In diesem Kapitel widmen wir uns der Darstellungstheorie der Symmetrischen Gruppe $$S_n$$ . Eine wichtige Anwendung dieser Darstellungstheorie ist die Konstruktion von irreduziblen Darstellungen von Matrixgruppen auf Tensorprodukträumen.
Rotational $SU(3)$ algebraic symmetry continues to generate new results in the shell model (SM). Interestingly, it is possible to have multiple $SU(3)$ algebras for nucleons occupying an oscillator shell $η$. Several different aspects of the multiple $SU(3)$ algebras are investigated using shell model and also deformed shell model based on Hartree-Fock single particle states with nucleons in $sdg$ orbits giving four $SU(3)$ algebras. Results show that one of the $SU(3)$ algebra generates prolate shapes, one oblate shape and the other two also generate prolate shape but one of them gives quiet small quadrupole moments for low-lying levels. These are inferred by using the standard form for the electric quadrupole transition operator and using quadrupole moments and $B(E2)$ values in the ground $K=0^+$ band in three different examples. Multiple $SU(3)$ algebras extend to interacting boson model and using $sdg$IBM, the structure of the four $SU(3)$ algebras in this model are studied by coherent state analysis and asymptotic formulas for $E2$ matrix elements. The results from $sdg$IBM further support the conclusions from the $sdg$ shell model examples.
Vibration and welding characteristics of a 94 kHz ultrasonic plastic welding system are studied. The 94 kHz ultrasonic plastic welding systems consist of a 30-mm-diameter bolt-clamped Langevin-type PZT longitudinal transducers with four PZT rings, a stepped horn (vibration transform ratio N = 3.0) with a supporting flange at a nodal position and a catenoidal horn (N = 3.13) with an 8-mm-diameter welding tip. Maximum vibration velocity of the 94 kHz welding tip was 3.2 m/s (peak-to-zero value) at loaded condition. The welding characteristics of the 1.0-mm-thick polypropylene sheet specimens using the 94 kHz welding system were studied. Using the 94 kHz system, a weld strength of more than 370 N per one welded area was obtained at a vibration velocity of 2.7 m/sp-0 (peak-to-zero value), welding time of 0.8 s and static pressure of 600 kPa.
This work develops an effective approach for studying the generation of second harmonics of the Lamb modes (LMs) in layered planar structures. Within second-order perturbation approximation, there are second-order bulk and surface/interface driving sources in layered planar structures when a primary LM propagates. These driving sources can be thought of as forcing functions of a series of double frequency Lamb modes (DFLMs). The total second-harmonic fields consist of a summation of DFLMs in the corresponding stress-free layered structures. Numerical simulation show that the forcing function associated with the soft adhesive layer of a layered planar structure plays a dominant role in the process of second-harmonic generation.
Conventional ultrasound systems with fixed transmit focus and dynamic receive focusing suffer from limited depth of field and poor SNR uniformity. Based on fixed receive focusing, this paper proposes an SNR-dependent 2-D retrospective filtering technique to extend the depth of field, in which both the sidelobe energy and the filter energy are minimized simultaneously. According to the estimated SNR of the unfiltered image, the proposed 2D filter can provide the optimal compromise between image quality and SNR while maintaining the moderate filter size. Simulations were performed to demonstrate the efficacy of the proposed technique. It has been shown that the proposed 2-D filter technique outperforms conventional 1-D lateral filter and classical 2-D Wiener filter in terms of both SNR and contrast resolution.
We present an integrated catheter for 3-D intracardiac echocardiography and ultrasound ablation. The device uses a 9 Fr (3 mm O.D.) catheter lumen with a 14 Fr (4.7 mm O.D.) tip. Real-time 3D imaging is achieved with a forward-looking 112 element, 5 MHz two-dimensional array built on a multi-layer flexible interconnect circuit. Transducer elements typically showed a 21% bandwidth and a pulse-echo insertion loss of 80 dB. The imaging array, attached to our real-time 3-D scanner, was used to image tissue phantoms and a fixed sheep heart. The ablation transducer is a ring of 10 MHz PZT-4 placed around the imaging array. The ring has a 4.5 mm O.D. and a 3.1 mm I.D. for a total area of 33.4 mm(2). Using a hydrophone, the spatial-peak, temporal-average intensity of the ablation ring was measured at a maximum of 500 cycles per burst and a PRF of 10.3 kHz to be 16.1 W/cm(2). The ablation ring was then used to heat tissue-mimicking rubber with absorption comparable to tissue. A temperature rise of 14 degreesC was recorded. In our final experiment, the imaging array was used to view a 1 cm thick piece of beef muscle with a 12 mm hole. The ablation ring was then used to create a lesion adjacent to the hole.
