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.

Effects of Thomson-scattering geometry on white-light imaging of an interplanetary shock: synthetic observations from forward magnetohydrodynamic modelling

Stereoscopic white-light imaging of a large portion of the inner heliosphere has been used to track interplanetary coronal mass ejections. At large elongations from the Sun, the white-light brightness depends on both the local electron density and the efficiency of the Thomson-scattering process. To quantify the effects of the Thomson-scattering geometry, we study an interplanetary shock using forward magnetohydrodynamic simulation and synthetic white-light imaging. Identifiable as an inclined streak of enhanced brightness in a time–elongation map, the travelling shock can be readily imaged by an observer located within a wide range of longitudes in the ecliptic. Different parts of the shock front contribute to the imaged brightness pattern viewed by observers at different longitudes. Moreover, even for an observer located at a fixed longitude, a different part of the shock front will contribute to the imaged brightness at any given time. The observed brightness within each imaging pixel results from a weighted integral along its corresponding ray-path. It is possible to infer the longitudinal location of the shock from the brightness pattern in an optical sky map, based on the east–west asymmetry in its brightness and degree of polarisation. Therefore, measurement of the interplanetary polarised brightness could significantly reduce the ambiguity in performing three-dimensional reconstruction of local electron density from white-light imaging.

Enhanced levels of cold shock proteins in Listeria monocytogenes LO28 upon exposure to low temperature and high hydrostatic pressure

Listeria monocytogenes is a psychrotrophic food-borne pathogen that is problematic for the food industry because of its ubiquitous distribution in nature and its ability to grow at low temperatures and in the presence of high salt concentrations. Here we demonstrate that the process of adaptation to low temperature after cold shock includes elevated levels of cold shock proteins (CSPs) and that the levels of CSPs are also elevated after treatment with high hydrostatic pressure (HHP). Two-dimensional gel electrophoresis combined with Western blotting performed with anti-CspB of Bacillus subtilis was used to identify four 7-kDa proteins, designated Csp1, Csp2, Csp3, and Csp4. In addition, Southern blotting revealed four chromosomal DNA fragments that reacted with a csp probe, which also indicated that a CSP family is present in L. monocytogenes LO28. After a cold shock in which the temperature was decreased from 37°C to 10°C the levels of Csp1 and Csp3 increased 10- and 3.5-fold, respectively, but the levels of Csp2 and Csp4 were not elevated. Pressurization of L. monocytogenes LO28 cells resulted in 3.5- and 2-fold increases in the levels of Csp1 and Csp2, respectively. Strikingly, the level of survival after pressurization of cold-shocked cells was 100-fold higher than that of cells growing exponentially at 37°C. These findings imply that cold-shocked cells are protected from HHP treatment, which may affect the efficiency of combined preservation techniques.

Models, moulds and mass production: the mechanics of stylistic influence form the Mediterranean to Bactria

Classical Greek and Roman influence on the material culture of Central Asia and northwestern India is often considered in the abstract. This article attempts to examine the mechanisms of craft production and movement of artisans and objects which made such influence possible, through four case studies: (1) Mould-made ceramics in Hellenistic eastern Bactria; (2) Plaster casts used in the production of metalware from Begram; (3) Terracotta figurines and the moulds used to produce them, from various archaeological sites; and (4) Mass production of identical gold adornments in the nomadic tombs from Tillya Tepe. The implications of such techniques for our understanding of the development of Gandhāran art are also discussed.

A bank lending channel or a credit supply shock?

Shifts in credit supply could have a bearing on house prices e.g. through financial innovations and changes in regulation independently of the existence of a bank lending channel of monetary policy. This paper assesses the responses of US house prices to an exogenous credit supply shock and compares them with the effects from variations in credit supply associated with a bank lending channel. The contribution of the study is twofold. First, innovations in credit supply are identified using a mortgage mix variable, thereby accounting for the market-based financial intermediaries. As a robustness check a survey variable of bank lending standards for mortgage loans is also used. Second, the policy-induced credit supply effect on house prices is disentangled and compared with the effect from an exogenous credit supply shock. It is shown that in the first 3 years credit supply shocks affect house prices exogenously rather than through the bank lending channel. Monetary policy has still a large impact on house prices, even when the bank lending channel is ‘turned off’.

The physical pendulum in an advanced undergraduate course in mechanics

The physical pendulum treated with a Hamiltonian formulation is a natural topic for study in a course in advanced classical mechanics. For the past three years, we have been offering a series of problem sets studying this system numerically in our third-year undergraduate courses in mechanics. The problem sets investigate the physics of the pendulum in ways not easily accessible without computer technology and explore various algorithms for solving mechanics problems. Our computational physics is based on Mathematica with some C communicating with Mathematica, although nothing in this paper is dependent on that choice. We have nonetheless found this system, and particularly its graphics, to be a good one for use with undergraduates.

