Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

Ideological dominance in recreation provision: towards a theory of Local Authority response to Compulsory Competitive Tendering in Britain

This paper considers how the delivery of public leisure services in Britain has been affected by the imposition of Compulsory Competitive Tendering (CCT) on the management of facilities. In particular, it focuses on the changing relationship between the central and local levels of government, theorising a tripartite local response to CCT, incorporating local statism, post-Fordist rejection of CCT and post- Fordist compliance with the aims of the central administration. The paper then discusses the actual implementation of CCT, relating the theorised responses to those witnessed in practice. This results in the delineation of a continuum of stances, ranging from pragmatic forms of local statism, such as the protection of the former direct labour force, to centrist attempts to combine the ethics of socialism with the mechanics of the market, to an outright rejection of state organisation and control. The paper concludes that although legitimate attempts have been made to protect local services, the outcome of the CCT process has undoubtedly been the regeneration of public leisure provision away from its service roots towards a market model of provision.

Animal disease and the limits of local knowledge: dealing with ticks and tick-borne diseases in South Africa

Some proponents of local knowledge, such as Sillitoe (2010), have expressed second thoughts about its capacity to effect development on the ‘revolutionary’ scale once predicted. Our argument in this article follows a similar route. Recent research into the management of livestock in South Africa makes clear that rural African livestock farmers experience uncertainty in relation to the control of stock diseases. State provision of veterinary services has been significantly reduced over the past decade. Both white and African livestock owners are to a greater extent left to their own devices. In some areas of animal disease management, African livestock owners have recourse to tried-and-tested local remedies, which are largely plant-based. But especially in the critical sphere of tick control, efficacious treatments are less evident, and livestock owners struggle to find adequate solutions to high tickloads. This is particularly important in South Africa in the early twenty-first century because land reform and the freedom to purchase land in the post-apartheid context affords African stockowners opportunities to expand livestock holdings. Our research suggests that the limits of local knowledge in dealing with ticks is one of the central problems faced by African livestock owners. We judge this not only in relation to efficacy but also the perceptions of livestock owners themselves. While confidence and practice varies, and there is increasing resort of chemical acaricides we were struck by the uncertainty of livestock owners over the best strategies.

On the approximation of local and linear radiative damping in the middle atmosphere

The validity of approximating radiative heating rates in the middle atmosphere by a local linear relaxation to a reference temperature state (i.e., ‘‘Newtonian cooling’’) is investigated. Using radiative heating rate and temperature output from a chemistry–climate model with realistic spatiotemporal variability and realistic chemical and radiative parameterizations, it is found that a linear regressionmodel can capture more than 80% of the variance in longwave heating rates throughout most of the stratosphere and mesosphere, provided that the damping rate is allowed to vary with height, latitude, and season. The linear model describes departures from the climatological mean, not from radiative equilibrium. Photochemical damping rates in the upper stratosphere are similarly diagnosed. Threeimportant exceptions, however, are found.The approximation of linearity breaks down near the edges of the polar vortices in both hemispheres. This nonlinearity can be well captured by including a quadratic term. The use of a scale-independentdamping rate is not well justified in the lower tropical stratosphere because of the presence of a broad spectrum of vertical scales. The local assumption fails entirely during the breakup of the Antarctic vortex, where large fluctuations in temperature near the top of the vortex influence longwave heating rates within the quiescent region below. These results are relevant for mechanistic modeling studies of the middle atmosphere, particularly those investigating the final Antarctic warming.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

The resting-state neurovascular coupling relationship: rapid changes in spontaneous neural activity in the somatosensory cortex are associated with haemodynamic fluctuations that resemble stimulus-evoked haemodynamics

