Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The beam mode

Using asymptotics, the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell vibrating in the beam mode (viz. circumferential wave order n = 1) are studied. Initially, the uncoupled wavenumbers of the acoustic fluid and the cylindrical shell structure are discussed. Simple closed form expressions for the structural wavenumbers (longitudinal, torsional and bending) are derived using asymptotic methods for low- and high-frequencies. It is found that at low frequencies the cylinder in the beam mode behaves like a Timoshenko beam. Next, the coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter mu due to the coupling. An asymptotic expansion involving mu is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (as modifications to the uncoupled wavenumbers) separately for low- and high-frequency ranges and further, within each frequency range, for large and small values of mu. Only the flexural wavenumber, the first rigid duct acoustic cut-on wavenumber and the first pressure-release acoustic cut-on wavenumber are considered. The general trend found is that for small mu, the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-acoustic duct. With increasing mu, the perturbations increase, until the coupled wavenumbers are better identified as perturbations to the pressure-release wavenumbers. The systematic derivation for the separate cases of small and large mu gives more insight into the physics and helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. This method of asymptotics is simple to implement using a symbolic computation package (like Maple). (C) 2008 Elsevier Ltd. All rights reserved.

Geometry-free stochastic analysis of BDS triple frequency signals

The paper presents a geometry-free approach to assess the variation of covariance matrices of undifferenced triple frequency GNSS measurements and its impact on positioning solutions. Four independent geometryfree/ ionosphere-free (GFIF) models formed from original triple-frequency code and phase signals allow for effective computation of variance-covariance matrices using real data. Variance Component Estimation (VCE) algorithms are implemented to obtain the covariance matrices for three pseudorange and three carrier-phase signals epoch-by-epoch. Covariance results from the triple frequency Beidou System (BDS) and GPS data sets demonstrate that the estimated standard deviation varies in consistence with the amplitude of actual GFIF error time series. The single point positioning (SPP) results from BDS ionosphere-free measurements at four MGEX stations demonstrate an improvement of up to about 50% in Up direction relative to the results based on a mean square statistics. Additionally, a more extensive SPP analysis at 95 global MGEX stations based on GPS ionosphere-free measurements shows an average improvement of about 10% relative to the traditional results. This finding provides a preliminary confirmation that adequate consideration of the variation of covariance leads to the improvement of GNSS state solutions.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

Dynamics and control of buckling type devices using SMA wire integrated beam

An analysis and design study using Shape Memory Alloy (SMA) wire integrated beam and its buckling shape control are reported. The dynamical system performance is analyzed with a mathematical set-up involving nonlocal and rate sensitive kinetics of phase transformation in the SMA wire. A standard phenomenological constitutive model reported by Brinson (1993) is modified by considering certain consistency conditions in the material property tensors and by eliminating spurious singularity. Considering the inhomogeneity effects, a finite element model of the SMA wire is developed. Simulations are carried out to study the buckling shape control of a beam integrated with SMA wire.

Fractional damping: Stochastic origin and finite approximations

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Network flow-control using asynchronous stochastic approximation

We propose several stochastic approximation implementations for related algorithms in flow-control of communication networks. First, a discrete-time implementation of Kelly's primal flow-control algorithm is proposed. Convergence with probability 1 is shown, even in the presence of communication delays and stochastic effects seen in link congestion indications. This ensues from an analysis of the flow-control algorithm using the asynchronous stochastic approximation (ASA) framework. Two relevant enhancements are then pursued: a) an implementation of the primal algorithm using second-order information, and b) an implementation where edge-routers rectify misbehaving flows. Next, discretetime implementations of Kelly's dual algorithm and primaldual algorithm are proposed. Simulation results a) verifying the proposed algorithms and, b) comparing the stability properties are presented.

Electromagnetic signatures of lightning near the HF frequency band

The dissertation deals with remote narrowband measurements of the electromagnetic radiation emitted by lightning flashes. A lightning flash consists of a number of sub-processes. The return stroke, which transfers electrical charge from the thundercloud to to the ground, is electromagnetically an impulsive wideband process; that is, it emits radiation at most frequencies in the electromagnetic spectrum, but its duration is only some tens of microseconds. Before and after the return stroke, multiple sub-processes redistribute electrical charges within the thundercloud. These sub-processes can last for tens to hundreds of milliseconds, many orders of magnitude longer than the return stroke. Each sub-process causes radiation with specific time-domain characteristics, having maxima at different frequencies. Thus, if the radiation is measured at a single narrow frequency band, it is difficult to identify the sub-processes, and some sub-processes can be missed altogether. However, narrowband detectors are simple to design and miniaturize. In particular, near the High Frequency band (High Frequency, 3 MHz to 30 MHz), ordinary shortwave radios can, in principle, be used as detectors. This dissertation utilizes a prototype detector which is essentially a handheld AM radio receiver. Measurements were made in Scandinavia, and several independent data sources were used to identify lightning sub-processes, as well as the distance to each individual flash. It is shown that multiple sub-processes radiate strongly near the HF band. The return stroke usually radiates intensely, but it cannot be reliably identified from the time-domain signal alone. This means that a narrowband measurement is best used to characterize the energy of the radiation integrated over the whole flash, without attempting to identify individual processes. The dissertation analyzes the conditions under which this integrated energy can be used to estimate the distance to the flash. It is shown that flash-by-flash variations are large, but the integrated energy is very sensitive to changes in the distance, dropping as approximately the inverse cube root of the distance. Flashes can, in principle, be detected at distances of more than 100 km, but since the ground conductivity can vary, ranging accuracy drops dramatically at distances larger than 20 km. These limitations mean that individual flashes cannot be ranged accurately using a single narrowband detector, and the useful range is limited to 30 kilometers at the most. Nevertheless, simple statistical corrections are developed, which enable an accurate estimate of the distance to the closest edge of an active storm cell, as well as the approach speed. The results of the dissertation could therefore have practical applications in real-time short-range lightning detection and warning systems.

