Casimir forces for inhomogeneous planar media

Casimir forces arise from vacuum uctuations. They are fully understood only for simple models, and are important in nano- and microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases condence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green's functions is at the boundary of current computer algebra technology. We further demonstrate that Lifshitz theory of electromagnetic vacuum energy can not be directly applied to calculate the Casimir stress for models of this type, and produce results that have led to alternative regularisations. Using a combination of our new computational framework and the new theory based on our results, we provide specic calculations of Casimir forces for planar dielectrics having permittivity that declines exponentially. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and describe a combined numerical and symbolic computational framework for calculating Casimir forces for arbitrary planar models.Publisher PD

The Investigation of Metameric Grays for the Testing of Spectral Changes in the D5000 Standard Illuminant

Very often, different results are obtained when colored originals and/or reproductions under different so-called standard light sources are evaluated. A possible explanation for the different results is that not all admissible standard sources have the same spectral power distribution, either due to differences in manufacturing or due to aging. A possible solution to the problem would be to determine how the spectral power distribution of a given illuminant differs from the standard (D5000) distribution by visually comparing suitable metameric grays with a stable non-selective gray under the illuminant in question. This comparison would serve as a quick and inexpensive way of testing the light source. Two major questions are involved in this investigation: (1) Are the color differences obtainable with metamers large enough to be useful? (2) What part does the variation of color response of individual observers play in this system? The first question was investigated using two sets of metameric grays data: initially Wyszecki\u27s metamers and systematic changes in the D5000 power distribution; and then MacAdam\u27s metameric grays based on real pigments from spectrophotometric data. The results for Wyszecki\u27s metamers indicated that reasonable color differences occurred between non-selective gray and metameric grays with systematic changes in the spectral power distribution of the illuminant. Similar results were obtained for MacAdam\u27s metamers but with less sensitivity, that is, there were smaller differences between the non-selective gray and the metameric grays. It was found that deviations from the D5000 spectral composition can indeed be picked up and the method is sufficiently sensitive for the Standard Observer. The second question, the variation of individual observers, was investigated using information based on the measurements by Stiles and Burch, and also the Standard Deviate Observer determined by Eugene Allen. The investigation was done by obtaining the color differences relating to the individual observers, and comparing them to the Standard Observer when comparing the selective and non-selective grays to the standard D5000 sources. The result of this investigation indicated that the color differences due to the variations between observers were larger than the color differences between the non- selective gray and the metameric grays due to the changes in the power distribution of the source. The conclusion is that this system of determining the changes in the spectral power distribution of the light source by the color differences between non-selective and selective metameric grays is inadequate because of the variances in individual observers

Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field

Chirality is one of the most fundamental properties of many physical, chemical and biological systems. However, the mechanisms underlying the onset and control of chiral symmetry are largely understudied. We investigate possibility of chirality control in a chemical excitable system (the BZ reaction) by application of a chiral (rotating) electric field using the Oregonator model. We find that unlike previous findings, we can achieve the chirality control not only in the field rotation direction, but also opposite to it, depending on the field rotation frequency. To unravel the mechanism, we further develop a comprehensive theory of frequency synchronization based on the response function approach. We find that this problem can be described by the Adler equation and show phase-locking phenomena, known as the Arnold tongue. Our theoretical predictions are in good quantitative agreement with the numerical simulations and provide a solid basis for chirality control in excitable media.Comment: 21 pages with 9 figures; update references; to appear in J. Chem. Phy

Compatibility of theta13 and the Type I Seesaw Model with A4 Symmetry

We derive formulae for neutrino masses and mixing angles in a type I seesaw framework with an underlying A4 flavor symmetry. In particular, the Majorana neutrino mass matrix includes contributions from an A4 triplet, 1, 1', and 1" flavon fields. Using these formulae, we constrain the general A4 parameter space using the updated global fits on neutrino mixing angles and mass squared differences, including results from the Daya Bay and RENO experiments, and we find predictive relations among the mixing parameters for certain choices of the triplet vacuum expectation value. In the normal hierarchy case, sizable deviation from maximal atmospheric mixing is predicted, and such deviation is strongly correlated with the value of theta13 in the range of ~ (8-10) degrees. On the other hand, such deviation is negligible and insensitive to theta13 in the inverted mass hierarchy case. We also show expectations for the Dirac CP phase resulting from the parameter scan. Future refined measurements of neutrino mixing angles will test these predicted correlations and potentially show evidence for particular triplet vev patterns.Comment: 22 Pages, 3 Figures; v2: version to appear in JHE

Riesz bases of exponentials for multi-tiling measures

Let $G$ be a closed subgroup of ${\mathbb R}^d$ and let $\nu$ be a Borel probability measure admitting a Riesz basis of exponentials with frequency sets in the dual group $G^{\perp}$. We form a multi-tiling measure $\mu = \mu_1+...+\mu_N$ where $\mu_i$ is translationally equivalent to $\nu$ and different $\mu_i$ and $\mu_j$ have essentially disjoint support. We obtain some necessary and sufficient conditions for $\mu$ to admit a Riesz basis of exponentials . As an application, the square boundary, after a rotation, is a union of two fundamental domains of $G = {\mathbb Z}\times {\mathbb R}$ and can be regarded as a multi-tiling measure. We show that, unfortunately, the square boundary does not admit a Riesz basis of exponentials of the form as a union of translate of discrete subgroups ${\mathbb Z}\times \{0\}$. This rules out a natural candidate of potential Riesz basis for the square boundary.Comment: To appear in Sampling Theory, Signal Processing, and Data Analysi

