Non-uniform Spacing Research Articles

Antenna Packing in Low-Power Systems: Communication Limits and Array Design

In this correspondence, we study design of transceiver antenna arrays and its impact on spectral efficiency of low-power systems. Our primary motivation is construction of practical and portable multi-antenna configurations with a very small and a-priori fixed volume for placing antennas. Using spectral efficiency as a target metric for array optimization, we show that any array configuration, transmit or receive, can be characterized via a parameter that we interpret as ldquoeffective degrees of freedom.rdquo For any array configuration, effective degrees of freedom describes an equivalent uncorrelated array, which results in the same low-power behavior of spectral efficiency. Joint optimization of transmit and receive antenna configurations decouples into maximizing effective degrees of freedom for transmitter and receiver separately. To achieve this goal, we introduce and study a theoretical benchmark of ldquolimiting degrees of freedom, rdquo which is the least upper bound on effective degrees of freedom, evaluated over all configurations with finite number of antennas. Limiting degrees of freedom therefore describes the best possible performance for any transceiver array which confines its elements inside a given space. We compute a closed-form expression for limiting degrees of freedom of a circular geometry. Finally, we present numerical procedure and examples for designing linear and square arrays with nonuniform spacing, which typically exhibit significant spectral efficiency gains over uniform arrays.

Results from trials of a planar, incoherent, synthetic aperture sonar for underwater imaging

Synthetic aperture sonar (SAS) techniques can yield high-resolution images with a small physical array. Their application in the underwater environment is usually confined to the deployment and synthesis of linear apertures. Incoherent SAS processing is a suboptimal approach compared with coherent SAS processing as the absence of phase information results in an inferior along-track resolution and a higher sidelobe level. The absence of phase information implies that incoherent processing is not constrained by phase-aliasing. Incoherent SAS can accommodate non-uniform inter-ping spacing and is tolerant to trajectory estimation errors of the order of the range-compressed pulse length. This presents new opportunities for a robust surveying system. Apertures of nonlinear shapes can be synthesised depending on the nature and requirement of the specific application and environment. Surveys can be conducted with minimal hardware deployment, such as by a diver. On the basis of this concept, tank trial results of a 3-dimensional incoherent SAS technique utilising the synthesis of 2D apertures are presented. Broadband pulses are employed to achieve optimal survey resolution. The feasibility of this technique is demonstrated for both monostatic and single-transmit, multiple-receive configurations. Practical results are shown for arbitrary-surface apertures sampled at non-uniformly separated positions.

LINEAR ANTENNA ARRAY DESIGN WITH USE OF GENETIC, MEMETIC AND TABU SEARCH OPTIMIZATION ALGORITHMS

Antenna array design techniques are focused on two main classes: uniformly spaced antenna arrays and the non-uniform spacing case. These include techniques based on mathematical programming, such as constrained programming and non-linear programming. More recently, meta-heuristics approaches have been successful at designing antenna arrays (5). In this work, this paper presents efficient methods of genetic algorithm (GA), memetic algorithm (MA) and tabu search algorithm (TSA) for the synthesis of linear antenna design. We present three examples of antenna array design to compare the efficiency of the algorithms through simple design to complex design. The GA, TSA and MA has been used to optimize the spacings between the elements of the linear array to produce a radiation pattern with minimum SLL and null placement control.

