Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Understanding the long term success of UK construction firms: the extent and role of 'hidden' corporate social responsibility

The construction sector is often described as lagging behind other major industries. At first this appears fair when considering the concept of corporate social responsibility (CSR). It is argued that CSR is ill-defined, with firms struggling to make sense of and engage with it. Literature suggests that the short-termism view of construction firms renders the long-term, triple-bottom-line principle of CSR untenable. This seems to be borne out by literature indicating that construction firms typically adopt a compliance-based approach to CSR instead of discretionary CSR which is regarded as adding most value to firms and benefiting the broadest group of stakeholders. However, this research conducted in the UK using a regional construction firm offers a counter argument whereby discretionary CSR approaches are well embedded and enacted within the firms’ business operations even though they are not formally articulated as CSR strategies and thus remain 'hidden'. This raises questions in the current CSR debate. First, is ‘hidden’ CSR relevant to the long term success of construction firms? and to what extent do these firms need to reinvent themselves to formally take advantage of the CSR agenda?

On the universal TRO of a JC*-triple, ideals and tensor products

In a development from material introduced in recent work, we discuss the interconnections between ternary rings of operators (TROs) and right C*-algebras generated by JC*-triples, deducing that every JC*-triple possesses a largest universally reversible ideal, that the universal TRO commutes with appropriate tensor products and establishing a reversibility criterion for type I JW*-triples.

A theoretical framework for energy and momentum consistency in subgrid-scale parameterization for climate models

A theoretical framework for the joint conservation of energy and momentum in the parameterization of subgrid-scale processes in climate models is presented. The framework couples a hydrostatic resolved (planetary scale) flow to a nonhydrostatic subgrid-scale (mesoscale) flow. The temporal and horizontal spatial scale separation between the planetary scale and mesoscale is imposed using multiple-scale asymptotics. Energy and momentum are exchanged through subgrid-scale flux convergences of heat, pressure, and momentum. The generation and dissipation of subgrid-scale energy and momentum is understood using wave-activity conservation laws that are derived by exploiting the (mesoscale) temporal and horizontal spatial homogeneities in the planetary-scale flow. The relations between these conservation laws and the planetary-scale dynamics represent generalized nonacceleration theorems. A derived relationship between the wave-activity fluxes-which represents a generalization of the second Eliassen-Palm theorem-is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

Retributivists! The harm principle is not for you!

Retributivism is often explicitly or implicitly assumed to be compatible with the harm principle, since the harm principle (in some guises) concerns the content of the criminal law, whilst retributivism concerns the punishment of those that break the law. In this essay I show that retributivism should not be endorsed alongside any version of the harm principle. For some versions of the harm principle, this is because retributivism is logically incompatible with it, or its grounds. For others, retributivists can only endorse the harm principle at the cost of endorsing implausible positions about the content of the criminal law.

An experimental test of response consistency in contingent valuation

We compare hypothetical and observed (experimental) willingness to pay (WTP) for a gradual improvement in the environmental performance of a marketed good (an office table). First, following usual practices in marketing research, subjects’ stated WTP for the improvement is obtained. Second, the same subjects participate in a real reward experiment designed to replicate the scenario valued in the hypothetical question. Our results show that, independently of the degree of the improvement, there are no significant median differences between stated and experimental data. However, subjects reporting extreme values of WTP (low or high) exhibit a more moderate behavior in the experiment.

Do real balance effects invalidate the Taylor principle in closed and open economies?

This paper examines the determinacy implications of forecast-based monetary policy rules that set the interest rate in response to expected future inflation in a Neo-Wicksellian model that incorporates real balance effects. We show that the presence of such effects in closed economies restricts the ability of the Taylor principle to prevent indeterminacy of the rational expectations equilibrium. The problem is exacerbated in open economies, particularly if the policy rule reacts to consumer-price, rather than domestic-price, inflation. However, determinacy can be restored in both closed and open economies with the addition of monetary policy inertia.

Fractal geometry of aggregate snowflakes revealed by triple wavelength radar measurements

Radar reflectivity measurements from three different wavelengths are used to retrieve information about the shape of aggregate snowflakes in deep stratiform ice clouds. Dual-wavelength ratios are calculated for different shape models and compared to observations at 3, 35 and 94 GHz. It is demonstrated that many scattering models, including spherical and spheroidal models, do not adequately describe the aggregate snowflakes that are observed. The observations are consistent with fractal aggregate geometries generated by a physically-based aggregation model. It is demonstrated that the fractal dimension of large aggregates can be inferred directly from the radar data. Fractal dimensions close to 2 are retrieved, consistent with previous theoretical models and in-situ observations.

HESS Opinions: On forecast (in)consistency in a hydro-meteorological chain: curse or blessing?

Flood forecasting increasingly relies on numerical weather prediction forecasts to achieve longer lead times. One of the key difficulties that is emerging in constructing a decision framework for these flood forecasts is what to dowhen consecutive forecasts are so different that they lead to different conclusions regarding the issuing of warnings or triggering other action. In this opinion paper we explore some of the issues surrounding such forecast inconsistency (also known as "Jumpiness", "Turning points", "Continuity" or number of "Swings"). In thsi opinion paper we define forecast inconsistency; discuss the reasons why forecasts might be inconsistent; how we should analyse inconsistency; and what we should do about it; how we should communicate it and whether it is a totally undesirable property. The property of consistency is increasingly emerging as a hot topic in many forecasting environments.

Neural stem cells, inflammation and NF-kappaB: basic principle of maintenance and repair or origin of brain tumours?

Several recent reports suggest that inflammatory signals play a decisive role in the self-renewal, migration and differentiation of multipotent neural stem cells (NSCs). NSCs are believed to be able to ameliorate the symptoms of several brain pathologies through proliferation, migration into the area of the lesion and either differentiation into the appropriate cell type or secretion of anti-inflammatory cytokines. Although NSCs have beneficial roles, current evidence indicates that brain tumours, such as astrogliomas or ependymomas are also caused by tumour-initiating cells with stem-like properties. However, little is known about the cellular and molecular processes potentially generating tumours from NSCs. Most pro-inflammatory conditions are considered to activate the transcription factor NF-kappaB in various cell types. Strong inductive effects of NF-kappaB on proliferation and migration of NSCs have been described. Moreover, NF-kappaB is constitutively active in most tumour cells described so far. Chronic inflammation is also known to initiate cancer. Thus, NF-kappaB might provide a novel mechanistic link between chronic inflammation, stem cells and cancer. This review discusses the apparently ambivalent role of NF-kappaB: physiological maintenance and repair of the brain via NSCs, and a potential role in tumour initiation. Furthermore, it reveals a possible mechanism of brain tumour formation based on inflammation and NF-kappaB activity in NSCs.