On wave action and phase in the non-canonical Hamiltonian formulation

The long time–evolution of disturbances to slowly–varying solutions of partial differential equations is subject to the adiabatic invariance of the wave action. Generally, this approximate conservation law is obtained under the assumption that the partial differential equations are derived from a variational principle or have a canonical Hamiltonian structure. Here, the wave action conservation is examined for equations that possess a non–canonical (Poisson) Hamiltonian structure. The linear evolution of disturbances in the form of slowly varying wavetrains is studied using a WKB expansion. The properties of the original Hamiltonian system strongly constrain the linear equations that are derived, and this is shown to lead to the adiabatic invariance of a wave action. The connection between this (approximate) invariance and the (exact) conservation laws of pseudo–energy and pseudomomentum that exist when the basic solution is exactly time and space independent is discussed. An evolution equation for the slowly varying phase of the wavetrain is also derived and related to Berry's phase.

A closer look at chaotic advection in the stratosphere: part I: geometric structure

The relevance of chaotic advection to stratospheric mixing and transport is addressed in the context of (i) a numerical model of forced shallow-water flow on the sphere, and (ii) a middle-atmosphere general circulation model. It is argued that chaotic advection applies to both these models if there is suitable large-scale spatial structure in the velocity field and if the velocity field is temporally quasi-regular. This spatial structure is manifested in the form of “cat’s eyes” in the surf zone, such as are commonly seen in numerical simulations of Rossby wave critical layers; by analogy with the heteroclinic structure of a temporally aperiodic chaotic system the cat’s eyes may be thought of as an “organizing structure” for mixing and transport in the surf zone. When this organizing structure exists, Eulerian and Lagrangian autocorrelations of the velocity derivatives indicate that velocity derivatives decorrelate more rapidly along particle trajectories than at fixed spatial locations (i.e., the velocity field is temporally quasi-regular). This phenomenon is referred to as Lagrangian random strain.

Rossby waves and two-dimensional turbulence in a large-scale zonal jet

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field. Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ[identical with] (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ [identical with] (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences. The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to K Kβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [double less-than sign] κ for typical eddy length and velocity scales.

Mobile-to-mobile MIMO transmit-receive diversity systems: analysis and performance in three-dimensional double-correlated channels

Mobile-to-mobile (M-to-M) communications are expected to play a crucial role in future wireless systems and networks. In this paper, we consider M-to-M multiple-input multiple-output (MIMO) maximal ratio combining system and assess its performance in spatially correlated channels. The analysis assumes double-correlated Rayleigh-and-Lognormal fading channels and is performed in terms of average symbol error probability, outage probability, and ergodic capacity. To obtain the receive and transmit spatial correlation functions needed for the performance analysis, we used a three-dimensional (3D) M-to-M MIMO channel model, which takes into account the effects of fast fading and shadowing. The expressions for the considered metrics are derived as a function of the average signal-to-noise ratio per receive antenna in closed-form and are further approximated using the recursive adaptive Simpson quadrature method. Numerical results are provided to show the effects of system parameters, such as distance between antenna elements, maximum elevation angle of scatterers, orientation angle of antenna array in the x–y plane, angle between the x–y plane and the antenna array orientation, and degree of scattering in the x–y plane, on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.

Spatial interaction among nontoxic phytoplankton, toxic phytoplankton and zooplankton: emergence in space and time

In homogeneous environments, by overturning the possibility of competitive exclusion among phytoplankton species, and by regulating the dynamics of overall plankton population, toxin-producing phytoplankton (TPP) potentially help in maintaining plankton diversity—a result shown recently. Here, I explore the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water. The spatial interactions among the species are represented in the form of reaction-diffusion equations. Suitable parametric conditions under which Turing patterns may or may not evolve are investigated. Spatiotemporal distributions of species biomass are simulated using the diffusivity assumptions realistic for natural planktonic systems. The study demonstrates that spatial movements of planktonic systems in the presence of TPP generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, thereby ensuring the persistence of multiple species in space and time. The overall results may potentially explain the sustainability of biodiversity and the spatiotemporal emergence of phytoplankton and zooplankton species under the influence of TPP combined with their physical movement in the subsurface water.

