Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.

Weyl problem and Casimir effects in spherical shell geometry

We compute the generic mode sum that quantifies the effect on the spectrum of a harmonic field when a spherical shell is inserted into vacuum. This encompasses a variety of problems including the Weyl spectral problem and the Casimir effect of quantum electrodynamics. This allows us to resolve several long-standing controversies regarding the question of universality of the Casimir self-energy; the resolution comes naturally through the connection to the Weyl problem. Specifically we demonstrate that in the case of a scalar field obeying Dirichlet or Neumann boundary conditions on the shell surface the Casimir self-energy is cutoff-dependent while in the case of the electromagnetic field perturbed by a conductive shell the Casimir self-energy is universal. We additionally show that an analog non-relativistic Casimir effect due to zero-point magnons takes place when a non-magnetic spherical shell is inserted inside a bulk ferromagnet.Comment: 9 pages, minor changes, additional references added, version to be published in Phys. Rev.

CoQ10 and Cognition a Review and Study Protocol for a 90-Day Randomized Controlled Trial Investigating the Cognitive Effects of Ubiquinol in the Healthy Elderly

Introduction: With an aging population there is an important need for the development of effective treatments for the amelioration of cognitive decline. Multiple mechanisms underlie age-related cognitive decline including cerebrovascular disease, oxidative stress, reduced antioxidant capacity and mitochondrial dysfunction. CoQ10 is a novel treatment which has the potential to improve brain function in healthy elderly populations due to established beneficial effects on mitochondrial function, vascular function and oxidative stress.Methods and Analysis: We describe the protocol for a 90-day randomized controlled trial which examines the efficacy of Ubiquinol (200 mg/day) vs. placebo for the amelioration of cognitive decline in a healthy (non-demented) elderly sample, aged 60 years and over. The primary outcome is the effect of Ubiquinol at 90 days compared to baseline on CogTrack composite measures of cognition. Additional cognitive measures, as well as measures of cardiovascular function, oxidative stress, liver function and mood will also be monitored across 30-, 60- and 90- day time points. Data analyses will involve repeated measures analysis of variance (ANOVA).Discussion: This study will be the first of its kind to provide important clinical and mechanistic data regarding the efficacy of Ubiquinol as a treatment for age-related cognitive decline in the healthy elderly with important implications for productivity and quality of life within this age group.Clinical Trial Registration: The trial has been registered with the Australian and New Zealand Clinical Trials Registry (ANZCTRN12618001841268)

Data for: Statin-Associated Cardiomyopathy Responds to Statin Withdrawal and Administration of Coenzyme Q10

SACM data DEIDENTIFIED.csv: data file which includes de-identified patient clinical data, echocardiographic data, and plasma data. The dates of service (DOS) , along with patient names, have have been removed from this data set for de-identification purposes. Each row represents a clinic visit in ascending chronological order, grouped by patient