Sum Mode Research Articles

The generation of sum and difference patterns using fractal subarrays

In this letter, we explore the potential for the application of fractal subarrays to the generation of sum and difference patterns. For the purposes of this investigation, a standard planar array is decomposed into two subarrays: one in the form of a Sierpinski carpet, and the other consisting of its complement. A methodology is then introduced for feeding the two subarrays in order to produce either a sum or a difference pattern. A particular example is considered in which directive gain plots are obtained for both the sum and difference modes of a 27×27 planar array. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 54–57, 1999.

The generation of sum and difference patterns using fractal subarrays

In this letter, we explore the potential for the application of fractal subarrays to the generation of sum and difference patterns. For the purposes of this investigation, a standard planar array is decomposed into two subarrays: one in the form of a Sierpinski carpet, and the other consisting of its complement. A methodology is then introduced for feeding the two subarrays in order to produce either a sum or a difference pattern. A particular example is considered in which directive gain plots are obtained for both the sum and difference modes of a 27×27 planar array. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 54–57, 1999.

Optimal Compromise Between Sum and Difference Patterns While Fixing Quasi-Nulls in Both

Methods previously developed for designing linear array monopulse antennas with relatively simple feed network requirements are extended to allow the suppression of jamming signals in both sum and difference modes.

Sub-Poissonian quantum-beat laser without inversion

Using the `dressed-atom-dressed-mode' approach and separating the decoupled atomic state, we investigate the statistical properties of a quantum-beat laser without inversion. While the fluctuations of the relative amplitude and phase are retained at their vacuum noise levels, the intensity fluctuations in the sum mode are reduced below the shot noise limit with an optimum Mandel parameter when the laser is operated well above threshold. In particular, we show that the decoupled atomic state significantly relaxes the parameter requirement for squeezing. The physical cause is also explained.

Squeezed Quantum-Beat Laser Without Inversion

A quantum-beat laser without inversion is proposed for producing two-mode suqeezing. Using the dressed-atom-dressed-mode approach, the master equation is derived and the variances in the sum mode intensity and in the relative amplitude and phase are calculated. When the laser is operated well above threshold, the intensity fluctuations in the sum mode are reduced below the shot noise limit with an optimum Mandel parameter of -0.5. At the same time, the fluctuations in the relative amplitude and phase are retained at their vaccum noise levels.

Symmetry relations for nonlinear pressure interactions on oscillating cylinders

Combination modes appear in the spectrum of the surface pressure signals when a circular cylinder is forced to oscillate at a frequency different from the von Karman vortex shedding frequency. The spatial symmetry of the sum and difference modes depends on the direction of cylinder oscillation, and is predictable with a simple set of symmetry relations. As a result of the symmetry relations, cross-flow oscillations of the cylinder aimed at enhancing fluctuating lift also channel energy into the fluctuating drag component through the combination modes.

BiCMOS implementation of a fuzzy system

BiCMOS circuits which can realise the different mathematical operations within a fuzzy system are presented in this paper. To maximise the operating speed of these circuits and increase the packing density, an analog approach is adopted throughout. The initial focus is on the design of circuits to implement fuzzification and intersection. The remainder of the paper focuses on the hardware implementation of implication and defuzzification, thus completing the fuzzy cell library. A major objective of this work is to maintain a design strategy which yields simple circuits so as to minimise cell density. Therefore, the circuits presented are relatively simple but effective with regard to the mathematical functions that they are required to generate within the cell. For example, fuzzification is achieved using the current spike derived from a CMOS inverter during switching. Both intersection and implication are realised using a single MOS transistor operating in the triode region. The remaining circuitry consists mainly of an operational amplifier in the summing mode to realise the function of defuzzification. The complete fuzzy system is simulated and a transfer characteristic is presented and discussed.

