Casimir effect for the scalar field under Robin boundary conditions: A functional integral approach

In this work we show how to define the action of a scalar field in a such a way that Robin boundary condition is implemented dynamically, i.e., as a consequence of the stationary action principle. We discuss the quantization of that system via functional integration. Using this formalism, we derive an expression for the Casimir energy of a massless scalar field under Robin boundary conditions on a pair of parallel plates, characterized by constants $c_1$ and $c_2$. Some special cases are discussed; in particular, we show that for some values of $c_1$ and $c_2$ the Casimir energy as a function of the distance between the plates presents a minimum. We also discuss the renormalization at one-loop order of the two-point Green function in the $\lambda\phi^4$ theory submitted to Robin boundary condition on a plate.Comment: 16 pages, 2 figures. Version 2: contains a new section on the renormalization of the two-point Green function in the presence of a flat boundary. Accepted for publication in J. Phys.

Casimir Effect: The Classical Limit

We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the ``relative Casimir energy", which we define for a configuration of disjoint conducting boundaries of arbitrary shapes, as the difference of Casimir energies between the given configuration and a configuration with the same boundaries infinitely far apart. Using path integration techniques, we show that the relative Casimir energy vanishes exponentially fast in temperature. This is consistent with a simple physical argument based on Kirchhoff's law. As a result the ``relative Casimir entropy", which we define in an obviously analogous manner, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the boundaries. Thus the Casimir force between disjoint pieces of the boundary, in the classical limit, is entropy driven and is governed by a dimensionless number characterizing the geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations in temperature from the behavior just described. These logarithmic deviations seem to arise due to our difficulty to separate the Casimir energy (and the other thermodynamical quantities) from the ``electromagnetic'' self-energy of each of the connected components of the boundary in a well defined manner. Our approach to the Casimir effect is not to impose sharp boundary conditions on the fluctuating field, but rather take into consideration its interaction with the plasma of ``charge carriers'' in the boundary, with the plasma frequency playing the role of a physical UV cutoff. This also allows us to analyze deviations from a perfect conductor behavior.Comment: latex, 56 pages, one eps figure. Major improvements of presentation (especially in Section 2). No change in the conclusions. Connection with the works of Balian et al. on the Casimir effect is clarified. Abstract changed, typos correcte

Topology, Mass and Casimir energy

The vacuum expectation value of the stress energy tensor for a massive scalar field with arbitrary coupling in flat spaces with non-trivial topology is discussed. We calculate the Casimir energy in these spaces employing the recently proposed {\it optical approach} based on closed classical paths. The evaluation of the Casimir energy consists in an expansion in terms of the lengths of these paths. We will show how different paths with corresponding weight factors contribute in the calculation. The optical approach is also used to find the mass and temperature dependence of the Casimir energy in a cavity and it is shown that the massive fields cannot be neglected in high and low temperature regimes. The same approach is applied to twisted as well as spinor fields and the results are compared with those in the literature.Comment: 18 pages, 1 figure, RevTex format, Typos corrected and references adde

Decoupling Inflation From the String Scale

When Inflation is embedded in a fundamental theory, such as string theory, it typically begins when the Universe is already substantially larger than the fundamental scale [such as the one defined by the string length scale]. This is naturally explained by postulating a pre-inflationary era, during which the size of the Universe grew from the fundamental scale to the initial inflationary scale. The problem then arises of maintaining the [presumed] initial spatial homogeneity throughout this era, so that, when it terminates, Inflation is able to begin in its potential-dominated state. Linde has proposed that a spacetime with compact negatively curved spatial sections can achieve this, by means of chaotic mixing. Such a compactification will however lead to a Casimir energy, which can lead to effects that defeat the purpose unless the coupling to gravity is suppressed. We estimate the value of this coupling required by the proposal, and use it to show that the pre-inflationary spacetime is stable, despite the violation of the Null Energy Condition entailed by the Casimir energy.Comment: 24 pages, 5 eps figures, references added, stylistic changes, version to appear in Classical and Quantum Gravit

