Offside goals and induced breaches of contract

An analysis of Global Resources Group Ltd v Mackay which explores the possibility of building links between the offside goals rule and nominate delict of inducing breach of contract

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review

Herschel observations of EXtra-Ordinary Sources (HEXOS): Methanol as a probe of physical conditions in Orion KL

We have examined methanol emission from Orion KL withthe Herschel/HIFI instrument, and detected two methanol bands centered at 524 GHz and 1061 GHz. The 524 GHz methanol band (observed in HIFI band 1a) is dominated by the isolated ΔJ = 0, K = −4 → −3, v_t = 0 Q branch, and includes 25 E-type and 2 A-type transitions. The 1061 GHz methanol band (observed in HIFI band 4b) is dominated by the ΔJ = 0, K = 7 → 6, v_t = 0 Q branch transitions which are mostly blended. We have used the isolated E-type v_t = 0 methanol transitions to explore the physical conditions in the molecular gas. With HIFI’s high velocity resolution, the methanol emission contributed by different spatial components along the line of sight toward Orion KL (hot core, low velocity flow, and compact ridge) can be distinguished and studied separately. The isolated transitions detected in these bands cover a broad energy range (upper state energy ranging from 80 K to 900 K), which provides a unique probe of the thermal structure in each spatial component. The observations further show that the compact ridge is externally heated. These observations demonstrate the power of methanol lines as probes of the physical conditions in warm regions in close proximity to young stars

Stratified shear flow instabilities at large Richardson numbers

Numerical simulations of stratified shear flow instabilities are performed in two dimensions in the Boussinesq limit. The density variation length scale is chosen to be four times smaller than the velocity variation length scale so that Holmboe or Kelvin-Helmholtz unstable modes are present depending on the choice of the global Richardson number Ri. Three different values of Ri were examined Ri =0.2, 2, 20. The flows for the three examined values are all unstable due to different modes namely: the Kelvin-Helmholtz mode for Ri=0.2, the first Holmboe mode for Ri=2, and the second Holmboe mode for Ri=20 that has been discovered recently and it is the first time that it is examined in the non-linear stage. It is found that the amplitude of the velocity perturbation of the second Holmboe mode at the non-linear stage is smaller but comparable to first Holmboe mode. The increase of the potential energy however due to the second Holmboe modes is greater than that of the first mode. The Kelvin-Helmholtz mode is larger by two orders of magnitude in kinetic energy than the Holmboe modes and about ten times larger in potential energy than the Holmboe modes. The results in this paper suggest that although mixing is suppressed at large Richardson numbers it is not negligible, and turbulent mixing processes in strongly stratified environments can not be excluded.Comment: Submitted to Physics of Fluid

Stochastic time-dependent current-density functional theory: a functional theory of open quantum systems

The dynamics of a many-body system coupled to an external environment represents a fundamentally important problem. To this class of open quantum systems pertains the study of energy transport and dissipation, dephasing, quantum measurement and quantum information theory, phase transitions driven by dissipative effects, etc. Here, we discuss in detail an extension of time-dependent current-density-functional theory (TDCDFT), we named stochastic TDCDFT [Phys. Rev. Lett. {\bf 98}, 226403 (2007)], that allows the description of such problems from a microscopic point of view. We discuss the assumptions of the theory, its relation to a density matrix formalism, and the limitations of the latter in the present context. In addition, we describe a numerically convenient way to solve the corresponding equations of motion, and apply this theory to the dynamics of a 1D gas of excited bosons confined in a harmonic potential and in contact with an external bath.Comment: 17 pages, 7 figures, RevTex4; few typos corrected, a figure modifie

Reversal of infall in SgrB2(M) revealed by Herschel/HIFI observations of HCN lines at THz frequencies

Aims. To investigate the accretion and feedback processes in massive star formation, we analyze the shapes of emission lines from hot molecular cores, whose asymmetries trace infall and expansion motions. Methods. The high-mass star forming region SgrB2(M) was observed with Herschel/HIFI (HEXOS key project) in various lines of HCN and its isotopologues, complemented by APEX data. The observations are compared to spherically symmetric, centrally heated models with density power-law gradient and different velocity fields (infall or infall+expansion), using the radiative transfer code RATRAN. Results. The HCN line profiles are asymmetric, with the emission peak shifting from blue to red with increasing J and decreasing line opacity (HCN to H^(13)CN). This is most evident in the HCN 12–11 line at 1062 GHz. These line shapes are reproduced by a model whose velocity field changes from infall in the outer part to expansion in the inner part. Conclusions. The qualitative reproduction of the HCN lines suggests that infall dominates in the colder, outer regions, but expansion dominates in the warmer, inner regions. We are thus witnessing the onset of feedback in massive star formation, starting to reverse the infall and finally disrupting the whole molecular cloud. To obtain our result, the THz lines uniquely covered by HIFI were critically important

Herschel observations of EXtra-Ordinary Sources (HEXOS): The present and future of spectral surveys with Herschel/HIFI

We present initial results from the Herschel GT key program: Herschel observations of EXtra-Ordinary Sources (HEXOS) and outline the promise and potential of spectral surveys with Herschel/HIFI. The HIFI instrument offers unprecedented sensitivity, as well as continuous spectral coverage across the gaps imposed by the atmosphere, opening up a largely unexplored wavelength regime to high-resolution spectroscopy. We show the spectrum of Orion KL between 480 and 560 GHz and from 1.06 to 1.115 THz. From these data, we confirm that HIFI separately measures the dust continuum and spectrally resolves emission lines in Orion KL. Based on this capability we demonstrate that the line contribution to the broad-band continuum in this molecule-rich source is ~20−40% below 1 THz and declines to a few percent at higher frequencies. We also tentatively identify multiple transitions of HD^(18)O in the spectra. The first detection of this rare isotopologue in the interstellar medium suggests that HDO emission is optically thick in the Orion hot core with HDO/H_2O ~ 0.02. We discuss the implications of this detection for the water D/H ratio in hot cores

Herschel observations of EXtra-Ordinary Sources (HEXOS): Observations of H_2O and its isotopologues towards Orion KL

We report the detection of more than 48 velocity-resolved ground rotational state transitions of H^(16)_2O, H^(18) _2O, and ^(17)_2O – most for the first time – in both emission and absorption toward Orion KL using Herschel/HIFI. We show that a simple fit, constrained to match the known emission and absorption components along the line of sight, is in excellent agreement with the spectral profiles of all the water lines. Using the measured H^(18)_2O line fluxes, which are less affected by line opacity than their H^(16)_2O counterparts, and an escape probability method, the column densities of H^(18)_2O associated with each emission component are derived. We infer total water abundances of 7.4 × 10^(−5), 1.0 × 10^(−5), and 1.6 × 10^(−5) for the plateau, hot core, and extended warm gas, respectively. In the case of the plateau, this value is consistent with previous measures of the Orion-KL water abundance as well as those of other molecular outflows. In the case of the hot core and extended warm gas, these values are somewhat higher than water abundances derived for other quiescent clouds, suggesting that these regions are likely experiencing enhanced water-ice sublimation from (and reduced freeze-out onto) grain surfaces due to the warmer dust in these sources