1,140 research outputs found
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 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 -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 . 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
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