Prolate Spheroidal Research Articles

Design of compact electromagnetic impulse radiating antenna for melanoma treatment

ABSTRACTCancer therapy is one of the several new applications which use nanosecond and subnanosecond high voltage pulses. New treatment based on electromagnetic (EM) fields have been developed as non-surgical and minimally invasive treatments of tumors. In particular, subnanosecond pulses can introduce important non-thermal changes in cell biology, especially the permeabilization of the cell membrane. The motivation behind this work is to launch intense subnanosecond pulses to the target (tumors) non-invasively. This works focuses on the design of a compact intense pulsed EM radiating antenna. In tense EM waves radiated at the first focal point of the Prolate Spheroidal Reflector (PSR) are focused at the second focal point where the target (tumor) is present. Two antennas with PSR but fed with different compact wave radiator are designed to focus pulsed field at the second focal point. The PSR with modified bicone antenna feed and PSR with elliptically tapered horn antenna feed are designed. The design parameters and radiation performance are discussed.

Some further estimates of the prolate spheroidal wave functions and their spectrum

AbstractWe complete here our recent work on explicit approximations of the Prolate Spheroidal Wave Functions (PSWFs) on the interval [-1,+1] and their associated spectra by pushing forward the methods in view of new results. We give in particular approximations of the ratio between large and small oscillations of PSWFs as well of the transition bandwidth for which the PSWF stops to take its largest values at the boundary of the interval. The aim of this work is two folds. On one hand, we prove a bunch of properties of the PSWFs and on the other hand, we illustrate the theoretical results by some numerical experiments.

Pollen morphology of <i>Verbascum</i> L. (Scrophulariaceae) in Northern and Central Iraq

The present study highlights the taxonomic values of the pollen features of 20 species of Verbascum L. in Iraq. The pollen grains were acetolysed and observed under Light and Electron microscopes. Our results showed that the pollen grains of these species are usually radially symmetrical, isopolar, tricolporate and display reticulate sculpturing. The variations were found in shape, size, and exine thickness. Most of the species are subprolate, prolate spheroidal, and prolate, whereas oblate spheroidal pollens were found only in V. thapsus. The pollen size among the species studied ranges from 16.2-32.5 µm. The majority of species are medium sized except V. agrimoniifolium and V. oreophilum that are small sized, and four species i.e. V. palmyrense, V. sinuatum, V. songaricum, and V. thapsus having both small and medium sized pollen grains. Moreover, the result showed that the exine thickness ranges from 0.87-4.75 µm, but this value can overlap between some species. Therefore, only the shape of pollen grains could be used to classify these species into groups.DOI: http://dx.doi.org/10.3329/bjpt.v21i2.21355Bangladesh J. Plant Taxon. 21(2): 159-165, 2014 (December)

An optimal control approach to ciliary locomotion

We consider a class of low Reynolds number swimmers, of prolate spheroidal shape, which can be seen as simplified models of ciliated microorganisms. Within this model, the form of the swimmer does not change, the propelling mechanism consisting in tangential displacements of the material points of swimmer's boundary. Using explicit formulas for the solution of the Stokes equations at the exterior of a translating prolate spheroid the governing equations reduce to a system of ODE's with the control acting in some of its coefficients (bilinear control system). The main theoretical result asserts the exact controllability of the prolate spheroidal swimmer. In the same geometrical situation, we consider the optimal control problem of maximizing the efficiency during a stroke and we prove the existence of a maximum. We also provide a method to compute an approximation of the efficiency by using explicit formulas for the Stokes system at the exterior of a prolate spheroid, with some particular tangential velocities at the fluid-solid interface. We analyze the sensitivity of this efficiency with respect to the eccentricity of the considered spheroid and show that for small positive eccentricity, the efficiency of a prolate spheroid is better than the efficiency of a sphere. Finally, we use numerical optimization tools to investigate the dependence of the efficiency on the number of inputs and on the eccentricity of the spheroid. The ``best'' numerical result obtained yields an efficiency of $30.66\%$ with $13$ scalar inputs. In the limiting case of a sphere our best numerically obtained efficiency is of $30.4\%$, whereas the best computed efficiency previously reported in the literature is of $22\%$.

