Conical Bores Research Articles

Collimator optimization for small animal radiation therapy at a micro-CT

PurposeIn radiation therapy of small animals treatment depths range from a few millimetres to several centimetres. In order to spare surrounding organs at risk steep dose gradients are necessary. To minimize the treatment time, and therefore the strain to the animals, a high dose rate is required. A description how these parameters can be optimized through an appropriate choice of collimators with different source surface distances (SSD) as well as different materials and geometries is presented. Material and methodsAn industrial micro-CT unit (Y.Fox, YXLON GmbH, Hamburg, Germany) was converted into a precision irradiator for small animals. Different collimators of either stainless steel (Fe) with cylindrical bores (SSD=42mm) or tungsten (W) with conical bores (SSD=14mm) were evaluated. The dosimetry of very small radiation fields presents a challenge and was performed with GafChromic EBT3 films (Ashland, Vayne, KY, USA) in a water phantom. The films were calibrated with an ionization chamber in the uncollimated field. Treatments were performed via a rotation of the objects with a fixed radiation source. ResultsAs expected, the shorter SSD of the W-collimators resulted in a (4.5±1.6)-fold increase of the dose rates compared to the corresponding Fe-collimators. The ratios of the dose rates at 1mm and 10mm depth in the water phantom was (2.6±0.2) for the Fe- and (4.5±0.1) for the W-collimators. For rotational treatments in a cylindrical plastic phantom maximum dose rates of up to 1.2Gy/min for Fe- and 5.1Gy/min for W-collimators were measured. ConclusionChoosing the smallest possible SSD leads to a high dose rate and a high surface dose, which is of advantage for the treatment of superficial target volumes. For larger SSD the dose rate is lower and the depth dose curve is shallower. This leads to a reduction of the surface dose and is best suited for treatments of deeper seated target volumes. Divergent collimator bores have, due to the reduced scatter within the collimators, a steeper penumbra. The dosimetry of small kilovoltage beams with Gafchromic EBT3 films in a water phantom has proven successful.

Numerical Study on Multi-Stable Oscillations of Woodwind Single-Reed Instruments

Single reed instruments with cylindrical and conical bores were studied numerically, focusing on the dependence of the acoustic mechanism on the bore geometry. As experimentally demonstrated by Idogawa et al. [J. Acoust. Soc. Am., Vol.98, p.540 (1993)], reed instruments can be characterized as multi-attractor systems, which exhibit multi-stable oscillations and hysteretic transitions among oscillating states with change of a control parameter, such as blowing pressure in the mouth. We numerically analyzed dynamical models of single reed instruments to clarify differences in the acoustic mechanisms between cylindrical and conical bore instruments. We analyzed a dynamical model of a cylindrical pipe fitted with a clarinet mouthpiece(CPCM), as a simplified model of the clarinet, and a dynamical model of a truncated cone with a clarinet mouthpiece (TCCM), as a model of conical-bore instruments, together with intermediately shaped models. We found a clear difference in the global structure of transition diagrams (i.e., the overall picture showing the transitions among all the excited states with change of the blowing pressure) between CPCM and TCCM, together with interesting structural changes of the transition diagrams in the intermediate models.

The Powered Scattering-Magnet Program at the NHMFL

The National High Magnetic Field Laboratory is developing several powered magnets employing novel configurations for use in photon and neutron scattering experiments. First is a split resistive magnet being built for Far-Infrared Scattering at the NHMFL in Tallahassee. This magnet has spurred the development of the novel Split Florida-Helix (SFH) technology. High-field test coils of the SFH concept have been designed and built. Test results are presented. Second, Series-Connected Hybrid magnets with horizontal, conical bores are being designed for neutron scattering experiments at the Hahn-Meitner Institute in Berlin and the Spallation Neutron Source in Oak Ridge, TN. A new resistive magnet technology, the Conical Florida-Bitter (CFB), is being developed suitable for use as the resistive insert of these magnets. A high-field CFB test coil has been designed and is under construction. The conceptual design of the eventual hybrid system is presented along with the detailed design of the high-field test coil.