Based on recent reports about the acoustical power distribution in SAW resonators we present an analytical method to determine the distribution of the dynamic strain and stress components in SAW resonators on LiTaO3. This enables us to calculate the absolute strain and stress values for each point in the layer of a resonator for any driving condition and frequency. The SAW resonator is described by a P-Matrix based model, which gives us the distribution of the potential power and the resulting energy density. For calculation of the relative strain and stress values we used the partial wave method. Using the correlation between the total acoustic power and the energy density distribution normal to the substrate surface, we can calculate the strain and stress values for a given input power. For the direct experimental verification of our calculations we measured the SAW induced displacements as a function of input power.
In this paper, the measured "rapid motion" includes components with minute amplitude on the order of several tens of micrometers up to several hundred Hertz, which has not been recognized in standard M-mode echocardiography, B-mode echocardiography, nor in conventional tissue Doppler imaging (TDI). By employing multiple 1-D configurations, each of which shows the axial component along the ultrasonic beam with fast acquisition intervals, the 2-D spatial distribution of the rapid velocity components is continuously obtained on the cross-sectional 2-D image.
We present results of a pilot study of ex vivo and in vivo acoustic radiation force impulse (ARFI) imaging demonstrating measurements of the mechanical properties of the medial and adventitial layers in the carotid, and popliteal arteries. The data was obtained on a commercial scanner, providing co-registered B-mode and Color Doppler images. A real-time ARFI imaging system capable of achieving frame rates of 0.75 Hz was developed. The 2-D and 1-D images of the tissue's response to brief and localized applications of radiation force show good correlation with B-mode and pathology based characterization of vessel geometry and plaque stiffness. Measurements of arterial response during both systole and diastole are presented. We address implementation issues and discuss the potential applications of this new vascular imaging method.
We present a new actuator based on glass capillary bonded to laser-cut PZT plate, for ultrasonic control of microparticles inside microfluidic channels. The actuator generates high velocity bending modes at low CMOS compatible 5-10 Vpp drive. The high velocity enables focusing of samples at the nodes and the antinodes of the bending waves in the capillary. Separation of 3 and 10 microns polystyrene microbeads in space by 800 /spl mu/m is achieved. E.Coli cells and blood cells can also be separated with particles with lower density than water being placed at the transverse velocity nodes and heavier particles at the antinodes.
Resolution and penetration are primary criteria for clinical image quality. Conventionally, high bandwidth for resolution was achieved with a short pulse, which results in a tradeoff between resolution and penetration. Coded excitation extends the bounds of this tradeoff by increasing signal-to-noise ratio (SNR) through appropriate coding on transmit and decoding on receive. Although used for about 50 years in radar, coded excitation was successfully introduced into commercial ultrasound scanners only within the last 5 years. This delay is at least partly due to practical implementation issues particular to diagnostic ultrasound, which are the focus of this paper. After reviewing the basics of biphase and chirp coding, we present simulation results to quantify tradeoffs between penetration and resolution under frequency-dependent attenuation, dynamic focusing, and nonlinear propagation. Next, we compare chirp and Golay code performance with respect to image quality and system requirements, then we show clinical images that illustrate the current applications of coded excitation in B-mode, harmonic, and flow imaging.
SAW devices are routinely frequency trimmed at the wafer level prior to the dicing process so to improve yield at the assembly level. The trimming can be achieved by using wet etching, reactive ion etching, ion beam milling, and other methods. It is also possible to trim the frequency of patterned SAW wafer by depositing dielectric thin films on the wafer but this method is usually done for the purpose of finger shorting protection from metallic particles. Reactive ion etching can be used to trim assembled SAW devices prior to encapsulation. This is seldom employed since it is considered costly, inefficiently, and difficult to perform in-situ. In this paper we propose trimming assembled SAW resonator (SAWR) by using the conventional crystal resonator fine-tuning process with gold thin film addition. Nowadays, the fine-tuning process is a necessary step in crystal resonator production. We show that this is a simple and well-controlled method to trim assembled SAW resonator also. This method provides a wide trimming rage and the gold film is thin enough not to short out the SAW transducers so that the SAW resonator's integrity can be maintained.
