mixed. In the present work, a mechanistic model for ultrasonic destratification is proposed and validated with destratification experiments done in water. Then, the same model is used to predict the destratification characteristics of cryogenic liquids such as liquid nitrogen (LN₂), liquid hydrogen (LH₂) and liquid ammonia (LNH₃). The destratification parameters are analysed for different frequencies of ultrasound and storage pressures by considering continuous and pulsed modes of ultrasonic operation. From the results, it is determined that use of high frequency ultrasound (low-power/continuous; high-power/pulsing) or low frequency ultrasound (continuous operation with moderate power) can both be effective in removing stratification.     

Absorption and emission spectral studies of Eu3+-doped PbO-PbF2 glass system

Judd-Ofelt parameters obtained from the absorption spectra of Eu³⁺ ions doped in PbO-PbF₂ glasses are intermediate between the values for fluoride and phosphate glass matrices. Eu³⁺ ions are coordinated to both oxide and fluoride ions. The calculated transition probabilities (As^-1) for the laser transition⁵D_o→⁷F₂ are 171 and 170 for 30PbO-70PbF₂ and 70PbO-30PbF₂ glasses respectively and are significantly lower compared to phosphate glasses. The calculated (β_R cal) and experimental (β_Rexpt) branching ratios for this transition show good agreement. The emission spectra display high energy transitions in the 440–570 nm region, a characteristic of parent matrices with low energy phonons such as the tellurite, germanate and fluoride glasses. The electron-phonon coupling strengths deduced from the excitation spectra of Eu³⁺ are 10.2 x 10⁻³ and 9.5 x l0⁻³ for 30PbO-70PbF₂ and 70PbO-30PbF₂ glasses respectively. The relative emission intensities of the low energy transitions to high energy transitions and the ratios of the most intense transitions⁵D₀→⁷F₂/⁵D₀→⁷F₇ significantly vary for the two glasses providing evidence for clustering of Eu³⁺ ions with increase in its concentration and increasing PbO content.     

The dual (p,q)-Alexander-Conway Hopf algebras and the associated universal ℐ-matrix

The dually conjugate Hopf algebrasFun _p,q (R) andU _p,q (R) associated with the two-parametric (p,q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebraU _p,q (R) is extracted. The universal ?-matrix forsFun _p,q (R) is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the ?-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal ?-matrix and the FRT matrix generators,L ^(±), forU _p,q (R) are derived from the ?-matrix.     

Scattering from extended targets in range-dependent fluctuating ocean-waveguides with clutter from theory and experiments

Bistatic, long-range measurements of acoustic scattered returns from vertically extended, air-filled tubular targets were made during three distinct field experiments in fluctuating continental shelf waveguides. It is shown that Sonar Equation estimates of mean target-scattered intensity lead to large errors, differing by an order of magnitude from both the measurements and waveguide scattering theory. The use of the Ingenito scattering model is also shown to lead to significant errors in estimating mean target-scattered intensity in the field experiments because they were conducted in range-dependent ocean environments with large variations in sound speed structure over the depth of the targets, scenarios that violate basic assumptions of the Ingenito model. Green's theorem based full-field modeling that describes scattering from vertically extended tubular targets in range-dependent ocean waveguides by taking into account nonuniform sound speed structure over the target's depth extent is shown to accurately describe the statistics of the targets' scattered field in all three field experiments. Returns from the man-made targets are also shown to have a very different spectral dependence from the natural target-like clutter of the dominant fish schools observed, suggesting that judicious multi-frequency sensing may often provide a useful means of distinguishing fish from man-made targets.