Should the Arteriovenous Fistula Be Created before Starting Dialysis?: A Decision Analytic Approach

Background: An arteriovenous fistula (AVF) is considered the vascular access of choice, but uncertainty exists about the\ud optimal time for its creation in pre-dialysis patients. The aim of this study was to determine the optimal vascular access\ud referral strategy for stage 4 (glomerular filtration rate ,30 ml/min/1.73 m2) chronic kidney disease patients using a decision\ud analytic framework.\ud Methods: A Markov model was created to compare two strategies: refer all stage 4 chronic kidney disease patients for an\ud AVF versus wait until the patient starts dialysis. Data from published observational studies were used to estimate the\ud probabilities used in the model. A Markov cohort analysis was used to determine the optimal strategy with life expectancy\ud and quality adjusted life expectancy as the outcomes. Sensitivity analyses, including a probabilistic sensitivity analysis, were\ud performed using Monte Carlo simulation.\ud Results: The wait strategy results in a higher life expectancy (66.6 versus 65.9 months) and quality adjusted life expectancy\ud (38.9 versus 38.5 quality adjusted life months) than immediate AVF creation. It was robust across all the parameters except\ud at higher rates of progression and lower rates of ischemic steal syndrome.\ud Conclusions: Early creation of an AVF, as recommended by most guidelines, may not be the preferred strategy in all predialysis\ud patients. Further research on cost implications and patient preferences for treatment options needs to be done\ud before recommending early AVF creation

Abrasive, Silica Phytoliths and the Evolution of Thick Molar Enamel in Primates, with Implications for the Diet of Paranthropus boisei

Background: Primates—including fossil species of apes and hominins—show variation in their degree of molar enamel thickness, a trait long thought to reflect a diet of hard or tough foods. The early hominins demonstrated molar enamel thickness of moderate to extreme degrees, which suggested to most researchers that they ate hard foods obtained on or near the ground, such as nuts, seeds, tubers, and roots. We propose an alternative hypothesis—that the amount of phytoliths in foods correlates with the evolution of thick molar enamel in primates, although this effect is constrained by a species ’ degree of folivory. Methodology/Principal Findings: From a combination of dietary data and evidence for the levels of phytoliths in plant families in the literature, we calculated the percentage of plant foods rich in phytoliths in the diets of twelve extant primates with wide variation in their molar enamel thickness. Additional dietary data from the literature provided the percentage of each primate’s diet made up of plants and of leaves. A statistical analysis of these variables showed that the amount of abrasive silica phytoliths in the diets of our sample primates correlated positively with the thickness of their molar enamel, constrained by the amount of leaves in their diet (R 2 = 0.875; p,.0006). Conclusions/Significance: The need to resist abrasion from phytoliths appears to be a key selective force behind the evolution of thick molar enamel in primates. The extreme molar enamel thickness of the teeth of the East African homini

The possible role of local air pollution in climate change in West Africa

The climate of West Africa is characterized by a sensitive monsoon system that is associated with marked natural precipitation variability. This region has been and is projected to be subject to substantial global and regional-scale changes including greenhouse-gas-induced warming and sea-level rise, land-use and land-cover change, and substantial biomass burning. We argue that more attention should be paid to rapidly increasing air pollution over the explosively growing cities of West Africa, as experiences from other regions suggest that this can alter regional climate through the influences of aerosols on clouds and radiation, and will also affect human health and food security. We need better observations and models to quantify the magnitude and characteristics of these impacts

Seizure prediction : ready for a new era

Acknowledgements: The authors acknowledge colleagues in the international seizure prediction group for valuable discussions. L.K. acknowledges funding support from the National Health and Medical Research Council (APP1130468) and the James S. McDonnell Foundation (220020419) and acknowledges the contribution of Dean R. Freestone at the University of Melbourne, Australia, to the creation of Fig. 3.Peer reviewedPostprin