Observing the effects of waveguide model elements in acoustic tube measurements

The theory of digital waveguide synthesis and its use in modeling virtual musical instruments, and in particular for cylindrical and conical bores, is well documented. Current models rely on certain approximations, however, particularly in cases where the theory provides no exact closed form solution, such as the reflection and transmission occurring at the bore’s open end. In this research, we observe, from a time domain, waveguide model perspective, how the theory corresponds to actual acoustic measurements. We consider four simple acoustic tube structures, incorporating both open and closed boundary conditions for both a simple cylinder and a cylinder with a conical flare, allowing us to isolate, and observe, the filtering effects of each model component.

An alternative to the traveling-wave approach for use in two-port descriptions of acoustic bores.

For more than a decade, the digital waveguide model for musical instruments has been improved through the simulation of cylindrical and conical bores. But several difficulties remain, such as instabilities due to growing exponentials which appear when two conical bores are connected with decreasing taper. In this paper, an alternative overcoming these difficulties is proposed and can be extended to shapes other than cylinders, cones, and hyperbolic horns. A two-port model with more general state variables than usual traveling waves works efficiently for any shape without discontinuities in cross section. The equations for connecting separate elements at discontinuities make this two-port model appropriate for use in time domain simulation of the physical behavior of the wind instrument and its interactions with the player. The potential of this new approach is illustrated by several detailed examples.

Physical model musical tone synthesis system employing truncated recursive filters

A tone synthesis system employs digital filtering methods to enable the practical usage of unstable filter elements in a real-time synthesis model. Truncated infinite impulse response (TIIR) filters are used to approximate portions of the reflection impulse response of an acoustic horn such as a trumpet bell. Methods for resetting filter state enable the use of internal unstable filter poles. Similar state resetting methods enable the use of unstable one-pole filters in the scattering junction formed between two conical acoustic bores. High quality tone synthesis can be achieved without the necessity of a complicated filter representing large sections of the bore of a woodwind instrument.

The discontinuous conical bore as a Sturm–Liouville problem

In some cases the reflection functions associated with the discontinuities in conical bores are growing exponentials [J. Martinez and J. Agul- ló, J. Acoust. Soc. Am. 84, 1613–1619 (1988)]. It is shown that discontinuities can be modeled by a Sturm–Liouville system using a pressurelike quantity as the dependent variable. For the subset of discontinuities exhibiting the growing exponential reflection function, the Sturm–Liouville potential function is an energy well. This well is shown to support exactly one trapped energy mode which corresponds to the growing exponential. It is shown that in the region surrounding the discontinuity for these systems, traveling Fourier components taken together with their reflected waves do not constitute a complete set and that the trapped mode is required to complete the set. On the other hand, for systems which do not exhibit the growing exponential, the Sturm–Liouville potential is an energy barrier with no trapped modes, and the Fourier components compose a complete set within the conical regions. Furthermore, a change of dependent variable can be used to go from a Sturm–Liouville description involving an energy well to one involving a barrier, thus eliminating the trapped mode.

Input response of cylindrical and conical bores with a single tone hole: Measurements and predictions

There exist few measurements on the acoustical response of tone holes in conical‐bore air columns. For practical application to woodwind design, the accuracy of predictive models is said to be insufficient [McCann and Mathews, J. Acoust. Soc. Am. 91, 2449 (A) (1992)]. Experiments performed test the transmission line model of air columns and tone holes. The input impedance was measured over the range 150–10 000 Hz for a single tone hole in a cylindrical bore and in a conical bore. The cylindrical bore had length 920 mm and radius 7.2 mm, and the conical bore had length 630 mm, entry radius 6.5 mm, and exit radius 12.5 mm. In woodwinds, the low‐frequency resonances control the playing frequencies. Hence, the resonance frequencies under 1 kHz were predicted from a model of the air column and tone hole. The measured and predicted resonance frequencies for the cylindrical bore agreed to within 6±6 cents and for the conical bore agreed to within 23±18 cents. The errors in the conical‐bore theory are largest at low frequencies. Work is underway to refine the theory of tone holes in conical bores.