It has been previously shown that high frequency ultrasound (20-100 MHz) can be used to detect cellular structure changes in tissues and cell ensembles. However, the changes seen in the backscattered ultrasound intensity and frequency spectrum are not fully understood. In this paper we attempt to better understand the nature of these changes by examination of the backscatter power spectra from cell ensembles (in pellet form) that have undergone two different types of cell death: by exposure to the chemotherapeutic cisplatin and by withdrawal of nutrients (decay). Three different ultrasound transducers were used, centered at 20MHz and 40MHz. In both death pathways, an increase of the midband fit of 10-12dB was measured, and there were significant changes in the spectral slopes. Furthermore, our initial analysis of the backscatter from single cells and polystyrene microspheres demonstrates the potential of the technique to assess scatterer size.
Generation of B-mode images involves envelope detection of the RF signals. Various detection algorithms are available. A trade of between performance, price, and complexity determines the choice of algorithm in an ultrasound system. A Hilbert transform (HT) and a subsequent computation of the magnitude give the ideal envelope, but the approach (IDE) is expensive and complex. A rectifier (REC) is a simple, low-cost solution, but the performance is severely degraded (especially in dynamic imaging). This study has investigated the possibility of providing a detector with a complexity and cost close to REC, while maintaining performance close to IDE. Two low-cost detectors have been implemented and evaluated on in-vivo data. The first approach is an expansion of the rectifier with a median filter (ERM). The second detector (TAS) approximates the HT by a time delay and the magnitude by a weighted sum of the real and imaginary signals. The four detectors were evaluated on in-vivo data acquired with a B-K Medical 2102 scanner interfaced to the sampling system RASMINE. Three data sets were acquired with three different center frequencies. Hundred images were acquired as the transducer was moved across the liver and the carotid artery of a 30 years old healthy male. The root-mean-square (RMS) error relative to the IDE, and a visual inspection determine the performance. For the 3.5 MHz data sets RMSE's of 15.7%, 1.6%, and 1.9% are obtained with REC, ERM, and TAS, respectively. The performance is similar to the two other data sets. Close to envelope detection is therefore obtainable with a simple detector (ERM or TAS), which is less complex and costly.
A major mechanism of cross-coupling in capacitive micromachined ultrasonic transducer (CMUT) arrays in immersion operation is represented by the acoustic interactions among the membranes. In this work, acoustic interactions are investigated by means of optical displacement measurements. Experiments are conducted on a variety of CMUTs, with different size and number of elements, using both air and liquids as coupling mediums. In past investigations, Stoneley-type interface waves propagating along the surface of a CMUT array have been identified as an important source of cross-coupling. Indeed, the experimental results herein reported indicate that mutual acoustic coupling through the liquid is mainly responsible for setting the membranes of coupled elements into motion.
We have developed a high-resolution method to estimate multiple velocities of flows within one sample volume of pulse echo ultrasound for small flows. The method uses maximum entropy method (MEM) to estimate the covariance matrix of a two-dimensional (2D) signal when data length is limited. The estimated covariance is used to calculate high-resolution 2D power spectrum of flows. The simulation and experiment results show that our method provides high-resolution estimations for multiple velocities when data length is limited and small flows are located.
For measurement of minute change in thickness using ultrasound, the phase tracking method based on the constraint least-squares approach has been developed. By using the thickness change of arterial wall measured by this method, local elastic characteristic of the arterial wall is calculated, and fast calculation makes a real-time 2D measurement of the elastic characteristics possible. We have developed a real-time measurement system that displays the 2D image of the elastic characteristics of the arterial wall. In order to assess the measurement accuracy of the system, we made a phantom of silicone tube, and the thickness change of the tube wall was measured by the system and another off-line ultrasound measurement system. From the experimental results, it was obtained that our novel system had an accuracy of about 0.2 /spl mu/m. using this system, we measured the thickness change of carotid arterial wall, and obtained real-time 2D images of the elastic characteristics.
