Casimir force between sharp-shaped conductors

Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest

Classical Casimir interaction in the plane-sphere geometry

We study the Casimir interaction in the plane-sphere geometry in the classical limit of high temperatures. In this limit, the finite conductivity of the metallic plates needs to be taken into account. For the Drude model, the classical Casimir interaction is nevertheless found to be independent of the conductivity so that it can be described by a single universal function depending only on the aspect ratio $x=L/R$ where $L$ is the interplate distance and $R$ the sphere radius. This universal function differs from the one found for perfect reflectors and is in principle amenable to experimental tests. The asymptotic approach of the exact result to the Proximity Force Approximation appears to be well fitted by polynomial expansions in $\ln x$.Comment: Updated version with minor modifications and addition of a referenc

Frequency and Distribution of Refractive Error in Adult Life: Methodology and Findings of the UK Biobank Study

PURPOSE: To report the methodology and findings of a large scale investigation of burden and distribution of refractive error, from a contemporary and ethnically diverse study of health and disease in adults, in the UK.METHODS:U K Biobank, a unique contemporary resource for the study of health and disease, recruited more than half a million people aged 40-69 years. A subsample of 107,452 subjects undertook an enhanced ophthalmic examination which provided autorefraction data (a measure of refractive error). Refractive error status was categorised using the mean spherical equivalent refraction measure. Information on socio-demographic factors (age, gender, ethnicity, educational qualifications and accommodation tenure) was reported at the time of recruitment by questionnaire and face-to-face interview.RESULTS: Fifty four percent of participants aged 40-69 years had refractive error. Specifically 27% had myopia (4% high myopia), which was more common amongst younger people, those of higher socio-economic status, higher educational attainment, or of White or Chinese ethnicity. The frequency of hypermetropia increased with age (7% at 40-44 years increasing to 46% at 65-69 years), was higher in women and its severity was associated with ethnicity (moderate or high hypermetropia at least 30% less likely in non-White ethnic groups compared to White).CONCLUSIONS: Refractive error is a significant public health issue for the UK and this study provides contemporary data on adults for planning services, health economic modelling and monitoring of secular trends. Further investigation of risk factors is necessary to inform strategies for prevention. There is scope to do this through the planned longitudinal extension of the UK Biobank study

Fluctuation induced quantum interactions between compact objects and a plane mirror

The interaction of compact objects with an infinitely extended mirror plane due to quantum fluctuations of a scalar or electromagnetic field that scatters off the objects is studied. The mirror plane is assumed to obey either Dirichlet or Neumann boundary conditions or to be perfectly reflecting. Using the method of images, we generalize a recently developed approach for compact objects in unbounded space [1,2] to show that the Casimir interaction between the objects and the mirror plane can be accurately obtained over a wide range of separations in terms of charge and current fluctuations of the objects and their images. Our general result for the interaction depends only on the scattering matrices of the compact objects. It applies to scalar fields with arbitrary boundary conditions and to the electromagnetic field coupled to dielectric objects. For the experimentally important electromagnetic Casimir interaction between a perfectly conducting sphere and a plane mirror we present the first results that apply at all separations. We obtain both an asymptotic large distance expansion and the two lowest order correction terms to the proximity force approximation. The asymptotic Casimir-Polder potential for an atom and a mirror is generalized to describe the interaction between a dielectric sphere and a mirror, involving higher order multipole polarizabilities that are important at sub-asymptotic distances.Comment: 19 pages, 7 figure

Casimir forces between arbitrary compact objects: Scalar and electromagnetic field

We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as an interaction between multipoles, generated by quantum source or current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As examples, we obtain this series for two spheres with Robin boundary conditions for a scalar field and dielectric spheres for the electromagnetic field. The full interaction at all separations is obtained for spheres with Robin boundary conditions and for perfectly conducting spheres.Comment: 24 pages, 3 figures, contribution to QFEXT07 proceeding

Temporal trends in frequency, type and severity of myopia and associations with key environmental risk factors in the UK: Findings from the UK Biobank Study

This study investigated temporal trends in the epidemiology of primary myopia and associations with key environmental risk factors in a UK population. Data were collected at recruitment (non-cycloplegic autorefraction, year of birth, sex, ethnicity, highest educational attainment, reason and age of first wearing glasses and history of eye disease) from 107,442 UK Biobank study participants aged 40 to 69 years, born between 1939 and 1970. Myopia was defined as mean spherical equivalent (MSE) ≤-1 dioptre (D). Temporal changes in myopia frequency by birth cohort (5-year bands using date of birth) and associations with environmental factors were analysed, distinguishing both type (childhood-onset, <18 years versus adult-onset) and severity (three categories: low -1.00 to -2.99D, moderate -3.00 to -5.99D or high ≥-6.00D). Overall myopia frequency increased from 20.0% in the oldest cohort (births 1939-1944) to 29.2% in the youngest (1965-1970), reflecting a relatively higher increase in frequency of adult-onset and low myopia. Childhood-onset myopia peaked in participants born in 1950-54, adult-onset myopia peaked in the cohort born a decade later. The distribution of MSE only shifted for childhood-onset myopia (median: -3.8 [IQR -2.4, -5.4] to -4.4 [IQR -3.0, -6.2]). The magnitude of the association between higher educational attainment (proxy for educational intensity) and myopia overall increased over time (adjusted Odds Ratio (OR) 2.7 [2.5, 2.9] in the oldest versus 4.2 [3.3, 5.2] in the youngest cohort), being substantially greater for childhood-onset myopia (OR 3.3 [2.8, 4.0] to 8.0 [4.2, 13]). Without delineating childhood-onset from adult-onset myopia, important temporal trends would have been obscured. The differential impact of educational experience/intensity on both childhood-onset and high myopia, amplified over time, suggests a cohort effect in gene-environment interaction with potential for increasing myopia frequency if increasing childhood educational intensity is unchecked. However, historical plateauing of myopia frequency does suggest some potential for effective intervention