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.

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.

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.

Does bacterial density in cystic fibrosis sputum increase prior to pulmonary exacerbation?

These findings strongly suggest that CFPE do not generally result from increased bacterial density within the airways. Instead, data presented here are consistent with alternative models of pulmonary exacerbation.

MEF2C-MYOCD and leiomodin1 suppression by miRNA-214 promotes smooth muscle cell phenotype switching in pulmonary arterial hypertension

Background Vascular hyperproliferative disorders are characterized by excessive smooth muscle cell (SMC) proliferation leading to vessel remodeling and occlusion. In pulmonary arterial hypertension (PAH), SMC phenotype switching from a terminally differentiated contractile to synthetic state is gaining traction as our understanding of the disease progression improves. While maintenance of SMC contractile phenotype is reportedly orchestrated by a MEF2C-myocardin (MYOCD) interplay, little is known regarding molecular control at this nexus. Moreover, the burgeoning interest in microRNAs (miRs) provides the basis for exploring their modulation of MEF2C-MYOCD signaling, and in turn, a pro-proliferative, synthetic SMC phenotype. We hypothesized that suppression of SMC contractile phenotype in pulmonary hypertension is mediated by miR-214 via repression of the MEF2C-MYOCD-leiomodin1 (LMOD1) signaling axis. Methods and Results In SMCs isolated from a PAH patient cohort and commercially obtained hPASMCs exposed to hypoxia, miR-214 expression was monitored by qRT-PCR. miR-214 was upregulated in PAH- vs. control subject hPASMCs as well as in commercially obtained hPASMCs exposed to hypoxia. These increases in miR-214 were paralleled by MEF2C, MYOCD and SMC contractile protein downregulation. Of these, LMOD1 and MEF2C were directly targeted by the miR. Mir-214 overexpression mimicked the PAH profile, downregulating MEF2C and LMOD1. AntagomiR-214 abrogated hypoxia-induced suppression of the contractile phenotype and its attendant proliferation. Anti-miR-214 also restored PAH-PASMCs to a contractile phenotype seen during vascular homeostasis. Conclusions Our findings illustrate a key role for miR-214 in modulation of MEF2C-MYOCD-LMOD1 signaling and suggest that an antagonist of miR-214 could mitigate SMC phenotype changes and proliferation in vascular hyperproliferative disorders including PAH.

CD28 Exerts Protective and Detrimental Effects in a Pulmonary Model of Paracoccidioidomycosis

T-cell immunity has been claimed as the main immunoprotective mechanism against Paracoccidioides brasiliensis infection, the most important fungal infection in Latin America. As the initial events that control T-cell activation in paracoccidioidomycosis (PCM) are not well established, we decided to investigate the role of CD28, an important costimulatory molecule for the activation of effector and regulatory T cells, in the immunity against this pulmonary pathogen. Using CD28-deficient (CD28(-/-)) and normal wild-type (WT) C57BL/6 mice, we were able to demonstrate that CD28 costimulation determines in pulmonary paracoccidioidomycosis an early immunoprotection but a late deleterious effect associated with impaired immunity and uncontrolled fungal growth. Up to week 10 postinfection, CD28(-/-) mice presented increased pulmonary and hepatic fungal loads allied with diminished production of antibodies and pro-and anti-inflammatory cytokines besides impaired activation and migration of effector and regulatory T (Treg) cells to the lungs. Unexpectedly, CD28-sufficient mice progressively lost the control of fungal growth, resulting in an increased mortality associated with persistent presence of Treg cells, deactivation of inflammatory macrophages and T cells, prevalent presence of anti-inflammatory cytokines, elevated fungal burdens, and extensive hepatic lesions. As a whole, our findings suggest that CD28 is required for the early protective T-cell responses to P. brasiliensis infection, but it also induces the expansion of regulatory circuits that lately impair adaptive immunity, allowing uncontrolled fungal growth and overwhelming infection, which leads to precocious mortality of mice.