On the time-domain description of conical bores

Traditionally the description of the acoustical behavior of a bore has been done in the frequency domain through the acoustical impedance or the reflection coefficient. Whenever the time-domain response of it (impulse response, reflection function) has been needed, it has usually been obtained through the Fourier transform (FT) of the corresponding frequency-domain function. However, there are a number of cases in which this approach is unsuitable because the FT leads to noncausal functions which cannot be understood physically as impulse responses or reflection functions. In such cases the time-domain calculation is unavoidable. This calculation leads to exponentially growing functions which obviously do not accept an FT. This article presents the time-domain calculation of the main basic functions (reflection and transmission functions associated with a single discontinuity, impulse responses of anechoic bores) which are needed to obtain the input reflection function and the impulse responses of a bore. The analytical calculation of an application case is also presented.

On the excitation mechanism in reed wind instruments

The production of self-sustained oscillations in reed woodwinds in based mainly on two physical mechanisms: the coupling mechanism—which makes use of the reflections coming from bore discontinuities—and the Bernoulli mechanism—which consists of a Venturi effect acting on the reed. As far as woodwinds with striking inward reeds are concerned, the only widely studied instrument has been the clarinet—a roundly cylindrical bore driven by a single reed—in which the coupling mechanism plays an essential role while the Bernoulli mechanism can be neglected in a first approach. However, little attention has been paid in the literature to the wider set of double-reed conical woodwinds (oboe, bassoon, shawms, etc.), in which sound production is based on the cooperation between both coupling and Bernoulli mechanisms. In this paper, both mechanisms are assessed and a comparative analysis is made of cylindrical and conical bores' input impulse responses, whose shape and strength are related to the intensity of the coupling mechanism. Due to the low intensity of the impulse response reflections in conical bores, the coupling mechanism in this case behaves mainly as a trigger of the intense Bernoulli mechanism, which is the one that strongly acts on the reed. Experimental results are also presented showing the bore input pressure for several instruments when producing a note attack, and illustrating the collaboration between both mechanisms.

On the reflection functions associated with discontinuities in conical bores

The decomposition of reflections by finite tubes into successive elementary reflections by the input, discontinuities, and output of the tubes is interesting for its physical reasoning and for calculations using multiconvolution. In the case of tubes with conical bores, Martinez and Agulló [J. Martinez and J. Agulló, J. Acoust. Soc. Am. 84, 1613–1619 (1988)] have stated that in certain cases, the elementary reflection functions can be growing (causal) exponentials. Although such functions do not have Fourier transforms, Agulló et al. have assumed that they are inverse Fourier transforms of functions of frequency. It is shown that this assumption is erroneous. but by using a Laplace transform (i.e., by introducing losses through a complex frequency), we have also shown that for a general class of physically feasible systems, the decomposition into growing exponentials is valid.

A comment on ‘‘Conical bores. Part I: Reflection functions associated with discontinuities’’ [J. Acoust. Soc. Am. 84, 1613–1619 (1988)] and ‘‘Alternatives to the impulse response h(t) to describe the acoustical behavior of conical ducts’’ [J. Acoust. Soc. Am. 84, 1606–1612 (1988)

According to J. Martínez and J. Agulló [J. Acoust. Soc. Am. 84, 1613–1619 (1988)] and Agulló et al. [J. Acoust. Soc. Am. 84, 1606–1612 (1988)], reflection functions and modified impulse responses can always be obtained from the corresponding frequency‐domain functions through a Fourier transform. The following letter is a revision of that conclusion.

