Adiabatic dynamics in a spin-1 chain with uniaxial single-spin anisotropy

We study the adiabatic quantum dynamics of an anisotropic spin-1 XY chain across a second order quantum phase transition. The system is driven out of equilibrium by performing a quench on the uniaxial single-spin anisotropy, that is supposed to vary linearly in time. We show that, for sufficiently large system sizes, the excess energy after the quench admits a non trivial scaling behavior that is not predictable by standard Kibble-Zurek arguments for isolated critical points or extended critical regions. This emerges from a competing effect of many accessible low-lying excited states, inside the whole continuous line of critical points.Comment: 17 pages, 8 figures, published versio

Planar Laser Imaging of Sprays for Liquid Rocket Studies

A planar laser imaging technique which incorporates an optical polarization ratio technique for droplet size measurement was studied. A series of pressure atomized water sprays were studied with this technique and compared with measurements obtained using a Phase Doppler Particle Analyzer. In particular, the effects of assuming a logarithmic normal distribution function for the droplet size distribution within a spray was evaluated. Reasonable agreement between the instrument was obtained for the geometric mean diameter of the droplet distribution. However, comparisons based on the Sauter mean diameter show larger discrepancies, essentially because of uncertainties in the appropriate standard deviation to be applied for the polarization ratio technique. Comparisons were also made between single laser pulse (temporally resolved) measurements with multiple laser pulse visualizations of the spray

Valence-bond states in dynamical Jahn-Teller molecular systems

We discuss a hopping model of electrons between idealized molecular sites with local orbital degeneracy and dynamical Jahn-Teller effect, for crystal field environments of sufficiently high symmetry. For the Mott-insulating case (one electron per site and large Coulomb repulsions), in the simplest two-fold degenerate situation, we are led to consider a particular exchange hamiltonian, describing two isotropic spin-1/2 Heisenberg problems coupled by a quartic term on equivalent bonds. This twin-exchange hamiltonian applies to a physical regime in which the inter-orbital singlet is the lowest-energy intermediate state available for hopping. This regime is favored by a relatively strong electron-phonon coupling. Using variational arguments, a large-N limit, and exact diagonalization data, we find that the ground state, in the one dimensional case, is a solid valence bond state. The situation in the two dimensional case is less clear. Finally, the behavior of the system upon hole doping is studied in one dimension.Comment: 11 pages, 5 figure

Structural design studies of a supersonic cruise arrow wing configuration

Structural member cross sections were sized with a system of integrated computer programs to satisfy strength and flutter design requirements for several variants of the arrow wing supersonic cruise vehicle. The resulting structural weights provide a measure of the structural efficiency of the planform geometry, structural layout, type of construction, and type of material including composites. The material distribution was determined for a baseline metallic structure and the results indicate that an approximate fatigue constraint has an important effect on the structural weight required for strength but, in all cases, additional material had to be added to satisfy flutter requirements with lighter mass engines with minimum fuel onboard. The use of composite materials on the baseline configuration was explored and indicated increased structural efficiency. In the strength sizing, the all-composite construction provided a lower weight design than the hybrid construction which contained composites only in the wing cover skins. Subsequent flutter analyses indicated a corresponding lower flutter speed

Surface Contribution to Raman Scattering from Layered Superconductors

Generalizing recent work, the Raman scattering intensity from a semi-infinite superconducting superlattice is calculated taking into account the surface contribution to the density response functions. Our work makes use of the formalism of Jain and Allen developed for normal superlattices. The surface contributions are shown to strongly modify the bulk contribution to the Raman-spectrum line shape below $2\Delta$, and also may give rise to additional surface plasmon modes above $2\Delta$. The interplay between the bulk and surface contribution is strongly dependent on the momentum transfer $q_\parallel$ parallel to layers. However, we argue that the scattering cross-section for the out-of-phase phase modes (which arise from interlayer Cooper pair tunneling) will not be affected and thus should be the only structure exhibited in the Raman spectrum below $2\Delta$ for relatively large $q_\parallel\sim 0.1\Delta/v_F$. The intensity is small but perhaps observable.Comment: 14 pages, RevTex, 6 figure