Backscatter coefficient estimation using tapers with gaps.

When using the backscatter coefficient (BSC) to estimate quantitative ultrasound parameters such as the effective scatterer diameter (ESD) and the effective acoustic concentration (EAC), it is necessary to assume that the interrogated medium contains diffuse scatterers. Structures that invalidate this assumption can affect the estimated BSC parameters in terms of increased bias and variance and decrease performance when classifying disease. In this work, a method was developed to mitigate the effects of echoes from structures that invalidate the assumption of diffuse scattering, while preserving as much signal as possible for obtaining diffuse scatterer property estimates. Backscattered signal sections that contained nondiffuse signals were identified and a windowing technique was used to provide BSC estimates for diffuse echoes only. Experiments from physical phantoms were used to evaluate the effectiveness of the proposed BSC estimation methods. Tradeoffs associated with effective mitigation of specular scatterers and bias and variance introduced into the estimates were quantified. Analysis of the results suggested that discrete prolate spheroidal (PR) tapers with gaps provided the best performance for minimizing BSC error. Specifically, the mean square error for BSC between measured and theoretical had an average value of approximately 1.0 and 0.2 when using a Hanning taper and PR taper respectively, with six gaps. The BSC error due to amplitude bias was smallest for PR (Nω = 1) tapers. The BSC error due to shape bias was smallest for PR (Nω = 4) tapers. These results suggest using different taper types for estimating ESD versus EAC.

A Low-Order Parametric Description of Left Ventricular Kinematics

An approximate description for the deformation of the left ventricle (LV) throughout the cardiac cycle is developed in terms of three time-dependent parameters. The reference configuration, corresponding to end-diastole, is represented as a thick-walled prolate spheroid. By using prolate spheroidal coordinates, a three-parameter family of mappings is defined to represent the deformed shapes of the LV wall, while identically conserving wall volume. The three parameters represent lengthening with constant internal volume, contraction with reduction of internal volume, and torsion. Feasibility is illustrated using echocardiography data from a healthy subject. The reference configuration was defined by fitting observed points on LV endocardial and epicardial surfaces in long-axis images at end diastole. Time-courses of parameters defining LV kinematics were obtained for best fit to longitudinal strains, circumferential strains and rotations (LS, CS and R) obtained from speckle tracking echocardiography at 36 LV regions. Fitted versus echocardiography-measured CS, LS and R were compared at the LV base, mid-wall and apex at the endocardium and epicardium. The RMS deviation between fitted and measured peak strains was 0.06 (LS) and 0.08 (CS). Fitted and measured LV volume changes during contraction agreed closely. Circumferential variations in strain, which may be significant in normal and pathological hearts, are not represented here. The results demonstrate feasibility of a low-order description of the deformation field in the LV myocardium, based on echocardiographic imaging data. Such a description provides a basis for low-order models of LV mechanics and eventual real-time patient-specific analysis of LV mechanical parameters.

Asynchronous processing of sparse signals

Unlike synchronous processing, asynchronous processing is more efficient in biomedical and sensing networks applications as it is free from aliasing constraints and quantization error in the amplitude, it allows continuous-time processing and more importantly data is only acquired in significant parts of the signal. We consider signal decomposers based on the asynchronous sigma delta modulator (ASDM), a non-linear feedback system that maps the signal amplitude into the zero-crossings of a binary output signal. The input, the zero-crossings and the ASDM parameters are related by an integral equation making the signal reconstruction difficult to implement. Modifying the model for the ASDM, we obtain a recursive equation that permits to obtain the non-uniform samples from the zero-time crossing values. Latticing the joint time-frequency space into defined frequency bands, and time windows depending on the scale parameter different decompositions are possible. We present two cascade low- and high-frequency decomposers, and a bank-of-filters parallel decomposer. This last decomposer using the modified ASDM behaves like a asynchronous analog to digital converter, and using an interpolator based on Prolate Spheroidal Wave functions allows reconstruction of the original signal. The asynchronous approaches proposed here are well suited for processing signals sparse in time, and for low-power applications.