Conical bores. Part I: Reflection functions associated with discontinuities

Reflection functions associated with discontinuities in conical bores are worked out for the usual cases found in woodwind instruments: taper and diameter discontinuities, open and closed ends, and open and closed holes. Radiation at open ends is considered through the impedance formulation for the open end of a cylindrical tube fitted with an infinite flange. The input impulse response of woodwinds, or related functions such as the plane-wave or spherical-wave reflection functions, can be calculated in the time domain by means of these reflection functions through multiple convolutions as shown in the companion article ‘‘Conical bores. Part II: Multiconvolution’’ [Martínez et al., J. Acoust. Soc. Am. 84, 1620–1627 (1988)].

Conical bores. Part II: Multiconvolution

The input impulse response, or related functions such as the plane-wave or spherical-wave reflection functions, of a conical bore with discontinuities can be calculated from the reflection functions associated with discontinuities by means of a multiconvolution process. This approach, as alternative to the Fourier transform of the acoustical impedance Z(f), is attractive because of the detailed description it gives of the pressure time evolution inside the bore. However, the calculation may become rather involved if each reflected and transmitted wave is followed individually, and numerical instability may arise whenever the implied reflection functions contain growing exponentials. The first difficulty has been overcome by summing up all outward traveling waves and all inward traveling waves to give a unique outward wave and a unique inward wave. Numerical instability has been avoided by using an iterative convolution algorithm. Internal damping due to viscous and thermal losses has been located at discontinuities and represented by means of damping functions through convolution products. The reflection functions used are presented in the companion article ‘‘Conical bores. Part I: Reflection functions associated with discontinuities’’ [Martínez and Agulló, J. Acoust. Soc. Am. 84, 1613–1619 (1988)].

Alternatives to the impulse response h(t) to describe the acoustical behavior of conical ducts

In unidimensional acoustical systems, the impulse response h(t) at the input section, which describes the pressure evolution originated at this section by the introduction of a flow unit impulse through it, relates pressure p(t) and flow u(t) at the input section by means of the convolution product p=h*u. If damping and radiation are small, it is interesting to find other functions of faster decay than h(t) in order to improve the convolution convergence. As alternatives to h(t), this article studies the impulse responses h′(t) and h″(t), which correspond to the modified systems that result when coupling the original acoustical system input section to a cylindrical anechoic termination and a conical anechoic termination, respectively. These functions h′(t) and h″(t) are related to the plane-wave reflection function Rp−(t) and spherical-wave reflection function Rs−(t), respectively. The comparison of these three impulse responses shows that the use of h′(t) and h″(t), though of faster decay than h(t) in principle, is not always advisable. For conical bores with small truncation, the convolution with h′(t) may lead to numerical instability more easily than that with h(t). On the other hand, the impulse response h″(t) turns out to be divergent for certain geometrical duct configurations, and thus it is useless as a kernel function in a convolution in these cases.

Interferometric inspection of small wire-drawing dies

The conical bores of small wire-drawing dies can be inspected by observing the fringe pattern produced by light reflected from the internal surface of the bore interfering with light which passes directly through the aperture. Information about cone angle, roundness and surface roughness can be obtained in this way.

Month in the Patent Office

Means for securing together the halves 1, 2, no, 1, of an aeroplane wing constructed, e.g. as in Specification 767,674, comprises a bolt or stud 28 with a threaded shank 4 and a nut 8 having a coned exterior and a conical bore to receive a coned lock‐nut 9. The bolt is conical and engages a bore 16 in the wing halves, nut 8 engaging a conical bore 26. In another arrangement, a stud 5, no. 2 having threaded ends 4 is pushed, at a temperature lower than that of the wing halves, into aligned parallel portions 7 of bores in said halves, and nuts 8 are applied to the ends 4 and engage the coned bore portions 6. Lock‐nuts 9 are then screwed on the ends and engage the conical bores in nuts 8. The ends of the nuts having turning flats or recesses 18, 19 may be cut off flush with the wing surfaces, after tightening.