FDTD verification of deep-set brain tumor hyperthermia using a spherical microwave source distribution

Although use of noninvasive microwave hyperthermia to treat cancer is problematic in many human body structures, careful selection of the source electric field distribution around the entire surface of the head can generate a tightly focused global power density maximum at the deepest point within the brain. An analytic prediction of the optimum volume field distribution in a layered concentric head model based on summing spherical harmonic modes is derived and presented. This ideal distribution is then verified using a three-dimensional finite difference time domain (FDTD) simulation with a discretized, MRI-based head model excited by the spherical source. The numerical computation gives a very similar dissipated power pattern as the analytic prediction. This study demonstrates that microwave hyperthermia can theoretically be a feasible cancer treatment modality for tumors in the head, providing a well-resolved "hot-spot" at depth without overheating any other healthy tissue.

MeV gamma ray detection algorithms for stacked silicon detectors

By making use of the signature of a gamma ray event as it appears in a stack of N=5 to 20 lithium-drifted silicon detectors and applying smart selection algorithms, gamma rays in the energy range of 1 to 8 MeV can be detected with good efficiency and selectivity. Examples of the types of algorithms used for different energy regions include the simple sum mode, the sum-coincidence mode used in segmented detectors, unique variations of sum-coincidence for an N-dimensional vector event, and a new and extremely useful mode for double escape peak spectroscopy at pair-production energies. The latter algorithm yields a spectrum similar to that of the pair spectrometer, but without the need for the dual external segments for double escape coincidence, and without the large loss in efficiency of double escape events. Background events due to Compton scattering are largely suppressed. Monte Carlo calculations were used to model the gamma ray interactions in the silicon in order to enable testing of a wide array of different algorithms on the event N-vectors for a large-N stack. >

Resonance in axisymmetric jets with controlled helical-mode input

This work involves active control of fundamental two- and three-dimensional amplified modes in an axisymmetric jet by introducing localized acoustic disturbances produced by an azimuthal array of miniature speakers placed close to the jet lip on the exit face. The independent control of each speaker output allowed different azimuthal amplitude and phase distributions of periodic inputs. The types of inputs used in this study consisted of conditions to force helical mode pairs with the same frequency and equal but opposite azimuthal wavenumbers, m = ±1, separately, or with axisymmetric ( m = 0) modes. Three forcing conditions were studied in detail. The first consisted of a weakly amplified helical mode pair which was essentially ‘superposed’ with the natural jet instability modes. This provided a reference to the second case which consisted of the same helical mode pairs along with an axisymmetric mode at the harmonic streamwise wavenumber. This combination led to the resonant growth of the otherwise weakly (linear) amplified subharmonic helical modes. A weakly nonlinear three-wave amplitude evolution equation with a coupling coefficient derived from the data was found to model the enhanced growth of the subharmonic helical modes well. The third case consisted of forcing only m = ±1 helical modes at a frequency which was close to the most amplified. This was compared to the results of Corke et al. (1991) who forced an axisymmetric mode at the same frequency and found it to lead to the enhanced growth of near-subharmonic modes, as well as numerous sum and difference modes. The helical modes had effects identical to the previous work and confirmed the resonant amplification of a near-subharmonic mode. The amplitude development was also well represented by the nonlinear amplitude equation, including the dependence of the streamwise amplification rate on the azimuthal change in the fundamental-mode initial amplitude. However, the coupling coefficient in this case was approximately one-third that with exact fundamental-subharmonic resonance. Finally we offer some explanation for the selection of the different mode frequencies in this case.

Two‐Phonon Combination Mode Spectra of AgGaS2

AbstractAbsorption spectra of (001)‐oriented AgGaS2 single crystals are measured in the wavenumber range from 400 to 900 cm−1. The spectra exhibit 12 structures due to two‐phonon combination modes which can be all interpreted as sum modes of zone‐centre phonons. Possible frequencies for the B1 and A2 modes are discussed. The results obtained are compared with second‐order Raman spectra of the compound.

