On the stability of travelling waves with vorticity obtained by minimisation

We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimisation of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimisation appears in Burton and Toland after a first maximisation). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period.Comment: NoDEA Nonlinear Differential Equations and Applications, to appea

Face pairing graphs and 3-manifold enumeration

The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph. These results are then applied to the enumeration of closed minimal P^2-irreducible 3-manifold triangulations, leading to a significant improvement in the performance of the enumeration algorithm. Results are offered for both orientable and non-orientable triangulations.Comment: 30 pages, 57 figures; v2: clarified some passages and generalised the final theorem to the non-orientable case; v3: fixed a flaw in the proof of the conical face lemm

First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

First principles phase diagram calculations were performed for the wurtzite-structure quasibinary systems AlN–GaN, GaN–InN, and AlN–InN. Cluster expansion Hamiltonians that excluded, and included, excess vibrational contributions to the free energy, Fvib, were evaluated. Miscibility gaps are predicted for all three quasibinaries, with consolute points, (XC,TC), for AlN–GaN, GaN–InN, and AlN–InN equal to (0.50, 305 K), (0.50, 1850 K), and (0.50, 2830 K) without Fvib, and (0.40, 247 K), (0.50, 1620 K), and (0.50, 2600 K) with Fvib, respectively. In spite of the very different ionic radii of Al, Ga, and In, the GaN–InN and AlN–GaN diagrams are predicted to be approximately symmetric

First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

We report first-principles phase diagram calculations for the binary systems HfC–TiC, TiC–ZrC, and HfC–ZrC. Formation energies for superstructures of various bulk compositions were computed with a plane-wave pseudopotential method. They in turn were used as a basis for fitting cluster expansion Hamiltonians, both with and without approximations for excess vibrational free energies. Significant miscibility gaps are predicted for the systems TiC–ZrC and HfC–TiC, with consolute temperatures in excess of 2000 K. The HfC–ZrC system is predicted to be completely miscibile down to 185 K. Reductions in consolute temperature due to excess vibrational free energy are estimated to be ~7%, ~20%, and ~0%, for HfC–TiC, TiC–ZrC, and HfC–ZrC, respectively. Predicted miscibility gaps are symmetric for HfC–ZrC, almost symmetric for HfC–TiC and asymmetric for TiC–ZrC

Aircraft interior noise reduction by alternate resonance tuning

Model problem development and analysis continues with the Alternate Resonance Tuning (ART) concept. The various topics described are presently at different stages of completion: investigation of the effectiveness of the ART concept under an external propagating pressure field associated with propeller passage by the fuselage; analysis of ART performance with a double panel wall mounted in a flexible frame model; development of a data fitting scheme using a branch analysis with a Newton-Raphson scheme in multiple dimensions to determine values of critical parameters in the actual experimental apparatus; and investigation of the ART effect with real panels as opposed to the spring-mass-damper systems currently used in much of the theory

Effects of Vacancies on Properties of Relaxor Ferroelectrics: a First-Principles Study

A first-principles-based model is developed to investigate the influence of lead vacancies on the properties of relaxor ferroelectric Pb(Sc1/2Nb1/2)O3 (PSN). Lead vacancies generate large, inhomogeneous, electric fields that reduce barriers between energy minima for different polarization directions. This naturally explains why relaxors with significant lead vacancy concentrations have broadened dielectric peaks at lower temperatures, and why lead vacancies smear properties in the neighborhood of the ferroelectric transition in PSN. We also reconsider the conventional wisdom that lead vacancies reduce the magnitude of dielectric response.Comment: 11 pages, 1 figur

Aircraft interior noise reduction by alternate resonance tuning

Existing interior noise reduction techniques for aircraft fuselages perform reasonably well at higher frequencies, but are inadequate at lower, particularly with respect to the low blade passage harmonics with high forcing levels found in propeller aircraft. A method is being studied which considers aircraft fuselages lines with panels alternately tuned to frequencies above and below the frequency to be attenuated. Adjacent panels would oscillate at equal amplitude, to give equal source strength, but with opposite phase. Provided these adjacent panels are acoustically compact, the resulting cancellation causes the interior acoustic modes to become cut off and therefore be non-propagating and evanescent. This interior noise reduction method, called Alternate Resonance Tuning (ART), is currently being investigated both theoretically and experimentally. This new concept has potential application to reducing interior noise due to the propellers in advanced turboprop aircraft as well as for existing aircraft configurations. This program summarizes the work carried out at Duke University during the third semester of a contract supported by the Structural Acoustics Branch at NASA Langley Research Center

3D MHD Modeling of the Gaseous Structure of the Galaxy: Synthetic Observations

We generated synthetic observations from the four-arm model presented in Gomez & Cox (2004) for the Galactic ISM in the presence of a spiral gravitational perturbation. We found that velocity crowding and diffusion have a strong effect in the l-v diagram. The v-b diagram presents structures at the expected spiral arm velocities, that can be explained by the off-the-plane structure of the arms presented in previous papers of this series. Such structures are observed in the Leiden/Dwingeloo HI survey. The rotation curve, as measured from the inside of the modeled galaxy, shows similarities with the observed one for the Milky Way Galaxy, although it has large deviations from the smooth circular rotation corresponding to the background potential. The magnetic field inferred from a synthetic synchrotron map shows a largely circular structure, but with interesting deviations in the midplane due to distortion of the field from circularity in the interarm regions.Comment: Accepted for publication in ApJ. Better quality figures in http://www.astro.umd.edu/~gomez/publica/3d_galaxy-3.pd

Current challenges in cell wall biology in the cereals and grasses

Plant cell walls consist predominantly of polysaccharides and lignin. There has been a surge of research activity in plant cell wall biology in recent years, in two key areas. Firstly, in the area of human health it is now recognized that cell wall polysaccharides are key components of dietary fiber, which carries significant health benefits. Secondly, plant cell walls are major constituents of lignocellulosic residues that are being developed as renewable sources of liquid transport biofuels. In both areas, the cell walls of the Poaceae, which include the cereals and grasses, are particularly important. The non-cellulosic wall polysaccharides of the Poaceae differ in comparison with those of other vascular plants, insofar as they contain relatively high levels of heteroxylans as “core” polysaccharide constituents and relatively smaller amounts of heteromannans, pectic polysaccharides, and xyloglucans. Certain grasses and cereals walls also contain (1,3;1,4)-β-glucans, which are not widely distributed outside the Poaceae. Although some genes involved in cellulose, heteroxylan, and (1,3;1,4)-β-glucan synthesis have been identified, mechanisms that control expression of the genes are not well defined. Here we review current knowledge of cell wall biology in plants and highlight emerging technologies that are providing new and exciting insights into the most challenging questions related to the synthesis, re-modeling and degradation of wall polysaccharides