SU-FF-J-118: A Method for Defining Segmentation Surfaces Using Nonparallel Contours

Purpose: Segmentation of anatomical structures from CT images for treatment planning has typically involved the process of manual delineation of contours on image slices. However, the original image slices are not always the best planes that allow accurate delineation of structures, and as a result, software tools that permit drawing of contours on oblique or even non-parallel planes are gradually becoming available. Unfortunately, what is missing still is the accompanying computational method for extracting surfaces from such contours. We investigate a novel approach for automatically generating a triangular surface mesh from contour lines defined on arbitrary, possibly intersecting planes. Method and Materials: Using contour delineation programs, we first obtain the defining equations of each contour plane as well as contour line segments delineated on each plane. The contour planes partition the entire space into convex sub-spaces. We compute a surface mesh within each subspace by extending our previously developed method for surface extraction from contours defined on two parallel planes. The entire surface is then constructed by merging surfaces within each subspace. Finally, a normal smoothing step is employed to fair the appearance of the surface. This has been implemented in CERR. Results: Testing the initial implementation on synthetic data reveals that our method is capable of extracting smooth, water-tight surface meshes from complex contour curves with arbitrary shape (e.g., either convex or non-convex) and arbitrary topology (e.g., consisting of either a single loop or multiple loops) that reside on arbitrarily oriented planes. Conclusion: We have developed a novel computational approach for extracting surfaces from contours delineated on planes that may have nonuniform spacing and may have arbitrary orientations. Our method meets the critical need for segmentation of anatomical structures in treatment planning systems using contours delineated from oblique or non-parallel planes.

Spinophilin Facilitates Dephosphorylation of Doublecortin by PP1 to Mediate Microtubule Bundling at the Axonal Wrist

The axonal shafts of neurons contain bundled microtubules, whereas extending growth cones contain unbundled microtubule filaments, suggesting that localized activation of microtubule-associated proteins (MAP) at the transition zone may bundle these filaments during axonal growth. Dephosphorylation is thought to lead to MAP activation, but specific molecular pathways have remained elusive. We find that Spinophilin, a Protein-phosphatase 1 (PP1) targeting protein, is responsible for the dephosphorylation of the MAP Doublecortin (Dcx) Ser 297 selectively at the "wrist" of growing axons, leading to activation. Loss of activity at the "wrist" is evident as an impaired microtubule cytoskeleton along the shaft. These findings suggest that spatially restricted adaptor-specific MAP reactivation through dephosphorylation is important in organization of the neuronal cytoskeleton.

Time‐resolved contrast‐enhanced carotid imaging using undersampled projection reconstruction acquisition

To investigate the utility of nonuniform angular spacing of projections in a three-dimensional (3D) hybrid undersampled projection reconstruction (PR) acquisition for contrast-enhanced (CE) time-resolved carotid imaging. Carotid CE magnetic resonance angiography (CE-MRA) was performed on seven healthy volunteers using a time-resolved hybrid sequence that combined undersampled PR acquisition in-plane and Cartesian slice encoding through-plane. The undersampling streak artifact comes mainly from the superior-inferior (S/I) direction in carotid imaging and is suppressed by nonuniform distribution of the projections. Phantom and volunteer studies were performed to demonstrate its efficacy. The undersampling streak artifact was significantly suppressed through a nonuniform distribution of the projection angles with more projections aligned along the S/I direction. The hybrid PR sequence combined with nonuniform distribution of the projection angles provided time-resolved images of the carotid arteries with high temporal resolution (two seconds per frame) and high spatial resolution (1.0 x 1.0 x 1.5 mm(3)) simultaneously. High-resolution dynamic imaging of the carotid arteries is feasible with the use of a hybrid undersampled PR acquisition. Undersampling streak artifact can be suppressed significantly through nonuniform distribution of the projections.

Submarine lava flow emplacement and faulting in the axial valley of two morphologically distinct spreading segments of the Mariana back‐arc basin from Wadatsumi side‐scan sonar images

