Rotational symmetry of a methane molecule and the bond angle

The rotational symmetry of a methane molecule can be used to great advantage to calculate the bond angle. The problem is worked out in this article.

Inertia in Japanese organizations: knowledge management routines and failure to innovate

This paper argues that features of Japanese organizations, previously held to be the foundations of innovation, change and flexibility, can equally be significant barriers to change, innovation and adaptation in turbulent economic environments. This paper draws on two in-depth case studies of Japanese organizations. It shows how, in both cases, these firms displayed specific weaknesses in the ways in which they integrate and bundle knowledge, in particular around their research and development (R&D) functions. Despite the adoption of strategies of technological innovation and internationalization, the data suggest that the pursuit of both strategies is beset by barriers of inertia. Embedded internal network connections and knowledge-sharing routines between central R&D and other divisions are inappropriate for the revised strategy. Existing external connections, with preferred suppliers and customers within keiretsu structures, and close relationships with existing R&D partners retard these firms' strategic flexibility. With a limited variety of latent routines, knowledge, capabilities and agency to draw on when needed, these firms have limited organizational responsiveness and high levels of path-dependency.

Friction and inertia: business change, corporate real estate portfolios and the UK office market

It has been asserted that business reorganisation and new working practices are transforming the nature of demand for business space. Downsizing, delayering, business process reengineering and associated initiatives alter the amount, type and location of space required by firms. The literature has neglected the impact of real estate market structures on the ability of organisations to successfully implement these new organisational forms or contemporary working practices. Drawing from UK research, the paper demonstrates that, while new working practices are widespread, their impact on the corporate real estate portfolio is less dramatic than often supposed. In part, this is attributed to inflexibility in market structures which constrains the supply of appropriate space.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

Rotational aesthetics: Michael Bay and contemporary cinema’s machine movement

Digital imaging technologies enable a mastery of the visual that in recent mainstream cinema frequently manifests as certain kinds of spatial reach, orientation and motion. In such a context Michael Bay’s Transformers franchise can be framed as a digital re-tooling of a familiar fantasy of vehicular propulsion, US car culture writ large in digitally crafted spectacles of diegetic speed, the vehicular chase film ‘2.0’. Movement is central to these films, calling up Scott Bukatman’s observation that in spectacular visual media ‘movement has become more than a tool of bodily knowledge; it has become an end in itself’ (2003: 125). Not all movements and not all instances of vehicular propulsion are the same however. How might we evaluate what is at stake in a film’s assertion of movement as an end in itself, and the form that assertion takes, its articulations of diegetic velocity, corporeality, and spatial penetration? Deploying an attentiveness towards the specificity of aesthetic detail and affective impact in Bay’s delineation of movement, this essay suggests that the franchise poses questions about the relationship of human movement to machine movement that exceed their narrative basis. Identifying a persistent rotational trope in the franchise that in its audio-visual articulation combines oddly anachronistic elements (evoking the mechanical rather than the digital), the article argues that the films prioritise certain fantasies of transformation and spatial penetration, and certain modes of corporeality, as one response to contemporary debates about digital technologisation, sustainable energy, and cinematic spectacle. In this way the franchise also represents a particular moment in a more widely discernible preoccupation in contemporary cinema with what we might call a ‘rotational aesthetics’ of action, a machine movement made possible by the digital, but which invokes earlier histories and fantasies of animation, propulsion, mechanization and mechanization to particular ends.

A regime-dependent balanced control variable based on potential vorticity

In this paper it is argued that rotational wind is not the best choice of leading control variable for variational data assimilation, and an alternative is suggested and tested. A rotational wind parameter is used in most global variational assimilation systems as a pragmatic way of approximately representing the balanced component of the assimilation increments. In effect, rotational wind is treated as a proxy for potential vorticity, but one that it is potentially not a good choice in flow regimes characterised by small Burger number. This paper reports on an alternative set of control variables which are based around potential vorticity. This gives rise to a new formulation of the background error covariances for the Met Office's variational assimilation system, which leads to flow dependency. It uses similar balance relationships to traditional schemes, but recognises the existence of unbalanced rotational wind which is used with a new anti-balance relationship. The new scheme is described and its performance is evaluated and compared to a traditional scheme using a sample of diagnostics.

Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Benchmarking 2D hydraulic models for urban flooding

This paper describes benchmark testing of six two-dimensional (2D) hydraulic models (DIVAST, DIVASTTVD, TUFLOW, JFLOW, TRENT and LISFLOOD-FP) in terms of their ability to simulate surface flows in a densely urbanised area. The models are applied to a 1·0 km × 0·4 km urban catchment within the city of Glasgow, Scotland, UK, and are used to simulate a flood event that occurred at this site on 30 July 2002. An identical numerical grid describing the underlying topography is constructed for each model, using a combination of airborne laser altimetry (LiDAR) fused with digital map data, and used to run a benchmark simulation. Two numerical experiments were then conducted to test the response of each model to topographic error and uncertainty over friction parameterisation. While all the models tested produce plausible results, subtle differences between particular groups of codes give considerable insight into both the practice and science of urban hydraulic modelling. In particular, the results show that the terrain data available from modern LiDAR systems are sufficiently accurate and resolved for simulating urban flows, but such data need to be fused with digital map data of building topology and land use to gain maximum benefit from the information contained therein. When such terrain data are available, uncertainty in friction parameters becomes a more dominant factor than topographic error for typical problems. The simulations also show that flows in urban environments are characterised by numerous transitions to supercritical flow and numerical shocks. However, the effects of these are localised and they do not appear to affect overall wave propagation. In contrast, inertia terms are shown to be important in this particular case, but the specific characteristics of the test site may mean that this does not hold more generally.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - II. Diurnal shape of soil heat flux

For vegetated surfaces, calculation of soil heat flux, G, with the Exact or Analytical method requires a harmonic analysis of below-canopy soil surface temperature, to obtain the shape of the diurnal course of G. When determining G with remote sensing methods, only composite (vegetation plus soil) radiometric brightness temperature is available. This paper presents a simple equation that relates the sum of the harmonic terms derived for the composite radiometric surface temperature to that of belowcanopy soil surface temperature. The thermal inertia, Gamma(,) for which a simple equation has been presented in a companion paper, paper I, is used to set the magnitude of G. To assess the success of the method proposed in this paper for the estimation of the diurnal shape of G, a comparison was made between 'remote' and in situ calculated values from described field sites. This indicated that the proposed method was suitable for the estimation of the shape of G for a variety of vegetation types and densities. The approach outlined in paper I, to obtain Gamma, was then combined with the estimated harmonic terms to predict estimates of G, which were compared to values predicted by empirical remote methods found in the literature. This indicated that the method proposed in the combination of papers I and II gave reliable estimates of G, which, in comparison to the other methods, resulted in more realistic predictions for vegetated surfaces. This set of equations can also be used for bare and sparsely vegetated soils, making it a universally applicable method. (C) 2007 Elsevier B.V. All rights reserved.

The three-dimensional vortical nature of atmospheric and oceanic turbulent flows

Using a novel numerical method at unprecedented resolution, we demonstrate that structures of small to intermediate scale in rotating, stratified flows are intrinsically three-dimensional. Such flows are characterized by vortices (spinning volumes of fluid), regions of large vorticity gradients, and filamentary structures at all scales. It is found that such structures have predominantly three-dimensional dynamics below a horizontal scale LLR, where LR is the so-called Rossby radius of deformation, equal to the characteristic vertical scale of the fluid H divided by the ratio of the rotational and buoyancy frequencies f/N. The breakdown of two-dimensional dynamics at these scales is attributed to the so-called "tall-column instability" [D. G. Dritschel and M. de la Torre Juárez, J. Fluid. Mech. 328, 129 (1996)], which is active on columnar vortices that are tall after scaling by f/N, or, equivalently, that are narrow compared with LR. Moreover, this instability eventually leads to a simple relationship between typical vertical and horizontal scales: for each vertical wave number (apart from the vertically averaged, barotropic component of the flow) the average horizontal wave number is equal to f/N times the vertical wave number. The practical implication is that three-dimensional modeling is essential to capture the behavior of rotating, stratified fluids. Two-dimensional models are not valid for scales below LR. ©1999 American Institute of Physics.