Although promise exists for patterns of resting-state blood oxygen level-dependent (BOLD) functional magnetic resonance imaging (fMRI) brain connectivity to be used as biomarkers of early brain pathology, a full understanding of the nature of the relationship between neural activity and spontaneous fMRI BOLD fluctuations is required before such data can be correctly interpreted. To investigate this issue, we combined electrophysiological recordings of rapid changes in multi-laminar local field potentials from the somatosensory cortex of anaesthetized rats with concurrent two-dimensional optical imaging spectroscopy measurements of resting-state haemodynamics that underlie fluctuations in the BOLD fMRI signal. After neural ‘events’ were identified, their time points served to indicate the start of an epoch in the accompanying haemodynamic fluctuations. Multiple epochs for both neural ‘events’ and the accompanying haemodynamic fluctuations were averaged. We found that the averaged epochs of resting-state haemodynamic fluctuations taken after neural ‘events’ closely resembled the temporal profile of stimulus-evoked cortical haemodynamics. Furthermore, we were able to demonstrate that averaged epochs of resting-state haemodynamic fluctuations resembling the temporal profile of stimulus-evoked haemodynamics could also be found after peaks in neural activity filtered into specific electroencephalographic frequency bands (theta, alpha, beta, and gamma). This technique allows investigation of resting-state neurovascular coupling using methodologies that are directly comparable to that developed for investigating stimulus-evoked neurovascular responses.

Occupying the margins: Labour integration and social exclusion in artisanal mining in Tanzania

This article examines the marginal position of artisanal miners in sub-Saharan Africa, and considers how they are incorporated into mineral sector change in the context of institutional and legal integration. Taking the case of diamond and gold mining in Tanzania, the concept of social exclusion is used to explore the consequences of marginalization on people's access to mineral resources and ability to make a living from artisanal mining. Because existing inequalities and forms of discrimination are ignored by the Tanzanian state, the institutionalization of mineral titles conceals social and power relations that perpetuate highly unequal access to resources. The article highlights the complexity of these processes, and shows that while legal integration can benefit certain wealthier categories of people, who fit into the model of an 'entrepreneurial small-scale miner', for others adverse incorporation contributes to socio-economic dependence, exploitation and insecurity. For the issue of marginality to be addressed within integration processes, the existence of local forms of organization, institutions and relationships, which underpin inequalities and discrimination, need to be recognized.

On the difficulties of present theoretical models to predict the oxidation state of atomic Au adsorbed on regular sites of CeO2(111)

The electronic structure and oxidation state of atomic Au adsorbed on a perfect CeO2(111) surface have been investigated in detail by means of periodic density functional theory-based calculations, using the LDA+U and GGA+U potentials for a broad range of U values, complemented with calculations employing the HSE06 hybrid functional. In addition, the effects of the lattice parameter a0 and of the starting point for the geometry optimization have also been analyzed. From the present results we suggest that the oxidation state of single Au atoms on CeO2(111) predicted by LDA+U, GGA+U, and HSE06 density functional calculations is not conclusive and that the final picture strongly depends on the method chosen and on the construction of the surface model. In some cases we have been able to locate two well-defined states which are close in energy but with very different electronic structure and local geometries, one with Au fully oxidized and one with neutral Au. The energy difference between the two states is typically within the limits of the accuracy of the present exchange-correlation potentials, and therefore, a clear lowest-energy state cannot be identified. These results suggest the possibility of a dynamic distribution of Au0 and Au+ atomic species at the regular sites of the CeO2(111) surface.

Available potential energy density for a multicomponent Boussinesq fluid with arbitrary nonlinear equation of state