High‐resolution, deep‐tow side‐scan sonar data were collected over two distinct spreading segments in the central part of the Mariana back‐arc basin. These data allow mapping of small fissures and faults and the distinguishing of hummocky from smooth lava flows. Using these data, we observe spatial variations in seafloor deformation and volcanic activity within each segment, and also significant differences in the degree of tectonic deformation between the two segments. One segment, characterized by an hourglass shape suggestive of magmatic processes dominating over tectonic processes, is in fact currently dominated by intense deformation rather than volcanism. The other segment, which exhibits morphology (wide and deep linear axial valley) typical of magma‐starved segments, is subjected to very limited deformation and is covered by mostly unfaulted, recent flows. Each segment also displays along‐axis variations in the degree of tectonic deformation and in lava flows freshness. We observe a decrease of lava effusion rate from segment centers toward their ends. We also investigated the apparent asymmetry of the Mariana basin. On the southern segment of the study area, azimuths of tectonic structures are divided into two groups, one segment‐parallel and one ∼15° oblique to strike of the segment. These two trends of linear features developed synchronously with volcanic activity. Currently oblique structures seem to be the most active ones. The tectonic structures that are parallel to the overall valley trend are distributed over the entire valley, whereas the oblique structures are only located proximal to the eastern valley wall. They are likely related to changes in the local stress field related to the obliquely trending eastern axial valley wall. Asymmetric character, such as nonuniform spacing and throw of faults, was not observed. These observations suggest that the asymmetry of the basin is not due to asymmetric spreading, but rather to eastward ridge jumps of several kilometers. Such small‐amplitude ridge jumps likely occurred frequently during basin development because the asymmetric character of the basin is strongly pronounced and no abandoned rift valley is recognizable within the entire basin.

COMPUTATIONAL MODELING ANALYSIS OF RADAR SCATTERING BY CLOTHING COVERED ARRAYS OF METALLIC BODY-WORN EXPLOSIVE DEVICES

In this study, we address the problem of detecting body- worn improvised explosive devices (IEDs) from a safe distance using radar. We have used a finite difference frequency domain (FDFD) model to simulate the radar signature of a typical scenario for body- worn IEDs, and have analyzed wrinkled clothing as a possible source of clutter, as well as the possibility for uniform versus nonuniform array spacing of explosive-filled metal pipes. Our analysis shows distinct characteristics of the pipe backscattered farfield signal for uniformly spaced pipes, with no significant clutter added when the metallic pipe is covered with wrinkled clothing.

On the accuracy of finite-difference solutions for nonlinear water waves

This paper considers the relative accuracy and efficiency of low- and high-order finite-difference discretisations of the exact potential-flow problem for nonlinear water waves. The method developed is an extension of that employed by Li and Fleming (Coastal Engng 30: 235–238, 1997) to allow arbitrary-order finite-difference schemes and a variable grid spacing. Time-integration is performed using a fourth-order Runge–Kutta scheme. The linear accuracy, stability and convergence properties of the method are analysed and high-order schemes with a stretched vertical grid are found to be advantageous relative to second-order schemes on an even grid. Comparison with highly accurate periodic solutions shows that these conclusions carry over to nonlinear problems and that the advantages of high-order schemes improve with both increasing nonlinearity and increasing accuracy tolerance. The combination of non-uniform grid spacing in the vertical and fourth-order schemes is suggested as optimal for engineering purposes.

Free vibration of rotating ring stiffened cylindrical shells with non-uniform stiffener distribution

In this research, the free vibration analysis of simply supported rotating cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and non-uniform stiffeners spacing distribution is investigated. Ritz method is applied while stiffeners are treated as discrete elements. In strain energy formulation, by adopting Sander's theorem, stretching and bending characteristics of shells are considered. Also stretching, bending and wrapping effects of stiffeners are investigated. The translational inertia in three directions for shell and stiffeners, and rotary inertia for stiffeners are considered. The effects of initial hoop tension, centrifugal and Coriolis forces due to the rotation of shell are studied. The polynomial functions are used for Ritz functions. Natural frequency results for rings with uniform spacing and constant eccentricity have been compared with analytical and experimental results of other researchers, which showed good agreement. Fortunately, the agreements of the presented analytical results with the experimental values are better than the analytical values. At constant total mass of stiffeners, the effects of non-uniform eccentricity distribution and non-uniform rings spacing distribution (separately and simultaneously) on natural frequencies are investigated. Moreover, the influence of rotating speed on natural frequencies for the so-called non-uniform stiffeners distribution is studied.