Taxonomy and pollen morphology of Ankyropetalum Fenzl (Caryophyllaceae) species in Türkiye.

There are 4 species belong to Ankyropetalum Fenzl (Caryophyllaceae) genus and three of them (A. reuteri Boiss. and Hausskn, A. arsusianum Kotschy ex Boiss. and A. gypsophiloides Fenzl) are distributed in Turkey. There are doubts about taxonomical studies depending on only morphological characteristics. This study has been made to put forth that palinological studies also contribute taxonomical studies. Pollen morphology of the three species belong to Ankyropetalum Fenzl (Caryophyllaceae) genus distributed in Turkey examined with ray microscope and electron microscope in this study. Results evaluated according to Duncan's multiple range test using SPSS statistic program. Pollen's polar and ecvatoral seeming photographs were taken in preparates. Morphology of pollens examined with 50 repetition for each taxon and morphological assessments were made. The common trait of pollens can be summarized as they are circular, oblate and prolate spheroidal, periporate (pore numbers ranged between 20-33), operculum is granulated, annulus is distinct, the form of pollens are tectat. Definition of pollens are given for each taxon, diagnostic specifications recognized as important are used for making diagnosis key. The difference between species are as below: A. arsusianum's pollen shape is oblate-spheroidal, type of pollen is periporate, pore numbers are between 23-33, form of pollen is tectat, ornamentation is perforate. A. reuteri's pollen shape is prolate-spheroidal, type of pollen is periporate, pore numbers are between 20-33, form of pollen is tectat, ornamentation is from perforate to eureticulate A. gypsophiloides pollen shape is oblate-spheroidal, type of pollen is periporate, pore numbers are between 21-30, form of pollen is tectat, ornamentation is perforate.

Three-dimensional electromechanical analysis of a conducting prolate spheroid on a grounded plane

This paper presents a 3D analysis of the electromechanics for a conducting prolate spheroid on a grounded plane under electric field. The objective of the analysis is to clarify the roles of tilt angle α between the particle and the plane on the electrostatic force and torque on the spheroid, which are the fundamentals of particle behavior in various applications. The method of multipole images and multipole re-expansion for the prolate spheroidal coordinates are applied to electric field calculation. The electrostatic force and torque on the spheroid are then determined. The calculation results show that the maximal field takes place at or near the higher pole of the spheroid for nonzero tilt angles. The electrostatic force is minimal and maximal when the spheroid lies and stands on the plane, respectively. We present empirical formulae for estimating the minimal and maximal force with error smaller than 1% for the major-to-minor axis ratio between 1 and 10. The electrostatic torque is in the increasing α direction, and it is magnified with increasing α from 0 to about 45°, and then reduces to zero at α = 90°. The torque variation may be estimated by a quadratic relationship. When the gravitational force of the particle is taken into account, the electromechanical behavior can be classified into three regimes, depending on the externally applied field and the tilt angle. The presence of the electrostatic torque enhances the probability of a spheroid particle to be lifted from the grounded plane by the electric field.

Modeling of spatial variations of growth within apical domes by means of the growth tensor. L Growth specified on dome axis

By using the growth tensor and a natural curvilinear coordinate system for description of the distribution of growth in plant organs, three geometric types of shoot apical domes (parabolic, elliptical and hyperbolic) were modeled. It was assumed that apical dome geometry remains unchanged during growth and that the natural coordinate systems are paraboloidal and prolate spheroidal. Two variants of the displacement velocity fields V were considered. One variant is specified by a constant relative elemental rate of growth along the axis of the dome. The second is specified by a rate increasing proportionally with distance from the geometric focus of the coordinate systems (and the apical dome). The growth tensor was used to calculate spatial variations of growth rates for each variant of each dome type. There is in both variants a clear tendency toward lower growth rates in the distal region of the dome. A basic condition for the existence of a tunica is met.