Analytical and experimental studies of impinging liquid jets

Impinging injectors are a common type of injector used in liquid propellant rocket engines and are typically used in engines where both propellants are injected as a liquid, e.g., engines using LOX/hydrocarbon and storable propellant combinations. The present research program is focused on providing the requisite fundamental understanding associated with impinging jet injectors for the development of an advanced a priori combustion stability design analysis capability. To date, a systematic study of the atomization characteristics of impinging liquid jets under cold-flow conditions have been completed. Effects of orifice diameter, impingement angle, pre-impingement length, orifice length-to-diameter ratio, fabrication procedure, jet flow condition and jet velocity under steady and oscillating, and atmospheric- and high-pressure environments have been investigated. Results of these experimental studies have been compared to current models of sheet breakup and drop formation. In addition, the research findings have been scrutinized to provide a fundamental explanation for a proven empirical correlation used in the design of stable impinging injector-based rocket engines

Spin liquid ground state in a two dimensional non-frustrated spin model

We consider an exchange model describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on the square lattice. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit, and is known to show a spin-Peierls-like dimerization in one dimension. In two dimensions we calculate energy gaps, susceptibilities, and correlation functions with a Green's Function Monte Carlo. We find a finite spin gap and no evidence of any kind of order. We conclude that the ground state is, most likely, a spin liquid of resonating valence bonds.Comment: 4 pages, 4 figures, Revte

Spray formation processes of impinging jet injectors

A study examining impinging liquid jets has been underway to determine physical mechanisms responsible for combustion instabilities in liquid bi-propellant rocket engines. Primary atomization has been identified as an important process. Measurements of atomization length, wave structure, and drop size and velocity distribution were made under various ambient conditions. Test parameters included geometric effects and flow effects. It was observed that pre-impingement jet conditions, specifically whether they were laminar or turbulent, had the major effect on primary atomization. Comparison of the measurements with results from a two dimensional linear aerodynamic stability model of a thinning, viscous sheet were made. Measured turbulent impinging jet characteristics were contrary to model predictions; the structure of waves generated near the point of jet impingement were dependent primarily on jet diameter and independent of jet velocity. It has been postulated that these impact waves are related to pressure and momentum fluctuations near the impingement region and control the eventual disintegration of the liquid sheet into ligaments. Examination of the temporal characteristics of primary atomization (ligament shedding frequency) strongly suggests that the periodic nature of primary atomization is a key process in combustion instability

Anomalous diffusion in a symbolic model

We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach revealed a rich diffusive scenario characterized by non-Gaussian distributions and, depending on the power law exponent and also on the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare with the numerical data, finding a good agreement. Because of its simplicity and flexibility, this model can be a candidate to describe real systems governed by power laws probabilities densities.Comment: Accepted for publication in Physica Script

Non linear sigma models and quantum spin systems

Microscopic models of quantum antiferromagnets are investigated on the basis of a mapping onto effective low energy hamiltonians. Lattice effects are carefully taken into account and their role is discussed. We show that the presence of an external staggered magnetic field modifies in a non trivial way the usual mapping onto the non linear sigma model, leading to the appearance of new terms, neglected in previous works. Our analysis is compared with Lanczos diagonalizations of S=1 Heisenberg chains in a staggered field, confirming the validity of the single mode approximation for the evaluation of the dynamical structure factor. The results are relevant for the interpretation of experiments in quasi-one dimensional compounds. Microscopic realizations of SU(4) spin chains are also discussed in the framework of spin-orbital lattice systems. The low energy physics is shown to be described by sigma models with topological angle $\theta$ in one dimension. This mapping strongly suggests that the one dimensional CP$^3$ model (with $\theta=\pi$) undergoes a second order phase transition as a function of the coupling.Comment: 11 pages, 5 figures, Corrected typos. To appear in Phys. Rev.