Dynamic simulation of a dipping fault using a three‐dimensional finite difference method with nonuniform grid spacing

We propose a method to analyze dynamic rupture processes of earthquakes with a dipping fault, using a three‐dimensional finite difference (FD) method with nonuniform grid spacing. This approach does not require aligning the fault plane to the FD grid for implementation of the FD method. It can be used to deal with a realistically complex fault geometry model. We validate our method by studying two dynamic source problems that have been analyzed by Madariaga et al. One is the instantaneous rupture of a circular fault embedded in a homogeneous elastic medium; the other is the spontaneous rupture of a rectangular fault which starts from a local circular asperity on the fault plane. Our numerical results for different dipping faults are similar with those obtained by Madariaga et al. using a horizontal fault plane model in full space, thus validating our method for dipping fault models.

Low-frequency noise from a bubble plume formed by a plunging water jet

Wind-driven, low-frequency ambient noise in the ocean may be due to bubble clouds created by wave breaking. To investigate this idea, a laboratory experiment was performed in which a vertical jet of fresh water plunged into a fresh water pool, to form a conical plume of bubbles beneath the surface. Both the jet speed, uj, and the air entrainment ratio, q, were carefully controlled and monitored. The power spectra of the sound from the plume, measured with an adjacent hydrophone, exhibit a sequence of nonuniformly spaced peaks below 1 kHz, which are associated with the resonances of the bubble-plume cavity. Each eigenfrequency scales accurately as (1/uj)1/2 and approximately as (1/q)1/4. A theoretical analysis of these scalings, based on a momentum-flux argument, shows that the sound speed profile within the plume varies as the square-root of depth down the axis. Using this square-root profile in the wave equation, an analytical solution for the pressure field within the plume is obtained, from which an explicit expression for the eigenfrequencies is derived. These theoretical eigenfrequencies, predicted from the conical geometry and square-root sound speed profile, exhibit the same nonuniform spacing and inverse-fractional power-law scalings as seen in the data. [Research supported by ONR.]

Nonuniform dual band array with optimum side-lobe levels

A linear symmetric stub-loaded dual-band rectangular microstrip antenna array (RMSA array) with nonuniform interelement spacing has been proposed for reduced side-lobe levels at both resonant frequencies. The interelement spacing has been optimized using a gradient search algorithm. It is observed that the side-lobe level reduces as a function of the number of elements. The predicted radiation patterns have been verified experimentally. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 615–617, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21424

Analytical and experimental modal analysis of nonuniformly ring-stiffened cylindrical shells

In this research, the free vibration analysis of cylindrical shells with circumferential stiffeners, i.e., rings with nonuniform stiffener eccentricity and unequal stiffener spacing, is investigated using analytical and experimental methods. The Ritz method is applied in analytical solution, while stiffeners are treated as discrete elements. The polynomial functions are used for Ritz functions. The effects of nonuniformity of stiffener distribution on natural frequencies are considered for free–free boundary conditions. Results show that, at constant stiffener mass, significant increments in natural frequencies can be achieved using nonuniform stiffener distribution. In experimental method, modal testing is performed to obtain modal parameters, including natural frequencies, mode shapes, and damping in each mode. Analytical results are compared with experimental ones, showing good agreement. Because of insufficient experimental modal data for nonuniform stiffener distribution, the results of modal testing obtained in this study could be a useful reference for validating the accuracy of other analytical and numerical methods for free vibration analysis.