Research on Multiband Impulse Radio UWB System based on PSWF in Multipath Fading Channel

This paper presents an architecture of Multiband Impulse Radio UWB (MB-IR-UWB) system based on Prolate Spheroidal Wave Function (PSWF) by binary time hopping pulse position modulation (TH-PPM) over multipath fading channel. In order to combat multipath fading, Rake receiver using maximal ratio combining (MRC) is applied to this system, which can successfully capture the unique multipath-rich property and multipath-clustering phenomenon of UWB channels. Through simulation, a comparison of system performance between different types of Rake receiver is analyzed. What’s more, considered multipath delay spread, a data rate estimation of the communicating system is given. Finally we get the conclusion that increasing data rate is best-achieved by increasing the number of subband instead of decreasing the symbol repetition period.

Numerical simulation of the whispering gallery modes in prolate spheroids

In this paper, we discuss the progress in the numerical simulation of the so-called ‘whispering gallery’ modes (WGMs) occurring inside a prolate spheroidal cavity. These modes are mainly concentrated in a narrow domain along the equatorial line of a spheroid and they are famous because of their extremely high quality factor. The scalar Helmholtz equation provides a sufficient accuracy for WGM simulation and (in a contrary to its vector version) is separable in spheroidal coordinates. However, the numerical simulation of ‘whispering gallery’ phenomena is not straightforward. The separation of variables yields two spheroidal wave ordinary differential equations (ODEs), first only depending on the angular, second on the radial coordinate. Though separated, these equations remain coupled through the separation constant and the eigenfrequency, so that together with the boundary conditions they form a singular self-adjoint two-parameter Sturm–Liouville problem.We discuss an efficient and reliable technique for the numerical solution of this problem which enables calculation of highly localized WGMs inside a spheroid. The presented approach is also applicable to other separable geometries. We illustrate the performance of the method by means of numerical experiments.

Pollen morphology of Centaurea L. (Asteraceae) in Iran

The genus Centaurea L. is one of the largest genera in the family Asteraceae. The number of taxa included in this genus ranges from 500 to 600 worldwide. Iran is one of the major centers of diversity for this genus. Pollen morphology has proved useful in the systematics of Asteraceae, as well as in that of some of its genera and species. The pollen morphology of 19 taxa of the genus Centaurea was investigated in detail by light and scanning electron microscopy. Examination under light microscopy showed pollen grains to be tricolporate, isopolar, radially symmetrical, oblate spheroidal, prolate spheroidal, subprolate, tectum perforate and scabrate. Based on the exine ornamentation observed under scanning electron microscopy, we identified two types of pollen grains, designated type I (dense acute spinules) and type II (sparse spinules). All of the taxa evaluated resemble Wagenitz's Jacea type. We present micrographs of pollen grains, together with descriptions of the characteristics of their structure. We found that the pollen characters (shape, exine structure, sculpturing) were useful for classification.

Null-field BIEM for solving a scattering problem from a point source to a two-layer prolate spheroid

In this paper, the acoustic scattering problem from a point source to a two-layer prolate spheroid is solved by using the null-field boundary integral equation method (BIEM) in conjunction with degenerate kernels. To fully utilize the spheroidal geometry, the fundamental solutions and the boundary densities are expanded by using the addition theorem and spheroidal harmonics in the prolate spheroidal coordinates, respectively. Based on this approach, the collocation point can be located on the real boundary, and all boundary integrals can be determined analytically. In real applications of a two-layer prolate spheroidal structure, it can be applied to simulate the kidney-stone biomechanical system. Here, we consider the confocal structure to simulate the kidney-stone system since its analytical solution can be analytically derived. The parameter study for providing some references in the clinical medical treatment is also considered. To check the validity of the null-field BIEM, a special case of the acoustic scattering problem of a point source by a rigid scatterer is also done by setting the density of the inner prolate spheroid to infinity. Results of the present method are compared with those obtained using the commercial finite element software ABAQUS.