Diverging from the dominant discourse- some implications of conflicting subject understandings in the education of teachers

This paper addresses beginning teachers thinking about the nature and purposes of their subject and the impact of this on their practice. Individual qualitative interviews were undertaken with 11 history teachers at the beginning of their teaching careers. Data was analysed using writing as the method of analysis and revealed that teachers whose thinking was at odds with dominant discourses, for example in the form of a national curriculum, encountered difficulties embracing pedagogies and aspects of the curriculum that do not accord with their own deep-seated beliefs, demonstrating a need for the initial training and professional development of teachers to forefront consideration of subject understandings.

Clusters, connectivity and catch-up: Bollywood and Bangalore in the Global Economy

In this article, we make two important contributions to the literature on clusters. First, we provide a broader theory of cluster connectivity that has hitherto focused on organization-based pipelines and MNE subsidiaries, by including linkages in the form of personal relationships. Second, we use the lens of social network theory to derive a number of testable propositions. We propose that global linkages with decentralized network structures have the highest potential for local spillovers. In the emerging economy context, our theory implies that clusters linked to the global economy by decentralized pipelines have potential for in-depth catch-up, focused in industry and technology scope. In contrast, clusters linked through decentralized personal relationships have potential for in-breadth catch-up over a range of related industries and technologies. We illustrate our theoretical propositions by contrasting two emerging economy case studies: Bollywood, the Indian filmed entertainment cluster in Mumbai and the Indian software cluster in Bangalore.

Simulations of angular momentum evolution in wind-fed CV precursors

It is thought that the secondary stars in cataclysmic variables (CVs) may undergo a period of mass loss in the form of a wind during the evolution of the system (Mullan et al. 1992). This wind is thought to magnetically brake the secondary star with a time-scale ~ 10^8 yr (e.g. van Paradijs 1986). When the secondary’s spin has been brought close to synchronism with the orbit it is possible for tidal torques to lock the secondary in synchronous rotation.

Diverging from the dominant discourse – some implications of conflicting subject understandings in the education of teachers

This paper addresses beginning teachers thinking about the nature and purposes of their subject and the impact of this on their practice. Individual qualitative interviews were undertaken with 11 history teachers at the beginning of their teaching careers. Data was analysed using writing as the method of analysis and revealed that teachers whose thinking was at odds with dominant discourses, for example in the form of a national curriculum, encountered difficulties embracing pedagogies and aspects of the curriculum that do not accord with their own deep-seated beliefs, demonstrating a need for the initial training and professional development of teachers to forefront consideration of subject understandings.

A semi-distributed ntegrated itrogen model for multiple source assessment in tchments (INCA): Part I — model structure and process equations

A new model has been developed for assessing multiple sources of nitrogen in catchments. The model (INCA) is process based and uses reaction kinetic equations to simulate the principal mechanisms operating. The model allows for plant uptake, surface and sub-surface pathways and can simulate up to six land uses simultaneously. The model can be applied to catchment as a semi-distributed simulation and has an inbuilt multi-reach structure for river systems. Sources of nitrogen can be from atmospheric deposition, from the terrestrial environment (e.g. agriculture, leakage from forest systems etc.), from urban areas or from direct discharges via sewage or intensive farm units. The model is a daily simulation model and can provide information in the form of time series at key sites, or as profiles down river systems or as statistical distributions. The process model is described and in a companion paper the model is applied to the River Tywi catchment in South Wales and the Great Ouse in Bedfordshire.