A survey of stand establishment and in-row spacing uniformity in Washington potato fields

Missing plants and non-uniform in-row plant spacing can result in economic loss for potato growers. In-row seedpiece and plant spacing uniformity of 70 Washington potato fields was measured, and factors contributing to missing plants investigated from 2000 through 2002. Ninety-one percent of the fields were planted with cut seedpieces, and the remaining 9% were planted with cut seedpieces, and the remaining 9% were planted with whole, uncut seed tubers. Russet-type cultivars were planted in 79% of the fields, and the remaining 21% were planted with red-skinned and yellow- and white-fleshed cultivars. Seedpiece or plant spacing deviated an average of 25% from the intended spacing mean, with a range of 7% to 43%. Coefficients of variation (CV) for grower in-row plant and seedpiece spacing ranged from 18% to 69% compared with a hand-planted check average of 13%. Based on the growers’ intentions, the average plant population of the 70 fields should have been 44,000 plants ha−1, but averaged only 40,600 plants ha−1. On average, 6% of the grower-intended stand was missing because of planter skips, while less than 1% was missing due to seedpiece failure or decay. There were 1,980 clumped seedpieces ha−1 and each clump typically contained two seedpieces. Twenty-one percent of the fields had at least 700 planter-skips ha−1 where three or more consecutive plants were missing. Despite management efforts, planters were typically unable to place seed uniformly at the intended spacing. Improved planter and seed-cutting-operation management along with new planter technology would likely improve Washington potato stands.

Mechanistic models for pool nucleate boiling heat transfer: input and validation

Correlations for nucleate boiling heat transfer should be improved, or in the long term possibly be replaced, by the development of mechanistic simulations that include the non-uniform spacing and variable characteristics of the nucleation sites and non-linear interactions between the sites. This paper discusses the interactions that should be included in simulations and some lessons from a first attempt to validate a particular simulation against experimental spatio-temporal data for wall temperature. Input data for nucleation site positions and characteristics are a particular problem and the prospects for obtaining this data from measurements that are independent of boiling are discussed.

Transient vaporization and burning in dense droplet arrays

Three-dimensional droplet-array combustion with an unsteady liquid-phase and a quasi-steady gas-phase is studied computationally by a generalized approach using a mass-flux potential function. Symmetric and asymmetric droplet arrays with non-uniform droplet size and non-uniform spacing are considered. Burning rates are computed and correlated with the number of droplets, an average droplet size, and an average spacing for the array through one similarity parameter for arrays as large as 1000 droplets. Total array vaporization rates are found to be maximized at a specific droplet number density that depends on liquid volume within the array. An unsteady liquid-phase model with either a uniform or a radially varying temperature distribution is coupled with the quasi-steady gas-phase solution for decane, heptane, and methanol fuels. Droplet interactions and liquid-phase heating have been shown to almost double the lifetime when compared to an isolated droplet. Depending on fuel type, initial temperature, and array geometry, droplets may initially burn with individual flames, transition to a single group flame, and transition back to individual flames as vaporization progresses. In most cases, group combustion occurs upon ignition and is the dominant mode of combustion.

Response of Maize and Soybean to Variability in Stand Uniformity

The literature indicates variable results in response to uneven stands. We tested the hypothesis that the effect of uneven stands on grain yield varies depending on the vegetative and reproductive plasticity of the species and cultivars. Treatments consisted of a uniform control, nonuniform plant spacing between plants, and uneven seedling emergence. For maize (Zea mays L.), average yield per plant (Yp) decreased 0.68 g for every unit increase in percentage coefficient of variation (CV) for vegetative biomass per plant (Vp). Contrarily, soybean [Glycine max (L.) Merr.] Yp was not affected by increments in plant size variation. A model based on the relationship between Yp and Vp and on mean and CV for Vp was used to estimate the effect of nonuniformity on grain yield in maize and soybean cultivars. Based on these models and assuming constant average Vp with a normal frequency distribution throughout different stand uniformity treatments, increases in CV for Vp resulted in less grain yield in maize but not in soybean. Reductions in vegetative biomass produced further yield drops according to the specific relationship between Yp and Vp. The effect of unevenness in plant sizes on maize grain yield would depend on the characteristics of the hybrid. A stable hybrid is characterized by low decreases in Vp in response to heterogeneity, low threshold Vp for prolificacy and for grain yield, and a low curvature in the Yp/Vp relationship.

