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

In silico analysis for the presence of HARDY an Arabidopsis drought tolerance DNA binding transcription factor product in chromosome 6 of Sorghum bicolor genome

Expression of the Arabidopsis HARDY (hrd) DNA binding transcription factor (555 bp present on chromosome 2) has been shown to increase WUE in rice by Karaba et al 2007 (PNAS, 104:15270–15275). We conducted a detail analysis of the complete sorghum genome for the similarity/presence of either DNA, mRNA or protein product of the Arabidopsis HARDY (hrd) DNA binding transcription factor (555 bp present on chromosome 2). Chromosome 6 showed a sequence match of 61.5 percent positive between 61 and 255 mRNA residues of the query region. Further confirmation was obtained by TBLASTN which showed that chromosome 6 of the sorghum genome has a region between 54948120 and 54948668 which has 80 amino acid similarities out of the 185 residues. A homology model was constructed and verified using Anolea, Gromos and Verify3D. Scanning the motif for possible activation sites revealed that there was a protein kinase C phosphorylation site between 15th and 20th residue. The study indicates the possibility of the presence of a DNA binding transcription factor in chromosome 6 of Sorghum bicolor with 60 percent similarity to that of Arabidopsis hrd DNA binding transcription factor

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.

Iso-geometric Integral Equation Solvers and their Compression via Manifold Harmonics

The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown, preconditioning, and so on. Likewise, the community has seen extensive investment in development of methods for higher order analysis, in both geometry and physics. Unfortunately, these standard geometric descriptors are $C^0$ at the boundary between patches with a few exceptions; as a result, one needs to define additional mathematical infrastructure to define physical basis sets for vector problems. In stark contrast, the geometric representation used for design is higher-order differentiable over the entire surface. Geometric descriptions that have $C^{2}$-continuity almost everywhere on the surfaces are common in computer graphics. Using these description for analysis opens the door to several possibilities, and is the area we explore in this paper. Our focus is on Loop subdivision based isogeometric methods. In this paper, our goals are two fold: (i) development of computational infrastructure necessary to effect efficient methods for isogeometric analysis of electrically large simply connected objects, and (ii) to introduce the notion of manifold harmonics transforms and its utility in computational electromagnetics. Several results highlighting the efficacy of these two methods are presented

Transient dynamics of subradiance and superradiance in open optical ensembles

We introduce a computational Maxwell-Bloch framework for investigating out of equilibrium optical emitters in open cavity-less systems. To do so, we compute the pulse-induced dynamics of each emitter from fundamental light-matter interactions and self-consistently calculate their radiative coupling, including phase inhomogeneity from propagation effects. This semiclassical framework is applied to open systems of quantum dots with different density and dipolar coupling. We observe that signatures of superradiant behavior, such as directionality and faster decay, are weak for systems with extensions comparable to $\lambda/2$. In contrast, subradiant features are robust and can produce long-term population trapping effects. This computational tool enables quantitative investigations of large optical ensembles in the time domain and could be used to design new systems with enhanced superradiant and subradiant properties.Comment: 5 pages, 5 figure

A Charge Conserving Exponential Predictor Corrector FEMPIC Formulation for Relativistic Particle Simulations

The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers, in large part, due to the method strictly following the proper space for representing fields, charges, and measuring currents. Unfortunately, leap-frog based solvers (and their other incarnations) are only conditionally stable. Recent advances have made Electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) methods built around unconditionally stable time stepping schemes were shown to conserve charge. Together with the use of a quasi-Helmholtz decomposition, these methods were both unconditionally stable and satisfied Gauss' Laws to machine precision. However, this architecture was developed for systems with explicit particle integrators where fields and velocities were off by a time step. While completely self-consistent methods exist in the literature, they follow the classic rubric: collect a system of first order differential equations (Maxwell and Newton equations) and use an integrator to solve the combined system. These methods suffer from the same side-effect as earlier--they are conditionally stable. Here we propose a different approach; we pair an unconditionally stable Maxwell solver to an exponential predictor-corrector method for Newton's equations. As we will show via numerical experiments, the proposed method conserves energy within a PIC scheme, has an unconditionally stable EM solve, solves Newton's equations to much higher accuracy than a traditional Boris solver and conserves charge to machine precision. We further demonstrate benefits compared to other polynomial methods to solve Newton's equations, like the well known Boris push.Comment: 12 pages, 15 figure