Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic and conservative interactions

We present a generalization of the Green-Kubo expressions for thermal transport coefficients $\mu$ in complex fluids of the generic form, $\mu= \mu_\infty +\int^\infty_0 dt V^{-1} _0$, i.e. a sum of an instantaneous transport coefficient $\mu_\infty$, and a time integral over a time correlation function in a state of thermal equilibrium between a current $J$ and a transformed current $J_\epsilon$. The streaming operator $\exp(t{\cal L})$ generates the trajectory of a dynamical variable $J(t) =\exp(t{\cal L}) J$ when used inside the thermal average $_0$. These formulas are valid for conservative, impulsive (hard spheres), stochastic and dissipative forces (Langevin fluids), provided the system approaches a thermal equilibrium state. In general $\mu_\infty \neq 0$ and $J_\epsilon \neq J$, except for the case of conservative forces, where the equality signs apply. The most important application in the present paper is the hard sphere fluid.Comment: 14 pages, no figures. Version 2: expanded Introduction and section II specifying the classes of fluids covered by this theory. Some references added and typos correcte

Structural Properties of Self-Attracting Walks

Self-attracting walks (SATW) with attractive interaction u > 0 display a swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >= 2, analogous to the \Theta transition of polymers. We are interested in the structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo simulations, we find that for u<u_{\mathrm{c}}, the structures are in the universality class of clusters generated by simple random walks. For u>u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class. The clusters are compact in both d=2 and d=3, but their interface is fractal: d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In d=1, where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites and the mean time to visit S sites.Comment: 15 pages, 8 postscript figures, submitted to Phys. Rev.

The labour supply effect of Education Maintenance Allowance and its implications for parental altruism

Education Maintenance Allowance (EMA) was a UK government cash transfer paid directly to children aged 16–18, in the first 2 years of post-compulsory full-time education. This paper uses the labour supply effect of EMA to infer the magnitude of the transfer response made by the parent, and so test for the presence of an ‘effectively altruistic’ head-of-household, who redistributes resources among household members so as to maximise overall welfare. Using data from the Longitudinal Study of Young People in England, an EMA payment of £30 per week is found to reduce teenagers’ labour supply by 3 h per week and probability of employment by 13 % points from a base of 43 %. We conclude that parents withdraw cash and in-kind transfers from their children to a value of between 22 and 86 % of what the child receives in EMA. This means we reject the hypothesis of an effectively altruistic head-of-household, and argue that making this cash transfer directly to the child produces higher child welfare than if the equivalent transfer were made to parents

Strain-Specific Differences in the Genetic Control of Two Closely Related Mycobacteria

The host response to mycobacterial infection depends on host and pathogen genetic factors. Recent studies in human populations suggest a strain specific genetic control of tuberculosis. To test for mycobacterial-strain specific genetic control of susceptibility to infection under highly controlled experimental conditions, we performed a comparative genetic analysis using the A/J- and C57BL/6J-derived recombinant congenic (RC) mouse panel infected with the Russia and Pasteur strains of Mycobacterium bovis Bacille Calmette Guérin (BCG). Bacillary counts in the lung and spleen at weeks 1 and 6 post infection were used as a measure of susceptibility. By performing genome-wide linkage analyses of loci that impact on tissue-specific bacillary burden, we were able to show the importance of correcting for strain background effects in the RC panel. When linkage analysis was adjusted on strain background, we detected a single locus on chromosome 11 that impacted on pulmonary counts of BCG Russia but not Pasteur. The same locus also controlled the splenic counts of BCG Russia but not Pasteur. By contrast, a locus on chromosome 1 which was indistinguishable from Nramp1 impacted on splenic bacillary counts of both BCG Russia and Pasteur. Additionally, dependent upon BCG strain, tissue and time post infection, we detected 9 distinct loci associated with bacillary counts. Hence, the ensemble of genetic loci impacting on BCG infection revealed a highly dynamic picture of genetic control that reflected both the course of infection and the infecting strain. This high degree of adaptation of host genetics to strain-specific pathogenesis is expected to provide a suitable framework for the selection of specific host-mycobacteria combinations during co-evolution of mycobacteria with humans