Housing or property? The dynamics of housing policy and property principles in the right to buy

This paper examines the interplay and tension between housing law and policy and property law, in the specific context of the right to buy (RTB). It focuses on funding arrangements between the RTB tenant and another party. It first examines how courts determine the parties' respective entitlements in the home, highlighting the difficulty of categorising, under traditional property law principles, a contribution in the form of the statutory discount conferred on the RTB tenant. Secondly, it considers possible exploitation of the RTB scheme, both at the macro level of exploitation of the policy underpinning the legislation and, at the micro level, of exploitation of the tenant. The measures contained in the Housing Act 2004 intended to curb exploitation of the RTB are analysed to determine what can be considered to be legitimate and illegitimate uses of the scheme. It is argued that, despite the government's implicit approval, certain funding arrangements by non-resident relatives fail to give effect to the spirit of the scheme.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

CSR: the co-evolution of grocery multiples in the UK (2005-2010)

Purpose – The purpose of this paper is to investigate if CSR is balanced between firm and wider society interests. Design/methodology/approach – A qualitative interpretive hermeneutic approach is used to analyse a variety of publically published secondary sources on the CSR of Tesco, Sainsburys, Morrisons and Co-operative in the UK grocery multiple sector (2005-2010). Findings – CSR strategic outcomes currently favour the firm more than society interests. A multilayered framework in the form of Social Responsibility of the Corporation (SRC) is designed and offered in support of balancing the business-society relationship more evenly. Research limitations/implications – This study is limited to firms originating from within the UK grocery multiple sector. Asda could not be included in the study as it does not publish CSR reports annually in the UK after becoming part of Walmart group. Practical implications – A framework for multi-level standardised definition of CSR in the form of SRC is offered. The inclusion of employees and members of the public on CSR/SRC boards is recommended to foster wider collaboration. The SRC framework promotes standardisation at global level while respecting diversity and firm heterogeneity at firm level. The findings may further contribute to GRI; UN Global Compact; WEF dialogues. Social implications – Recommendations are made to extend CSR board diversity for improved dialogue with communities. The SRC framework may be applied at global; national; industry and firm level. The framework can be applied internationally or locally. Future studies may offer quantitative attributes for balancing CSR/SRC. Originality/value – A globally unique and universally applicable framework for evaluating CSR activities is proposed. Future studies may extend the authors' framework to other industries, national environments or globally in the pursuit of balance between firm and society. Furthermore, firms may also adopt the framework to support CSR activities.

Multinational subsidiary sales and performance in South East Asia

We extend the theory of the multinational enterprise (MNE) by exploring the concept of subsidiary-specific advantages (SSAs) as a driver for subsidiary performance. We investigate the relationship of host country-specific advantages (host CSAs) in the form of market attractiveness, SSAs and subsidiary sales as they affect subsidiary performance. From an original primary dataset of 101 British multinational (MNE) subsidiaries in six South East Asian countries, our analysis reveals three significant findings. First, host market attractiveness has a statistically positive impact on the performance of subsidiaries. Second, the three traditional SSAs of general management, marketing capabilities and invested capital enhance subsidiary performance. Third, we examine geographic direction and types of customers for subsidiary sales by following international accounting standards. We find that these subsidiaries generate on average 95 percent of total sales from the Asia Pacific region and 91 percent of total sales from external customers. Our findings have important research and managerial implications.

Asset recombination in international partnerships as a source of improved innovation capabilities in China

Purpose This paper examines how multinational enterprises (MNEs) and local partners, including suppliers, customers, and competitors in China, improve their innovation capabilities through collaboration. We analyse this collaboration as a three-way interaction between the ownership-specific (O) advantages or firm-specific assets (FSAs) of the MNE subsidiary, the FSAs of the local partner, and the location-specific assets of the host location. Design/methodology/approach Our propositions are examined through a survey of 320 firms, supplemented with 30 in-depth case studies, based in mainland China. Findings We find that the recombination of asset-type (Oa) FSAs and transaction-type (Ot) FSAs from both partners leads to new innovation-related ownership advantages, or ‘recombinant advantages’. Ot FSAs, in the form of access to local suppliers, customers or government networks are particularly important for reducing the liability of foreignness for MNEs. Originality/value The study reveals important patterns of reciprocal transfer, sharing, and integration for different asset categories (tacit, codified) and different forms of FSA and explicitly links these to different innovation performance outcomes. The paper reports on these findings, making an empirical contribution in an important context (China-based partnerships). We also contribute to conceptual developments, connecting various kinds of FSA, tacit and codifiable assets and ‘recombinant advantages’. Limited conceptual, methodological, and empirical contributions are made in linking asset integration with (measurable) innovation performance outcomes in international partnerships.