Dielectric Response of a Charged Prolate Spheroid in an Electrolyte Solution

We derived the so-called standard set of electrokinetic equations in prolate spheroidal coordinates for all ionic strengths, zeta potentials, and applied electric field frequencies, with the assumption, however, that the particle’s electrophoretic mobility is small. We subsequently solved these equations using finite differences methods. We show that the dipolar coefficient of a prolate spheroid reduces to that of a sphere in the corresponding limit, but deviates strongly from it when the eccentricity of the spheroid is large, for the same particle volume. We also verified that a previously published analytical theory (Chassagne and Bedeaux, J. Colloid Interface Sci., 326:240, 2008) is in good agreement with the numerical results for a large range of zeta potentials, ionic strengths, and frequencies.

Self-Assembly of Janus Ellipsoids II: Janus Prolate Spheroids

In self-assembly, the anisotropy of the building blocks and their formation of complex structures have been the subject of considerable recent research. Extending recent research on Janus particles and completing the study of Janus spheroids, we conduct a systematic investigation on the self-assembly of Janus prolate spheroids based on a primitive model that we proposed. Janus prolate spheroids are particles that have a prolate spheroidal body and two hemi-surfaces along the major axis coded with different chemical properties. Using Monte Carlo simulations, we investigate the effects of the aspect ratio on the self-assembly process. In contrast to the vesicle-like aggregates for Janus oblate spheroids, we obtain various ordered cluster structures for Janus prolate spheroids through self-assembly. With an increasing aspect ratio, we find a transition of cluster morphology, from vesicles to tubular micelles and micelles. In particular, a relatively small change in the aspect ratio leads to a rather significant change in morphology. We apply a cluster analysis to understand the mechanism associated with such a transition.

WE-E-134-01: Preliminary Application of a Multitaper Generalized Spectrum Approach to Quantify Scatterer Nonrandomness in Breast Lesions

Purpose: The generalized spectrum (GS) has been used to quantify nonrandomness of scattering sources and to characterize breast and liver tissues. In this work, we implement a multitaper GS approach creating parametric images of GS features that describe the degree of nonrandom structure in breast lesions. Methods: This IRB-approved, HIPAA compliant study recruited subjects who were scheduled for core biopsy of a suspicious breast mass. Subjects were scanned with a Siemens Acuson S2000 using a linear array transducer at 15MHz. Radiofrequency (RF) echo data were obtained in radial (parallel to breast lactiferous ducts) and antiradial planes. Cases (n=34) were selected based on the availability of biopsy results and a lesion size of at least 3mm in both planes. The multitaper GS was obtained by computing the correlation matrix of the Fourier transform of RF signal segments tapered by Prolate Spheroidal Sequences. Nonrandomness was quantified by parameterizing the collapsed average of the GS. A region of interest (ROI) within each lesion and each plane was defined,and the mean and standard deviation of the nonrandomness within it were computed. Results: Cases were grouped into: fibroadenoma (n=12, median diameter (MD)=7.6mm),other benign(n=11, MD=8.2mm), invasive ductal carcinoma (IDC) (n=5, MD=6.3mm), and other malignant(n=6, MD=6.9mm). The IDC nonrandomness inter-case median of the mean and standard deviation was 64% and 59% of the values from other lesions, and the fractional difference in the standard deviation of the nonrandomness between the radial and antiradial views for the IDC cases was 59% smaller than the values for other lesions. Conclusion: Preliminary results indicate that the spatial distribution of scatterers within IDCs is more homogeneously random compared to other lesions. However, inter-case variability was comparable to the median values. Future work will expand the population and use beam steered acquisitions to test for anisotropy in these features. This work was supported, in part, by NIH (grants R01CA111289, R21HD061896, R21HD063031, and R01HD072077) and the Consejo Nacional de Ciencia y Tecnologia of Mexico (Reg. 206414).