The response and symmetry properties of a cylinder wake subjected to localized surface excitation

Symmetric and antisymmetric periodic disturbances introduced directly into the boundary layer on a circular cylinder at low Reynolds number are shown by experiment to be capable of modifying the vortex formation process and changing the vortex shedding frequency. Spectral measurements have shown that the antisymmetric vortex shedding mode is strongly coupled to the symmetric first harmonic mode. When symmetric excitation is applied, three different shapes of the mean velocity profiles can be identified as the forcing amplitude is increased. At low forcing amplitudes nonlinear interaction between the forcing field and the natural wake oscillator produces sum and difference modes. Symmetric forcing with intermediate-amplitude disturbances suppresses the natural shedding frequency, and the dominant vortex shedding energy appears as a sinuous mode at half the excitation frequency. At high symmetric forcing amplitudes a threshold is reached, above which the large-scale vortices do not form. The symmetries of the combination modes follow two simple rules based on the symmetries of the interacting modes. The symmetry rules provide an explanation for the fundamental difference in wake structure that occurs between symmetric forcing and antisymmetric forcing.

The Weighting Function of a Neutron Capture Detection System

This paper reports on a set of efficiencies and response functions for 18 gamma rays in the range from 02. to 8.4 MeV experimentally determined via a (p,{gamma}) coincidence method for a neutron capture detection setup. This consists of two cylindrical deuterated hexabenzene (C{sub 6}D{sub 6}) liquid scintillators placed symmetrically and normally with respect to the beam and operated in sum mode. A pulse-height weighing function is derived from this data set and applied to the measurement of neutron capture in the 1.5-keV resonance of {sup 56}Fe relative to capture in the 5.2-eV resonance of {sup 109}Ag. A value of {Gamma}{sub {ital n}} = 62.9 {plus minus} 2.1 meV has been obtained for the neutron width, in good agreement with the value of {Gamma}{sub {ital n}} = 61.7 {plus minus} 0.9 meV from transmission measurements. The extension of the validity of this weighing function to samples of different thickness and composition is discussed.

Mode selection and resonant phase locking in unstable axisymmetric jets

This paper presents experimental results on the nonlinear phase locking present in the resonant growth of unstable modes in the shear layer of an axisymmetric jet. The initial instability modes scale with the exiting shear layer and grow convectively with downstream distance. Because of the special condition at the exit lip of the jet, the initial growth of modes is very sensitive to local unsteady pressure fields. A part of the unsteady field is stochastic in nature. To a larger extent, the pressure field at the lip of the jet contains the imprint of the downstream-developing instability modes, in particular the first unstable axisymmetric mode and its subharmonic. These are felt at the lip of the jet as a result of the energetic processes of the first vortex rollup and vortex pairing. As a result, a resonant feedback exists which under special conditions makes the initial region of this flow in some sense absolutely unstable. The features of this process are brought out by the normalized crossbispectrum or cross-bicoherence between the instantaneous unsteady pressure at the lip of the jet and velocity time series measured at the same azimuthal position for different downstream locations. These give a measure of the nonlinear phase locking between the principle modes and their sum and difference modes. Analysis of these show a perfect nonlinear phase locking at the fundamental axisymmetric and subharmonic frequencies between the pressure field at the lip and the velocity field at the downstream locations corresponding to the energy saturations of the fundamental and subharmonic modes. This resonance process can be suppressed or enhanced by low-amplitude axisymmetric mode forcing at the natural preferred frequency of slightly detuned cases. Contrasted to this is the behaviour of the fundamental m = ± 1 helical mode. This mode was found to have the same spatial growth rate as the axisymmetric mode and a streamwise frequency approximately 20 % higher, in agreement with theoretical predictions. However, short-time spectral estimates showed that these two fundamental modes do not exist at the same time or space. This suggests that each is a basin of attraction which suppresses the existence of the other. The apparent non-deterministic switching observed between these modes is probably the result of the response of the jet to stochastic input of axisymmetric or non-axisymmetric disturbances. This scenario may lead to a low-dimensional temporal model based on the interaction between these two modes which captures most of the early random nature seen in our experiments.