Continuum sea ice rheology determined from subcontinuum mechanics

[1] A method is presented to calculate the continuum-scale sea ice stress as an imposed, continuum-scale strain-rate is varied. The continuum-scale stress is calculated as the area-average of the stresses within the floes and leads in a region (the continuum element). The continuum-scale stress depends upon: the imposed strain rate; the subcontinuum scale, material rheology of sea ice; the chosen configuration of sea ice floes and leads; and a prescribed rule for determining the motion of the floes in response to the continuum-scale strain-rate. We calculated plastic yield curves and flow rules associated with subcontinuum scale, material sea ice rheologies with elliptic, linear and modified Coulombic elliptic plastic yield curves, and with square, diamond and irregular, convex polygon-shaped floes. For the case of a tiling of square floes, only for particular orientations of the leads have the principal axes of strain rate and calculated continuum-scale sea ice stress aligned, and these have been investigated analytically. The ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain-rate principal axes and an isotropic, continuum-scale sea ice rheology. We present a lemon-shaped yield curve with normal flow rule, derived from ensemble averages of sea ice stress, suitable for direct inclusion into the current generation of sea ice models. This continuum-scale sea ice rheology directly relates the size (strength) of the continuum-scale yield curve to the material compressive strength.

Future shock or e-hype?: the impact of online shopping on UK retail property

This research examines the impact of ecommerce on sales and rental values and on the future space and ownership/leasing requirements of UK retailers for 2000-2005. The independent study, commissioned by BCSC (and funded by BCSC Educational Trust with support from the RICS Education Trust), included a major postal survey, follow-up interviews, a retail focus group, and shopper survey and case study of Cyberton, a town in the South East of England. The study was conducted by the Research Department of The College of Estate Management between June and December 2000.

Activation of p21-activated protein kinase alpha (alpha PAK) by hyperosmotic shock in neonatal ventricular myocytes.

The p21-activated protein kinases (PAKs) may participate in signalling from Cdc42/Rac1 to the stress-regulated MAPKs (SAPKs/JNKs and p38-/HOG-1-related-MAPKs). We characterized the expression and regulation of alpha PAK in cultured ventricular myocytes. alpha PAK was specifically immunoprecipitated from myocyte extracts. High basal alpha PAK activity was detected in unstimulated myocytes. Its activity was increased rapidly (<30 s) by hyperosmotic shock in the presence of okadaic acid, and was maximal by 3 min (187 +/- 7% relative to unstimulated cells). Endothelin-1 and interleukin-1beta, which also activate SAPKs/JNKs, did not increase alpha PAK activity and presumably act through different PAK isoforms or other mechanisms.

Stimulation of multiple mitogen-activated protein kinase sub-families by oxidative stress and phosphorylation of the small heat shock protein, HSP25/27, in neonatal ventricular myocytes.

We investigated the activation of three subfamilies of mitogen-activated protein kinases (MAPKs), namely the stress-activated protein kinases/c-Jun N-terminal kinases (SAPKs/JNKs), the extracellularly responsive kinases (ERKs) and p38-MAPK, by oxidative stress as exemplified by H2O2 in primary cultures of neonatal rat ventricular myocytes. The 46 and 54 kDa species of SAPKs/JNKs were activated 5- and 10-fold, respectively, by 0.1 mM H2O2 (the maximally effective concentration). Maximal activation occurred at 15-30 min, but was still detectable after 2 h. Both ERK1 and ERK2 were activated 16-fold by 0.1 mM H2O2 with a similar time course to the SAPKs/JNKs, and this was comparable with their activation by 1 microM PMA, the most powerful activator of ERKs that we have so far identified in these cells. The activation of ERKs by H2O2 was inhibited by PD98059, which inhibits the activation of MAPK (or ERK) kinases, and by the protein kinase C (PKC) inhibitor, GF109203X. ERK activation was also inhibited by down-regulation of PMA-sensitive PKC isoforms. p38-MAPK was activated by 0.1 mM H2O2 as shown by an increase in its phosphorylation. However, maximal phosphorylation (activation) was more rapid (<5 min) than for the SAPKs/JNKs or the ERKs. We studied the downstream consequences of p38-MAPK activation by examining activation of MAPK-activated protein kinase 2 (MAPKAPK2) and phosphorylation of the MAPKAPK2 substrate, the small heat shock protein HSP25/27. As with p38-MAPK, MAPKAPK2 was rapidly activated (maximal within 5 min) by 0.1 mM H2O2. This activation was abolished by 10 microM SB203580, a selective inhibitor of certain p38-MAPK isoforms. The phosphorylation of HSP25/27 rapidly followed activation of MAPKAPK2 and was also inhibited by SB203580. Phosphorylation of HSP25/27 was associated with a decrease in its aggregation state. These data indicate that oxidative stress is a powerful activator of all three MAPK subfamilies in neonatal rat ventricular myocytes. Activation of all three MAPKs has been associated with the development of the hypertrophic phenotype. However, stimulation of p38-MAPK and the consequent phosphorylation of HSP25/27 may also be important in cardioprotection.