Longitudinal imaging of microvascular remodelling in proliferative diabetic retinopathy using adaptive optics scanning light ophthalmoscopy

Purpose To characterise longitudinal changes in the retinal microvasculature of type 2 diabetes mellitus (T2DM) as exemplified in a patient with proliferative diabetic retinopathy (PDR) using an adaptive optics scanning light ophthalmoscope (AOSLO). Methods A 35-year-old T2DM patient with PDR treated with scatter pan-retinal photocoagulation at the inferior retina 1 day prior to initial AOSLO imaging along with a 24-year-old healthy control were imaged in this study. AOSLO vascular structural and perfusion maps were acquired at four visits over a 20-week period. Capillary diameter and microaneurysm area changes were measured on the AOSLO structural maps. Imaging repeatability was established using longitudinal imaging of microvasculature in the healthy control. Results Capillary occlusion and recanalisation, capillary dilatation, resolution of local retinal haemorrhage, capillary hairpin formation, capillary bend formation, microaneurysm formation, progression and regression were documented over time in a region 2° superior to the fovea in the PDR patient. An identical microvascular network with same capillary diameter was observed in the control subject over time. Conclusions High-resolution serial AOSLO imaging enables in vivo observation of vasculopathic changes seen in diabetes mellitus. The implications of this methodology are significant, providing the opportunity for studying the dynamics of the pathological process, as well as the possibility of identifying highly sensitive and non-invasive biomarkers of end organ damage and response to treatment

A Language and Hardware Independent Approach to Quantum-Classical Computing

Heterogeneous high-performance computing (HPC) systems offer novel architectures which accelerate specific workloads through judicious use of specialized coprocessors. A promising architectural approach for future scientific computations is provided by heterogeneous HPC systems integrating quantum processing units (QPUs). To this end, we present XACC (eXtreme-scale ACCelerator) --- a programming model and software framework that enables quantum acceleration within standard or HPC software workflows. XACC follows a coprocessor machine model that is independent of the underlying quantum computing hardware, thereby enabling quantum programs to be defined and executed on a variety of QPUs types through a unified application programming interface. Moreover, XACC defines a polymorphic low-level intermediate representation, and an extensible compiler frontend that enables language independent quantum programming, thus promoting integration and interoperability across the quantum programming landscape. In this work we define the software architecture enabling our hardware and language independent approach, and demonstrate its usefulness across a range of quantum computing models through illustrative examples involving the compilation and execution of gate and annealing-based quantum programs

Effects of Environment, Genetics and Data Analysis Pitfalls in an Esophageal Cancer Genome-Wide Association Study

The development of new high-throughput genotyping technologies has allowed fast evaluation of single nucleotide polymorphisms (SNPs) on a genome-wide scale. Several recent genome-wide association studies employing these technologies suggest that panels of SNPs can be a useful tool for predicting cancer susceptibility and discovery of potentially important new disease loci.In the present paper we undertake a careful examination of the relative significance of genetics, environmental factors, and biases of the data analysis protocol that was used in a previously published genome-wide association study. That prior study reported a nearly perfect discrimination of esophageal cancer patients and healthy controls on the basis of only genetic information. On the other hand, our results strongly suggest that SNPs in this dataset are not statistically linked to the phenotype, while several environmental factors and especially family history of esophageal cancer (a proxy to both environmental and genetic factors) have only a modest association with the disease.The main component of the previously claimed strong discriminatory signal is due to several data analysis pitfalls that in combination led to the strongly optimistic results. Such pitfalls are preventable and should be avoided in future studies since they create misleading conclusions and generate many false leads for subsequent research

Thermal Properties of the Binary-Filler Composites with Few-Layer Graphene and Copper Nanoparticles

The thermal properties of an epoxy-based binary composites comprised of graphene and copper nanoparticles are reported. It is found that the "synergistic" filler effect, revealed as a strong enhancement of the thermal conductivity of composites with the size-dissimilar fillers, has a well-defined filler loading threshold. The thermal conductivity of composites with a moderate graphene concentration of ~15 wt% exhibits an abrupt increase as the loading of copper nanoparticles approaches ~40 wt%, followed by saturation. The effect is attributed to intercalation of spherical copper nanoparticles between the large graphene flakes, resulting in formation of the highly thermally conductive percolation network. In contrast, in composites with a high graphene concentration, ~40 wt%, the thermal conductivity increases linearly with addition of copper nanoparticles. The electrical percolation is observed at low graphene loading, less than 7 wt.%, owing to the large aspect ratio of graphene. At all concentrations of the fillers, below and above the electrical percolation threshold, the thermal transport is dominated by phonons. The obtained results shed light on the interaction between graphene fillers and copper nanoparticles in the composites and demonstrate potential of such hybrid epoxy composites for practical applications in thermal interface materials and adhesives.Comment: 25 pages, 4 figure