Circular harmonics beamforming with spheroidal baffles

Circular microphone arrays have been well studied when mounted on cylindrical and spherical baffles. In this paper, the oblate and prolate spheroids are explored as a baffle for a microphone array system. It is shown that the prevailing methods for analysis of circular arrays may be easily adapted to this class of baffle, and that the use of these baffles represent a continuously variable geometry with edge cases that are the cylindrical and spherical baffles, and the array in empty space with no baffle. The performance—in the form of directivity index, maximum side-lobe level and main beam resolution—of spheroidally baffled arrays is analyzed with respect to errors created by transducer noise, positioning error, and modal aliasing, for both delay-and-sum and eigenbeamforming arrays. It is shown that the noise and position errors depend strongly on the spheroidal eccentricity while the aliasing error is fairly independent of baffle shape. Simulations of example arrays are used to show that while the prolate spheroidal baffle is of little advantage compared to current systems, the oblate spheroidal baffle can be used to create a significantly smaller array with only a relatively minor performance degradation.

Performance Analysis of Multiple Access 60 GHz System Using Frequency-shifted Gaussian Pulse and Non-carrier PSWF Pulse

In this paper, a kind of impulse radio (IR) 60 GHz pulse based on Prolate Spheroidal Wave Functions (PSWF) is proposed. The capacity and performance for multiple access 60 GHz communication system based on carrier pulse and impulse radio pulse are analyzed separately. Both frequency-shifted Gaussian pulse and Prolate Spheroidal Wave Functions (PSWF) pulse are considered and devised according to the federal communication commission (FCC) power constraints. Pulse position modulation (PPM) with time hopping spread spectrum (THSS) is employed in the multiple access 60GHz communication system. The channel capacity and error probability for 60GHz communication system with different pulse waveforms over additive white Gaussian noise (AWGN) channel are compared and analyzed. The simulation results showed that the PSWF pulse 60GHz system with has better channel capacity and error probability performance than frequency-shifted Gaussian pulse 60GHz system.

Myrsine parvifolia (Primulaceae) in sandy coastal plains marginal to Atlantic rainforest: a case of pollination by wind or by both wind and insects?

This study examined the pollination ecology of Myrsine parvifolia in an area of sandy coastal plain, namely restinga. Male and female plants were distributed in an aggregated form with sex ratio of 1.7♂:1♀. Flowers are open dish-shaped, greenish-white, odorless, and devoid of nectaries. The female flower has a well-exposed sessile stigma. The anthers of the male flower release pollen grains in a powdery cloud. The pollen grains are small, dry, prolate spheroidal, 3–5-colpate and have a scabrous exine. We concluded that M. parvifolia is wind pollinated by: the presence of pollen grains in the air; fruit production in inflorescences isolated from access by biotic pollinators, but not by wind; the female flowers were not visited by biotic agents. Our results reinforce the hypothesis that pollination by wind is the main pollination system in Myrsine. Pollen limitation has been recorded for M. parvifolia and also for other dioecious insect-pollinated species from restinga as Guapira opposita and Tapirira guianensis, but not for Coccoloba arborescens and Protium brasiliense. Natural and manual fruit set of all of them was low, suggesting that other factors, in addition to pollen limitation, are involved in the regulation of fruit production. Studies on floral biology may help to clarify the variable rates of pollen limitation found for the dioecious species from restinga. However, as they are woody and perennial, and therefore pass through several reproductive cycles throughout life, factors that influence female reproductive success may vary over the reproductive events, due to abiotic and biotic conditions.