Finnish Dosimetric Practice for Epithermal Neutron Beam Dosimetry in Boron Neutron Capture Therapy

Boron neutron capture therapy (BNCT) is a form of chemically targeted radiotherapy that utilises the high neutron capture cross-section of boron-10 isotope to achieve a preferential dose increase in the tumour. The BNCT dosimetry poses a special challenge as the radiation dose absorbed by the irradiated tissues consists of several dose different components. Dosimetry is important as the effect of the radiation on the tissue is correlated with the radiation dose. Consistent and reliable radiation dose delivery and dosimetry are thus basic requirements for radiotherapy. The international recommendations for are not directly applicable to BNCT dosimetry. The existing dosimetry guidance for BNCT provides recommendations but also calls for investigating for complementary methods for comparison and improved accuracy. In this thesis the quality assurance and stability measurements of the neutron beam monitors used in dose delivery are presented. The beam monitors were found not to be affected by the presence of a phantom in the beam and that the effect of the reactor core power distribution was less than 1%. The weekly stability test with activation detectors has been generally reproducible within the recommended tolerance value of 2%. An established toolkit for epithermal neutron beams for determination of the dose components is presented and applied in an international dosimetric intercomparison. The measured quantities (neutron flux, fast neutron and photon dose) by the groups in the intercomparison were generally in agreement within the stated uncertainties. However, the uncertainties were large, ranging from 3-30% (1 standard deviation), emphasising the importance of dosimetric intercomparisons if clinical data is to be compared between different centers. Measurements with the Exradin type 2M ionisation chamber have been repeated in the epithermal neutron beam in the same measurement configuration over the course of 10 years. The presented results exclude severe sensitivity changes to thermal neutrons that have been reported for this type of chamber. Microdosimetry and polymer gel dosimetry as complementary methods for epithermal neutron beam dosimetry are studied. For microdosimetry the comparison of results with ionisation chambers and computer simulation showed that the photon dose measured with microdosimetry was lower than with the two other methods. The disagreement was within the uncertainties. For neutron dose the simulation and microdosimetry results agreed within 10% while the ionisation chamber technique gave 10-30% lower neutron dose rates than the two other methods. The response of the BANG-3 gel was found to be linear for both photon and epithermal neutron beam irradiation. The dose distribution normalised to dose maximum measured by MAGIC polymer gel was found to agree well with the simulated result near the dose maximum while the spatial difference between measured and simulated 30% isodose line was more than 1 cm. In both the BANG-3 and MAGIC gel studies, the interpretation of the results was complicated by the presence of high-LET radiation.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Accuracy of absorbed dose in external photon beam radiotherapy : what level is sufficient and how to approach it?

Radiation therapy (RT) plays currently significant role in curative treatments of several cancers. External beam RT is carried out mostly by using megavoltage beams of linear accelerators. Tumor eradication and normal tissue complications correlate to dose absorbed in tissues. Normally this dependence is steep and it is crucial that actual dose within patient accurately correspond to the planned dose. All factors in a RT procedure contain uncertainties requiring strict quality assurance. From hospital physicist´s point of a view, technical quality control (QC), dose calculations and methods for verification of correct treatment location are the most important subjects. Most important factor in technical QC is the verification that radiation production of an accelerator, called output, is within narrow acceptable limits. The output measurements are carried out according to a locally chosen dosimetric QC program defining measurement time interval and action levels. Dose calculation algorithms need to be configured for the accelerators by using measured beam data. The uncertainty of such data sets limits for best achievable calculation accuracy. All these dosimetric measurements require good experience, are workful, take up resources needed for treatments and are prone to several random and systematic sources of errors. Appropriate verification of treatment location is more important in intensity modulated radiation therapy (IMRT) than in conventional RT. This is due to steep dose gradients produced within or close to healthy tissues locating only a few millimetres from the targeted volume. The thesis was concentrated in investigation of the quality of dosimetric measurements, the efficacy of dosimetric QC programs, the verification of measured beam data and the effect of positional errors on the dose received by the major salivary glands in head and neck IMRT. A method was developed for the estimation of the effect of the use of different dosimetric QC programs on the overall uncertainty of dose. Data were provided to facilitate the choice of a sufficient QC program. The method takes into account local output stability and reproducibility of the dosimetric QC measurements. A method based on the model fitting of the results of the QC measurements was proposed for the estimation of both of these factors. The reduction of random measurement errors and optimization of QC procedure were also investigated. A method and suggestions were presented for these purposes. The accuracy of beam data was evaluated in Finnish RT centres. Sufficient accuracy level was estimated for the beam data. A method based on the use of reference beam data was developed for the QC of beam data. Dosimetric and geometric accuracy requirements were evaluated for head and neck IMRT when function of the major salivary glands is intended to be spared. These criteria are based on the dose response obtained for the glands. Random measurement errors could be reduced enabling lowering of action levels and prolongation of measurement time interval from 1 month to even 6 months simultaneously maintaining dose accuracy. The combined effect of the proposed methods, suggestions and criteria was found to facilitate the avoidance of maximal dose errors of up to even about 8 %. In addition, their use may make the strictest recommended overall dose accuracy level of 3 % (1SD) achievable.