In this paper, the concept of available potential energy (APE) density is extended to a multicomponent Boussinesq fluid with a nonlinear equation of state. As shown by previous studies, the APE density is naturally interpreted as the work against buoyancy forces that a parcel needs to perform to move from a notional reference position at which its buoyancy vanishes to its actual position; because buoyancy can be defined relative to an arbitrary reference state, so can APE density. The concept of APE density is therefore best viewed as defining a class of locally defined energy quantities, each tied to a different reference state, rather than as a single energy variable. An important result, for which a new proof is given, is that the volume integrated APE density always exceeds Lorenz’s globally defined APE, except when the reference state coincides with Lorenz’s adiabatically re-arranged reference state of minimum potential energy. A parcel reference position is systematically defined as a level of neutral buoyancy (LNB): depending on the nature of the fluid and on how the reference state is defined, a parcel may have one, none, or multiple LNB within the fluid. Multiple LNB are only possible for a multicomponent fluid whose density depends on pressure. When no LNB exists within the fluid, a parcel reference position is assigned at the minimum or maximum geopotential height. The class of APE densities thus defined admits local and global balance equations, which all exhibit a conversion with kinetic energy, a production term by boundary buoyancy fluxes, and a dissipation term by internal diffusive effects. Different reference states alter the partition between APE production and dissipation, but neither affect the net conversion between kinetic energy and APE, nor the difference between APE production and dissipation. We argue that the possibility of constructing APE-like budgets based on reference states other than Lorenz’s reference state is more important than has been previously assumed, and we illustrate the feasibility of doing so in the context of an idealised and realistic oceanic example, using as reference states one with constant density and another one defined as the horizontal mean density field; in the latter case, the resulting APE density is found to be a reasonable approximation of the APE density constructed from Lorenz’s reference state, while being computationally cheaper.

Local and average structure in zinc cyanide: towards an understanding of the atomistic origin of negative thermal expansion

Neutron diffraction at 11.4 and 295 K and solid-state 67Zn NMR are used to determine both the local and average structures in the disordered, negative thermal expansion (NTE) material, Zn(CN)2. Solid-state NMR not only confirms that there is head-to-tail disorder of the C≡N groups present in the solid, but yields information about the relative abundances of the different Zn(CN)4-n(NC)n tetrahedral species, which do not follow a simple binomial distribution. The Zn(CN)4 and Zn(NC)4 species occur with much lower probabilities than are predicted by binomial theory, supporting the conclusion that they are of higher energy than the other local arrangements. The lowest energy arrangement is Zn(CN)2(NC)2. The use of total neutron diffraction at 11.4 K, with analysis of both the Bragg diffraction and the derived total correlation function, yields the first experimental determination of the individual Zn−N and Zn−C bond lengths as 1.969(2) and 2.030(2) Å, respectively. The very small difference in bond lengths, of ~0.06 Å, means that it is impossible to obtain these bond lengths using Bragg diffraction in isolation. Total neutron diffraction also provides information on both the average and local atomic displacements responsible for NTE in Zn(CN)2. The principal motions giving rise to NTE are shown to be those in which the carbon and nitrogen atoms within individual Zn−C≡N−Zn linkages are displaced to the same side of the Zn···Zn axis. Displacements of the carbon and nitrogen atoms to opposite sides of the Zn···Zn axis, suggested previously in X-ray studies as being responsible for NTE behavior, in fact make negligible contribution at temperatures up to 295 K.

Strong armies, slow adaptation: civil-military relations and diffusion of military power

Why are some states more willing to adopt military innovations than others? Why, for example, were the great powers of Europe able to successfully reform their military practices to better adapt to and participate in the so-called military revolution of the sixteenth and seventeenth centuries while their most important extra-European competitor, the Ottoman Empire, failed to do so? This puzzle is best explained by two factors: civil-military relations and historical timing. In the Ottoman Empire, the emergence of an institutionally strong and internally cohesive army during the early stages of state formation—in the late fourteenth century—equipped the military with substantial bargaining powers. In contrast, the great powers of Europe drew heavily on private providers of military power during the military revolution and developed similar armies only by the second half of the seventeenth century, limiting the bargaining leverage of European militaries over their rulers. In essence, the Ottoman standing army was able to block reform efforts that it believed challenged its parochial interests. Absent a similar institutional challenge, European rulers initiated military reforms and motivated officers and military entrepreneurs to participate in the ongoing military revolution.

Industrial relations in South-Eastern Europe: disaggregating the contexts

This study critically evaluates industrial relations (IR) in South-Eastern Europe and points towards future practical and research-oriented opportunities in the region. A survey of organizational policies and practices has been used to explore the state of IR in both private and public organizations in this region. Specifically, the data, collected in 2009–2010 (including the latest changes due to the economic crisis), cover 840 different organizations located in Slovenia, Serbia, Bulgaria, Greece and Cyprus. We discuss the development of ‘regional-specific’ IR policies, the ‘importing’ of varieties of capitalism models, the diffusion of the European Union social model and the role of foreign MNCs in changing IR in the region.