A weaker Agulhas Current leads to more Agulhas leakage

Time series of transports in the Agulhas region have been constructed by simulating Lagrangian drifter trajectories in a 1/10 degree two-way nested ocean model. Using these 34 year long time series it is shown that smaller (larger) Agulhas Current transport leads to larger (smaller) Indian-Atlantic inter-ocean exchange. When transport is low, the Agulhas Current detaches farther downstream from the African continental slope. Moreover, the lower inertia suppresses generation of anti-cyclonic vorticity. These two effects cause the Agulhas retroflection to move westward and enhance Agulhas leakage. In the model a 1 Sv decrease in Agulhas Current transport at 32°S results in a 0.7 ± 0.2 Sv increase in Agulhas leakage.

Coriolis perturbations in the infrared spectrum of ethylene

Rotational structure has been resolved and analyzed in two of the infrared‐active perpendicular bands of C2H4 vapor: the Type b fundamental band, ν10, at 826 cm—1, and the Type c fundamental band, ν7, at 949 cm—1. Many of the individual PP and RR branch lines have been observed. The analysis has been confined to values of the quantum number K≥3, for which energy levels ethylene shows no detectable deviations from a symmetric‐top rotational structure. The analysis reveals a Coriolis interaction between ν7 and ν10, and between ν4 and ν10, and values of the Coriolis constants ζ7,10z and ζ4,10y are obtained; these are related to normal coordinate calculations for the appropriate symmetry species, and force constants are derived to fit the observed zeta constants. The band center of ν10 has been revised from the original figure of 810 cm—1 to the new value, 826 cm—1, and the inactive frequency ν4 is estimated to lie at 1023±3 cm—1, in good agreement with the previous estimate of 1027 cm—1. The change in the value of ν10 leads to a suggested change in the value of the Raman‐active fundamental ν6 from 1236 to 1222 cm—1. New combination bands have been observed at 2174 cm—1, assigned as ν3+ν10; and at 2252 cm—1, assigned as ν4+ν6; also rotational structure has been resolved and analyzed in the ν6+ν10 band at 2048 cm—1. The new data obtained for the C2H4 molecule are summarized in Table XII, with all of the other data presently available on the vibrational and rotational constants.

Vibration–rotation variational calculations: precise results on HCN up to 25 000 cm−1

Variation calculations of the vibration–rotation energy levels of many isotopomers of HCN are reported, for J=0, 1, and 2, extending up to approximately 8 quanta of each of the stretching vibrations and 14 quanta of the bending mode. The force field, which is represented as a polynomial expansion in Morse coordinates for the bond stretches and even powers of the angle bend, has been refined by least squares to fit simultaneously all observed data on the Σ and Π state vibrational energies, and the Σ state rotational constants, for both HCN and DCN. The observed vibrational energies are fitted to roughly ±0.5 cm−1, and the rotational constants to roughly ±0.0001 cm−1. The force field has been used to predict the vibration rotation spectra of many isotopomers of HCN up to 25 000 cm−1. The results are consistent with the axis‐switching assignments of some weak overtone bands reported recently by Jonas, Yang, and Wodtke, and they also fit and provide the assignment for recent observations by Romanini and Lehmann of very weak absorption bands above 20 000 cm−1.

The equilibrium structure of HCN

The equilibrium structure of HCN has been determined from the previously published ground state rotational constants of eight isotopomers by using (B0‐Be) values obtained from a variational calculation of the vibration–rotation spectrum. The results are re(CH)=1.065 01(8) Å, and re(CN)=1.153 24(2) Å.

Selection rules for rovibronic transitions in symmetric top molecules

A simple diagrammatic rule is presented for determining the rotational selection rules governing transitions between any pair of vibronic states in electric dipole spectra of symmetric top molecules. The rule is useful in cases where degenerate vibronic levels with first-order Coriolis splittings occur, because it gives immediately the selection rule for the (+l) and (-l) components in any degenerate state. The rule is also helpful in determining the symmetry species and the effective zeta constants in overtone and combination levels involving degenerate vibrations. Particular attention is devoted to the conventions concerning the signs of zeta constants.