Stability Properties of the Time Domain Electric Field Integral Equation Using a Separable Approximation for the Convolution with the Retarded Potential

The state of art of time domain integral equation (TDIE) solvers has grown by leaps and bounds over the past decade. During this time, advances have been made in (i) the development of accelerators that can be retrofitted with these solvers and (ii) understanding the stability properties of the electric field integral equation. As is well known, time domain electric field integral equation solvers have been notoriously difficult to stabilize. Research into methods for understanding and prescribing remedies have been on the uptick. The most recent of these efforts are (i) Lubich quadrature and (ii) exact integration. In this paper, we re-examine the solution to this equation using (i) the undifferentiated form of the TD-EFIE and (ii) a separable approximation to the spatio-temporal convolution. The proposed scheme can be constructed such that the spatial integrand over the source and observer domains is smooth and integrable. As several numerical results will demonstrate, the proposed scheme yields stable results for long simulation times and a variety of targets, both of which have proven extremely challenging in the past.Comment: 9 pages, 13 figures. To be published in IEEE Transactions on Antennas and Propagatio

Electric field distortions in structures of the twist bend nematic (NTB) phase of a bent-core liquid crystal

Dielectric spectroscopy of a twist bend nematic phase of an achiral bent core liquid crystalline compound under DC bias is used to investigate its response to electric field. Two collective relaxation processes are revealed, these are assigned to distortions of helicoidal structure by the external bias field. Frequency of the mode depends primarily on the helicoidal angle and has anomalous, softening- like behaviour at the nematic to the twist bend nematic transition. A coupling of dielectric anisotropy with electric field gives rise to a new equilibrium periodic structure in the time scale involved. The modulus of the wave vector gradually vanishes on increasing the bias field (except for the initial behaviour, which is just the opposite). Transition from the twist bend to the splay bend structure is clearly observed by a sudden drop in the frequency of this mode, which decreases almost linearly with increasing field. Results agree with predictions from current models for the periodically distorted a twist bend nematic phase.Comment: 14 PAGES, 7 FIGURES, submitted to Physical Review Letter

The Cutting Edge of Conservation

Mention the word ‘conservation’ and for most people the mental images evoked are of tigers,elephants, giant pandas, marine turtles, or of imposing liana-festooned tropical rain forests. But conservation is as much about these iconic creatures and habitats as it is about other, less photogenic things: the tribal forest-dweller who depends on wild fruits for her livelihood and subsistence; the hill farmer deciding between growing an organic apple orchard or selling his land to a developer wanting to build a mountain-view resort; the decision-makers sitting in far-off cities amending the wildlife protection act, or formulating policies about land use

Scale invariant correlations and the distribution of prime numbers

Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.Comment: 13 pages, 8 figures, version to appear in J. Phys.

Evaluation of bone excision on occipital area of simulated human skull

Surgical effects of bone and soft tissue tumours, whether for biopsy or full excision have been researched from as early as the 1970’s [1]. These researches though have as main focus the biological (histological) rather the mechanical aspects of the effects [2]. With technological advances in biomedical and biomechanical modelling, a plethora of researchers have been exploring the possibilities of understanding [3] or even predicting musculoskeletal behaviour under different loading conditions [4]. This research is seeking to bridge these two different facets by looking into the mechanical effects bone tumour surgery might have to the structural rigidity of a simulated human skull

Can HERA See an eu−−>ece u --> e c Signal of a Virtual Leptoquark?

Virtual leptoquarks could be detected at HERA through some nonstandard effects. Here we explore the possibility that virtual leptoquarks could be discovered via $e u --> e c$ scattering, assuming integrated luminosity of 200 pb$^{-1}$ and charm identification efficiency of 1%. We study the implications of low energy data for the leptoquarks couplings and find that the most relevant bound for the HERA cross sections comes from inclusive $c --> e^+e^-~+~any$. This bound implies that the $e u --> e c$ cross sections for virtual leptoquarks are just too small for observation of the signal. With an improvement by a factor of ~2 on the luminosity or on charm identification it could be possible to see virtual leptoquarks with {\it maximum couplings} up to ~1.5 - 2 TeV. However, the prospects for discovering the virtual particles if their couplings are somewhat below present bounds are very dim. We point out that this cross section could be very large for leptoquarks lighter than HERA's kinematical limit, and if such a leptoquark is discovered we recommend searching for a possible $e u --> e c$ signal. Our results may also serve as an update on the maximum cross sections for leptoquark mediated $e u --> \mu c$ scattering.Comment: 15 Pages (LaTeX), including 4 postscript figures at the end of the file. Feynman diagrams available by reques

The Effectiveness of Dietary-Induced Ketogenesis on Cognition in Older Adults: A Scoping Review of the Literature

There is growing interest in the effect of dietary interventions in people living with memory impairment and delaying cognitive decline. Investigation of alterations in glucose metabolism and dietary-induced ketogenesis in older adults is a recent growing area of research. Ketone bodies are an important alternative energy source in the brain and may be beneficial to people developing or who already have memory impairment or those with Alzheimer’s disease. This scoping review aims to evaluate the available evidence on dietary-induced ketogenesis and its effect on cognition in older adults and the factors affecting feasibility of the dietary interventions to inform the design of future studies. The scoping review methodology explored the current knowledge about dietary interventions related to dietary-induced ketogenesis and cognition in older adults and identify gaps in the literature. Eleven dietary intervention studies included in the review demonstrated that both medium-chain triglyceride supplementation and ketogenic diets induce ketosis. Nine of these studies demonstrated that dietary-induced ketogenesis could lead to an improvement in cognitive functions, but the evidence remains inconclusive. Most of the included studies showed evidence to suggest that dietary-induced ketogenesis improves cognitive functions in older adults. However, the number of published papers is small and there were differences in the design and types of the dietary interventions (medium-chain triglyceride supplementation, ketogenic diet) along with high drop-out rates in some studies which limits the generalization of the findings. Although methodologies used in the studies vary, the findings warrant the need for further research with larger sample sizes in people at different stages of cognitive impairment, and to develop strategies to improve adherence to the intervention