Leadership identity in a small island developing state: the Jamaican context

While the role of leadership in improving schools is attracting more worldwide attention, there is a need for more research investigating leaders’ experiences in different national contexts. Using focus-group and semi-structured interview data, this paper explores the background, identities and experiences of a small group of Jamaican school leaders who were involved in a leadership development programme. By drawing on the concepts of culture, socialisation and identity, the paper examines how the participants’ journeys of becoming and being school leaders are influenced by national-level societal and cultural issues, experienced at a local level. The findings suggest that in becoming school leaders, the participants perceived that they had a strong sense of agency in attempting to change the social structures within the institutions they lead and in the surrounding local communities, which in turn, they hope, will have a lasting effect on the nation as a whole.

Palaeoenvironmental evidence for the impact of the crusades on the local and regional environment of medieval (13th–16th century) northern Latvia, eastern Baltic

This paper evaluates the impact of the crusades on the landscape and environment of northern Latvia between the 13th–16th centuries (medieval Livonia). The crusades replaced tribal societies in the eastern Baltic with a religious state (Ordenstaat) run by the military orders and their allies, accompanied by significant social, cultural and economic developments. These changes have previously received little consideration in palaeoenvironmental studies of past land use in the eastern Baltic region, but are fundamental to understanding the development and expansion of a European Christian identity. Sediment cores from Lake Trikāta, located adjacent to a medieval castle and settlement, were studied using pollen, macrofossils, loss-on-ignition and magnetic susceptibility. Our results show that despite continuous agricultural land use from 500 BC, the local landscape was still densely wooded until the start of the crusades in AD 1198 when a diversified pattern of pasture, meadow and arable land use was established. Colonisation followed the crusades, although in Livonia this occurred on a much smaller scale than in the rest of the Ordenstaat; Trikāta is atypical showing significant impact following the crusades with many other palaeoenvironmental studies only revealing more limited impact from the 14th century and later. Subsequent wars and changes in political control in the post-medieval period had little apparent effect on agricultural land use.

Preferred response of the East Asian summer monsoon to local and non-local anthropogenic sulphur dioxide emissions

In this study, the atmospheric component of a state-of-the-art climate model (HadGEM2-ES) that includes earth system components such as interactive chemistry and eight species of tropospheric aerosols considering aerosol direct, indirect, and semi-direct effects, has been used to investigate the impacts of local and non-local emissions of anthropogenic sulphur dioxide on the East Asian summer monsoon (EASM). The study focuses on the fast responses (including land surface feedbacks, but without sea surface temperature feedbacks) to sudden changes in emissions from Asia and Europe. The initial responses, over days 1–40, to Asian and European emissions show large differences. The response to Asian emissions involves a direct impact on the sulphate burden over Asia, with immediate consequences for the shortwave energy budget through aerosol–radiation and aerosol–cloud interactions. These changes lead to cooling of East Asia and a weakening of the EASM. In contrast, European emissions have no significant impact on the sulphate burden over Asia, but they induce mid-tropospheric cooling and drying over the European sector. Subsequently, however, this cold and dry anomaly is advected into Asia, where it induces atmospheric and surface feedbacks over Asia and the Western North Pacific (WNP), which also weaken the EASM. In spite of very different perturbations to the local aerosol burden in response to Asian and European sulphur dioxide emissions, the large scale pattern of changes in land–sea thermal contrast, atmospheric circulation and local precipitation over East Asia from days 40 onward exhibits similar structures, indicating a preferred response, and suggesting that emissions from both regions likely contributed to the observed weakening of the EASM. Cooling and drying of the troposphere over Asia, together with warming and moistening over the WNP, reduces the land–sea thermal contrast between the Asian continent and surrounding oceans. This leads to high sea level pressure (SLP) anomalies over Asia and low SLP anomalies over the WNP, associated with a weakened EASM. In response to emissions from both regions warming and moistening over the WNP plays an important role and determines the time scale of the response.