Geometrical optics for scalar, electromagnetic and gravitational waves in curved spacetime

The geometrical-optics expansion reduces the problem of solving wave equations to one of solving transport equations along rays. Here we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general relativity. We show that each is governed by a wave equation with the same principal part. It follows that: each wave propagates at the speed of light along rays (null generators of hypersurfaces of constant phase); the square of the wave amplitude varies in inverse proportion to the cross section of the beam; and the polarization is parallel-propagated along the ray (the Skrotskii/Rytov effect). We show that the optical scalars for a beam, and various Newman-Penrose scalars describing a parallel-propagated null tetrad, can be found by solving transport equations in a second-order formulation. Unlike the Sachs equations, this formulation makes it straightforward to find such scalars beyond the first conjugate point of a congruence, where neighbouring rays cross, and the scalars diverge. We discuss differential precession across the beam which leads to a modified phase in the geometrical-optics expansion.Comment: 17 pages, 1 figure. Proceedings for IV Amazonian Symposium on Physics, Belem, Brazil at UFPA on 18-22 Sep 201

The Information Geometry of the One-Dimensional Potts Model

In various statistical-mechanical models the introduction of a metric onto the space of parameters (e.g. the temperature variable, $\beta$, and the external field variable, $h$, in the case of spin models) gives an alternative perspective on the phase structure. For the one-dimensional Ising model the scalar curvature, ${\cal R}$, of this metric can be calculated explicitly in the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) / \sqrt{\sinh^2 (h) + \exp (- 4 \beta)}$. This is positive definite and, for physical fields and temperatures, diverges only at the zero-temperature, zero-field ``critical point'' of the model. In this note we calculate ${\cal R}$ for the one-dimensional $q$-state Potts model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B (q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts analogue of $\sinh^2 (h) + \exp (- 4 \beta)$. This is no longer positive definite, but once again it diverges only at the critical point in the space of real parameters. We remark, however, that a naive analytic continuation to complex field reveals a further divergence in the Ising and Potts curvatures at the Lee-Yang edge.Comment: 9 pages + 4 eps figure

It’s driving her mad: gender differences in the effects of commuting on psychological well-being

In this paper, we seek to explore the effects of commuting time on the psychological well-being of men and women in the UK. We use annual data from the British Household Panel Survey in a fixed effects panel framework that includes variables known to determine well-being, as well as factors which may provide compensation for commuting such as income, job satisfaction and housing quality. Our results show that, even after all these variables are considered, commuting still has an important detrimental effect on the well-being of women, but not men, and this result is robust to numerous different specifications. We explore possible explanations for this gender difference and can find no evidence that it is due to women´s shorter working hours or weaker occupational position. Rather women´s greater sensitivity to commuting time seems to be a result of their larger responsibility for day-to-day household tasks, including childcare

Measuring the societal value of lifetime health

This paper considers two societal concerns in addition to health maximisation: first, concerns for the societal value of lifetime health for an individual; and second, concerns for the value of lifetime health across individuals. Health-related social welfare functions (HRSWFs) have addressed only the second concern. We propose a model that expresses the former in a metric – the adult healthy-year equivalent (AHYE) – that can be incorporated into standard HRSWFs. An empirical study based on this formulation shows that both factors matter: health losses in childhood are weighted more heavily than losses in adulthood and respondents wish to reduce inequalities in AHYEs

Measuring the societal value of lifetime health

This paper considers two societal concerns in addition to health maximisation: first, concerns for the societal value of lifetime health for an individual; and second, concerns for the value of lifetime health across individuals. Health-related social welfare functions (HRSWFs) have addressed only the second concern. We propose a model that expresses the former in a metric – the adult healthy-year equivalent (AHYE) – that can be incorporated into standard HRSWFs. An empirical study based on this formulation shows that both factors matter: health losses in childhood are weighted more heavily than losses in adulthood and respondents wish to reduce inequalities in AHYEs

Hardening electronic devices against very high total dose radiation environments

The possibilities and limitations of hardening silicon semiconductor devices to the high neutron and gamma radiation levels and greater than 10 to the eighth power rads required for the NERVA nuclear engine development are discussed. A comparison is made of the high dose neutron and gamma hardening potential of bipolar, metal insulator semiconductors and junction field effect transistors. Experimental data is presented on device degradation for the high neutron and gamma doses. Previous data and comparisons indicate that the JFET is much more immune to the combined neutron displacement and gamma ionizing effects than other transistor types. Experimental evidence is also presented which indicates that p channel MOS devices may be able to meet the requirements

The Standard Model Fermion Spectrum From Complex Projective spaces

It is shown that the quarks and leptons of the standard model, including a right-handed neutrino, can be obtained by gauging the holonomy groups of complex projective spaces of complex dimensions two and three. The spectrum emerges as chiral zero modes of the Dirac operator coupled to gauge fields and the demonstration involves an index theorem analysis on a general complex projective space in the presence of topologically non-trivial SU(n)xU(1) gauge fields. The construction may have applications in type IIA string theory and non-commutative geometry.Comment: 13 pages. Typset using LaTeX and JHEP3 style files. Minor typos correcte