Raman selection rules for vibration-rotation transitions in symmetric top molecules

Symmetry restrictions on Raman selection rules can be obtained, quite generally, by considering a Raman allowed transition as the result of two successive dipole allowed transitions, and imposing the usual symmetry restrictions on the dipole transitions. This leads to the same results as the more familiar polarizability theory, but the vibration-rotation selection rules are easier to obtain by this argument. The selection rules for symmetric top molecules involving the (+l) and (-l) components of a degenerate vibrational level with first-order Coriolis splitting are derived in this paper. It is shown that these selection rules depend on the order of the highest-fold symmetry axis Cn, being different for molecules with n=3, n=4, or n ≧ 5; moreover the selection rules are different again for molecules belonging to the point groups Dnd with n even, and Sm with 1/2m even, for which the highest-fold symmetry axes Cn and Sm are related by m=2n. Finally it is shown that an apparent anomaly between the observed Raman and infra-red vibration-rotation spectra of the allene molecule is resolved when the correct selection rules are used, and a value for the A rotational constant of allene is derived without making use of the zeta sum rule.

Conditional symmetric instability in sting-jet storms

Sting jets are transient mesoscale jets of air that descend from the tip of the cloud head towards the top of the boundary layer in severe extratropical cyclones and can lead to damaging surface wind gusts. This recently identified jet is distinct from the well-documented jets associated with the cold and warm conveyor belts. One mechanism proposed for their development is the release of conditional symmetric instability (CSI). Here the spatial distribution and temporal evolution of several CSI diagnostics in four severe storms are analysed. A sting jet has been identified in three of these storms; for comparison, we also analysed one storm that did not have a sting jet, even though it hadmany of the apparent features of sting-jet storms. The sting-jet storms are distinct from the non-sting-jet storms by having much greater andmore extensive conditional instability (CI) and CSI. CSI is released by ascending air parcels in the cloud head in two of the sting-jet storms and by descending air parcels in the other sting-jet storm. By contrast, only weak CI to ascending air parcels is present at the cloud-head tip in the non-sting-jet storm. CSI released by descending air parcels, as diagnosed by decaying downdraught slantwise convective available potential energy (DSCAPE), is collocated with the sting jets in all three sting-jet storms and has a localisedmaximum in two of them. Consistent evolutions of saturated moist potential vorticity are found.We conclude that CSI release has a role in the generation of the sting jet, that the sting jet may be driven by the release of instability to both ascending and descending parcels, and that DSCAPE could be used as a discriminating diagnostic for the sting jet based on these four case-studies.

Symmetric Push-Sum Protocol for decentralised aggregation

Gossip (or Epidemic) protocols have emerged as a communication and computation paradigm for large-scale networked systems. These protocols are based on randomised communication, which provides probabilistic guarantees on convergence speed and accuracy. They also provide robustness, scalability, computational and communication efficiency and high stability under disruption. This work presents a novel Gossip protocol named Symmetric Push-Sum Protocol for the computation of global aggregates (e.g., average) in decentralised and asynchronous systems. The proposed approach combines the simplicity of the push-based approach and the efficiency of the push-pull schemes. The push-pull schemes cannot be directly employed in asynchronous systems as they require synchronous paired communication operations to guarantee their accuracy. Although push schemes guarantee accuracy even with asynchronous communication, they suffer from a slower and unstable convergence. Symmetric Push- Sum Protocol does not require synchronous communication and achieves a convergence speed similar to the push-pull schemes, while keeping the accuracy stability of the push scheme. In the experimental analysis, we focus on computing the global average as an important class of node aggregation problems. The results have confirmed that the proposed method inherits the advantages of both other schemes and outperforms well-known state of the art protocols for decentralized Gossip-based aggregation.

The importance of surface pressure changes in the response of the atmosphere to zonally-symmetric thermal and mechanical forcing

he classical problem of the response of a balanced, axisymmetric vortex to thermal and mechanical forcing is re-examined, paying special attention to the lower boundary condition. The correct condition is DΦ/Dt = 0, where Φ is the geopotential and D/Dt the material derivative, which explicitly accounts for a mass redistribution as part of the mean-flow response. This redistribution is neglected when using the boundary condition Dp/Dt = 0, which has conventionally been applied in this problem. It is shown that applying the incorrect boundary condition, and thereby ignoring the surface pressure change, leads to a zonal wind acceleration δū/δt that is too strong, especially near the surface. The effect is significant for planetary-scale forcing even when applied at tropopause level. A comparison is made between the mean-flow evolution in a baroclinic life-cycle, as simulated in a fully nonlinear, primitive-equation model, and that predicted by using the simulated eddy fluxes in the zonally-symmetric response problem. Use of the correct lower boundary condition is shown to lead to improved agreement.

Periodic Reordering

For many networks in nature, science and technology, it is possible to order the nodes so that most links are short-range, connecting near-neighbours, and relatively few long-range links, or shortcuts, are present. Given a network as a set of observed links (interactions), the task of finding an ordering of the nodes that reveals such a range-dependent structure is closely related to some sparse matrix reordering problems arising in scientific computation. The spectral, or Fiedler vector, approach for sparse matrix reordering has successfully been applied to biological data sets, revealing useful structures and subpatterns. In this work we argue that a periodic analogue of the standard reordering task is also highly relevant. Here, rather than encouraging nonzeros only to lie close to the diagonal of a suitably ordered adjacency matrix, we also allow them to inhabit the off-diagonal corners. Indeed, for the classic small-world model of Watts & Strogatz (1998, Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442) this type of periodic structure is inherent. We therefore devise and test a new spectral algorithm for periodic reordering. By generalizing the range-dependent random graph class of Grindrod (2002, Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1–066702-7) to the periodic case, we can also construct a computable likelihood ratio that suggests whether a given network is inherently linear or periodic. Tests on synthetic data show that the new algorithm can detect periodic structure, even in the presence of noise. Further experiments on real biological data sets then show that some networks are better regarded as periodic than linear. Hence, we find both qualitative (reordered networks plots) and quantitative (likelihood ratios) evidence of periodicity in biological networks.

Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.