Determination of the critical points in the phonon dispersion curves of SnS 2 by means of the simultaneous analysis of i.r. and Raman two-phonon spectra

The explanation of the two-phonon spectrum of SnS 2 is achieved in terms of sum and overtone modes of the A and Γ points by comparing the observed polarization properties of the i.r. and Raman structures with those predicted by the selection rules.

Variable geometry capacitive probes for multipurpose sensing

A capacitive array for robotic proximity and feature sensing has been designed, modeled, and tested. The basic probe consists of alternating metallic strip electrodes. One set of strips makes up the drive plate. The other set consists of tiny receivers. Both sum and differential modes of operations are used to allow one to detect proximity and features, respectively. Modeling has encompassed calculation of admittance changes (ΔY) due to the introduction of materials with simple geometric configurations. The theory is developed in detail using the Lorentz reciprocity theorem. The relationship between the spatial frequency of the probe electrodes and the interrogation field penetration is also discussed. Testing has involved scanning a two-port configured probe system over a test piece with known features and flaws. Four capabilities of the probe have been examined: distance ranging, edge detection, field optimization (changing the electric field pattern of the probe to enhance output signal), and complex pattern recognition (filtering). Both dielectric and metal objects have been investigated.

Optimization of Difference Pattern Sidelobes in the Presence of Fictitious Blockage

A method to improve in a particular azimuthal sector the difference radiation pattern sidelobe level of a monopulse antenna of the corporate-fed array type is presented. The technique consists of inserting a central fictitious blockage in the difference aperture distribution that has no effect on the sum mode. No excessive feed complexity or losses are introduced since the feed network is realized with only an extra power divider. The method is applied to a monopulse circular aperture with a central fictitious blockage and a prescribed aperture distribution. The relative size of the blockage is optimized to reduce the difference sidelobe level. In an example presented, the peak difference sidelobe level was decreased 8 dB along the principal plane by the introduction of a blockage that equalled one-third the aperture diameter. However, this improvement was at the expense of higher sidelobe levels in planes at azimuthal angles greater than 20° from the principal plane.

Synthesis of sum and difference patterns for two-section monopulse arrays

A quadratic programming method is described for studying simultaneous sum and difference synthesis compromises, and establishing performance bounds, under the restriction of a two-section array feed network. A composite objective function is minimised, subject to a union of separate sets of sidelobe constraints, for the sum and difference modes of operation, to avoid a conflicting constraint set. Examples are given to illustrate the principal features of the method.

Bipolar and bilateral voltage-current/current-voltage converters using operational amplifiers in summing mode

A practical bipolar, bilateral voltage-source to current-source converter scheme using two operational amplifiers (OA's) in summing mode is described. The scheme also behaves as a current-voltage (I-V) converter when certain specific constraints are observed. The summing mode application of OA's has its effect on the range of operation whose safe limits are discussed. The scheme is versatile, is largely insensitive to supply voltage variations, and can be used with conversion factor scaling for the desired output range with a specific input range excursion.

High-energy gamma ray spectrometer for heavy-ion induced experiments

A gamma-ray detector system of large NaI(Tl) crystals has been constructed to investigated heavy ion reaction mechanisms and highly excited nuclear structure with heavy ion beams. The NaI(Tl) crystals have as a whole a cross section of hexagonal shape of 30 cm between the parallel sides and a length of 20 cm, and are composed of seven substructures based on a honeycomb shape. This is designed for detection of high energy gamma rays with high resolution, and also for use as an anti-Compton spectrometer for a Germanium detector. A good energy resolution of 2.7 (3.2)% fwhm was obtained for 22.3 MeV gamma rays with 18 (39)% detection effeciency of the full-energy-loss peak with anti-Compton mode (sum mode) operation of the trapezoidal NaI(Tl) crystals. Compton scattering background in a spectrum by a Ge detector was successfully reduced by about 60% in applying the trapezoidal NaI(Tl) crystals for Compton suppression. The performance of the spectrometer is discussed.