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

Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis

A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\leq N\leq 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass-gaps in the spectrum of the Hamiltonians are presented. The expression for the integration measure is consistent with the absence of mass gap for theories with extended supersymmetry (in the absence of additional matter hypermultiplets and/or Chern-Simons couplings), while for the minimally supersymmetric case, there is a mass-gap, the scale of which is set by a renormalized level number, in agreement with indications from existing literature. The realization of the supersymmetry algebra and the Hamiltonian in terms of the gauge invariant variables is also presented.Comment: 31 pages, References added, typos correcte

Predictive haemodynamics in a one-dimensional human carotid artery bifurcation. Part II: application to graft design

A Bayesian surrogate modelling technique is proposed that may be able to predict an optimal bypass graft configuration for patients suffering with stenosis in the internal carotid artery (ICA). At the outset, this statistical technique is considered as a means for identifying key geometric parameters influencing haemodynamics in the human carotid bifurcation. This methodology uses a design of experiments (DoE) technique to generate candidate geometries for flow analysis. A pulsatile one dimensional Navier-Stokes solver incorporating fluid-wall interactions for a Newtonian fluid which predicts pressure and flow in the carotid bifurcation (comprising a stenosed segment in the internal carotid artery) is used for the numerical simulations. Two metrics, pressure variation factor (PVF) and maximum pressure (pm) are employed to directly compare the global and local effects, respectively, of variations in the geometry. The values of PVF and pm are then used to construct two Bayesian surrogate models. These models are statistically analysed to visualise how each geometric parameter influences PVF and pm. Percentage of stenosis is found to influence these pressure based metrics more than any other geometric parameter. Later, we identify bypass grafts with optimal geometric and material properties which have low values of PVF on five test cases with 70%, 75%, 80%, 85% and 90% stenosis in the ICA, respectively

Massive Spin-2 fields of Geometric Origin in Curved Spacetimes

We study the consistency of a model which includes torsion as well as the metric as dynamical fields and has massive spin-2 particle in its spectrum. The massive spin-2 mode resides in the torsion, rather than in the metric. It is known that this model is tachyon- and ghost-free in Minkowski background. We show that this property remains valid and no other pathologies emerge in de Sitter and anti-de Sitter backgrounds, with some of our results extending to arbirary Einstein space backgrounds. This suggests that the model is consistent, at least at the classical level, unlike, e.g., the Fierz--Pauli theory.Comment: 17 pages, Clarifying remarks added in section 5, minor changes, version to be published in the Phys. Rev.

Satellite based potential fishing zone (PFZ) advisories - acceptance levels and benefits derived by the user community along the Kerala coast

Intensive validation studies of potential fishing zone (PFZ) advisories generated using integration of ocean colour monitor (OCM) derived chlorophyll concentration and advanced very high resolution radiometer (AVHRR) derived sea surface temperatures (SST) were undertaken by the Indian National Centre for Ocean Information Services (INCOIS) along Kerala coast during the period 2003-2011. There is a positive relationship between PFZ advisories and occurrence/abundance of commercially important pelagic fishes such as oilsardine, Indian mackerel, anchovies, carangids and coastal tunas. Fishing operations undertaken on or closer to dates on which related SST/chlorophyll images have been received yielded positive results. As the gap increases, the yield within PFZ is likely to come down unless the features remain more or less in the same location as revealed by succeeding satellite imagery. The present paper revealed that the fish catch (CPUE) and net profit earned are higher within PFZ compared to the results of operations outside PFZ. The usefulness of PFZ advisories, the only short term marine fishery forecast available in the country for fisherfolk towards obtaining comparatively higher catch per unit effort for the above mentioned major pelagics is proved beyond doubt from the results of more than 100 controlled experiments conducted within and outside PFZ with identical fishing gear along Kerala coast

Unimpeded permeation of water through helium-leak-tight graphene-based membranes

Permeation through nanometer pores is important in the design of materials for filtration and separation techniques and because of unusual fundamental behavior arising at the molecular scale. We found that submicron-thick membranes made from graphene oxide can be completely impermeable to liquids, vapors and gases, including helium, but allow unimpeded permeation of water (H2O permeates through the membranes at least 10^10 times faster than He). We attribute these seemingly incompatible observations to a low-friction flow of a monolayer of water through two dimensional capillaries formed by closely spaced graphene sheets. Diffusion of other molecules is blocked by reversible narrowing of the capillaries in low humidity and/or by their clogging with water