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

"Capital Intensity and U.S. Country Population Growth during the Late Nineteenth Century"

The United States witnessed substantial growth in manufacturing and urban populations during the last half of the nineteenth century. To date, no convincing evidence has been presented to explain the shift in population to urban areas. We find evidence that capital intensity, particularly new capital in the form of steam horsepower, played a significant role in drawing labor into counties and by inference into urban areas. This provides support for the hypothesis that the locational decisions of manufacturers and their placement of capital in urban areas fueled urban growth in the nineteenth century.urbanization, capital intensity, regional population growth, technological change

ISM gas studies towards the TeV PWN HESS J1825-137 and northern region

HESS J1825-137 is a pulsar wind nebula (PWN) whose TeV emission extends across ~1 deg. Its large asymmetric shape indicates that its progenitor supernova interacted with a molecular cloud located in the north of the PWN as detected by previous CO Galactic survey (e.g Lemiere, Terrier & Djannati-Ata\"i 2006). Here we provide a detailed picture of the ISM towards the region north of HESS J1825-137, with the analysis of the dense molecular gas from our 7mm and 12mm Mopra survey and the more diffuse molecular gas from the Nanten CO(1-0) and GRS $^{13}$CO(1-0) surveys. Our focus is the possible association between HESS J1825-137 and the unidentified TeV source to the north, HESS J1826-130. We report several dense molecular regions whose kinematic distance matched the dispersion measured distance of the pulsar. Among them, the dense molecular gas located at (RA, Dec)=(18.421h,-13.282$^{\circ}$) shows enhanced turbulence and we suggest that the velocity structure in this region may be explained by a cloud-cloud collision scenario. Furthermore, the presence of a H$\alpha$ rim may be the first evidence of the progenitor SNR of the pulsar PSR J1826-1334 as the distance between the H$\alpha$ rim and the TeV source matched with the predicted SNR radius R$_{\text{SNR}}$~120 pc. From our ISM study, we identify a few plausible origins of the HESS J1826-130 emission, including the progenitor SNR of PSR J1826-1334 and the PWN G018.5-0.4 powered by PSR J1826-1256. A deeper TeV study however, is required to fully identify the origin of this mysterious TeV source.Comment: 19 figures, 27 pages, accepted by MNRA

Shocked H2 and Fe+ Dynamics in the Orion Bullets

Observations of H2 velocity profiles in the two most clearly defined Orion bullets are extremely difficult to reconcile with existing steady-state shock models. We have observed [FeII] 1.644um velocity profiles of selected bullets and H2 1-0 S(1) 2.122um velocity profiles for a series of positions along and across the corresponding bow-shaped shock fronts driven into the surrounding molecular cloud. Integrated [FeII] velocity profiles of the brightest bullets are consistent with theoretical bow shock predictions. However, observations of broad, singly-peaked H2 1-0 S(1) profiles at a range of positions within the most clearly resolved bullet wakes are not consistent with molecular shock modelling. A uniform, collisionally broadened background component which pervades the region in both tracers is inconsistent with fluorescence due to the ionizing radiation of the Trapezium stars alone.Comment: 20 pages including 18 figures, published in MNRA

Irrigation and drainage performance assessment: practical guidelines

Irrigation management / Drainage / Performance evaluation / Performance indexes / Evapotranspiration / Precipitation / Water balance / Participatory rural appraisal / Databases / Simulation

Generalised Nonorthogonal Matrix Elements: Unifying Wick's Theorem and the Slater-Condon Rules

Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder then their orthogonal counterparts. While several different approaches have been developed, these are predominantly derived from the first-quantised generalised Slater-Condon rules and usually require biorthogonal occupied orbitals to be computed for each matrix element. For coupling terms between nonorthogonal excited configurations, a second-quantised approach such as the nonorthogonal Wick's theorem is more desirable, but this fails when the two reference determinants have a zero many-body overlap. In this contribution, we derive an entirely generalised extension to the nonorthogonal Wick's theorem that is applicable to all pairs of determinants with nonorthogonal orbitals. Our approach creates a universal methodology for evaluating any nonorthogonal matrix element and allows Wick's theorem and the generalised Slater-Condon rules to be unified for the first time. Furthermore, we present a simple well-defined protocol for deriving arbitrary coupling terms between nonorthogonal excited configurations. In the case of overlap and one-body operators, this protocol recovers efficient formulae with reduced scaling, promising significant computational acceleration for methods that rely on such terms.Comment: 17 pages, 0 figure

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