Nonlinear dynamic analysis of rolling element bearings due to cage run-out and number of balls

This paper presents an analytical model to investigate the nonlinear dynamic behavior due to cage run-out and number of balls in a rotating system supported by rolling element bearings. Due to run-out of the cage, the rolling elements no longer stay equally spaced. The mathematical model takes into account the sources of nonlinearity such as the Hertzian contact force and cage run-out resulting transition from no contact to contact state between rolling elements and races. The contact between the rolling elements and races is treated as nonlinear springs. The nonlinear stiffness is obtained by application of Hertzian contact deformation theory. The implicit-type numerical integration technique Newmark- β with Newton–Raphson method is used to solve the nonlinear differential equations iteratively. The results are presented in the form of fast Fourier transformations (FFT) and phase trajectories. It is implied from the obtained FFT that due to the non-uniform spacing the ball passage frequency is modulated with the cage frequency.

Dense gas extraction using a hollow fiber membrane contactor: experimental results versus model predictions

Hollow fiber membrane contactors offer a number of advantages over dispersed phase contactors for mass transfer operations such as extraction of aqueous feeds. In addition, dense gases provide benefits that traditional extraction solvents do not. A mathematical model of a membrane contactor was developed that predicts the steady state fluid velocities and solute concentrations by solving the applicable conservation equations. The gravitational force term was included because the low kinematic viscosity of dense gases can render buoyancy-induced flow significant. A method of calculating the individual and overall mass transfer coefficients from the model results is also presented. The model was validated by comparing predicted Sherwood versus Graetz numbers for tube flow to those obtained from the classical equations that have been repeatedly confirmed by experiment. The three boundary conditions examined were constant wall concentration, constant flux, and linear variation of wall concentration with length. For all three cases the model predictions were in close agreement with those of the classical equations over a wide range of Graetz numbers, except for the constant flux condition at Graetz numbers greater than about 1000. This exception reflects a limit on the mass transfer rate imposed by the constant flux boundary condition. Graetz numbers greater than 1000 (found with short tubes or very high velocities) are not usually encountered in practical applications. Model results are compared to experimental data for the extraction of isopropanol or acetone from water into dense CO 2, obtained over a range of flow rates using modules of different packing densities. Overall the model predicted the data reasonably well, proving the model to be a useful tool for evaluating potential new applications of the technology. For the isopropanol extractions the average absolute errors in the predicted mass transfer coefficients and yields were 29% and 31%, respectively, while for the acetone work the average absolute errors were 39% and 11%. In both cases the predicted mass transfer coefficients were lower than the observed values at the highest aqueous flow rates studied; usually the error became less negative (then increasingly positive in some instances) with decreasing flow rate. This trend is partly attributable to flow maldistribution (leading to reduced efficiency) caused by unavoidable non-uniform fiber spacing and variation in fiber diameter. Other possible sources of modeling error are discussed as well. With acetone, most of the resistance to mass transfer was in the aqueous phase boundary layer, as expected for a solute with a relatively high partition coefficient ( m A). On the other hand, for isopropanol (a lower m A compound) a greater portion of the resistance was attributable to the solvent-filled pore and the solvent phase boundary layer, although the aqueous resistance was still significant. Mass transfer coefficients and yields were higher for acetone than for isopropanol, and aqueous boundary layer penetration was more rapid; both results were a consequence of the higher m A of acetone. For both solutes, usually the mass transfer coefficient increased with increasing aqueous phase Graetz number, as expected when the aqueous phase mass transfer resistance is important. Moreover, yield generally increased with increasing solvent/feed ratio as anticipated.