The maximum entropy moment closure for the two-moment approximation of the radiative transfer equation is presented. The resulting moment equations, known as the M1 model, are solved using a finite-volume method with adaptive mesh refinement (AMR) and two Riemann-solver based flux function solvers: a Roe-type and a Harten-Lax van Leer (HLL) solver. Three different boundary schemes are also presented and discussed. When compared to the discrete ordinates method (DOM) in several representative one- and two-dimensional radiation transport problems, the results indicate that while the M1 model cannot accurately resolve multi-directional radiation transport occurring in low-absorption media, it does provide reasonably accurate solutions, both qualitatively and quantitatively, when compared to the DOM predictions in most of the test cases involving either absorbing-emitting or scattering media. The results also show that the M1 model is computationally less expensive than DOM for more realistic radiation transport problems involving scattering and complex geometries.

We compare two popular scenario tree generation methods in the context of financial optimization: Moment matching and scenario reduction. Using a simple problem with a known analytic solution, we find that moment matching - accompanied by a check to ensure absence of arbitrage opportunities - replicates this solution precisely. On the other hand, even if the scenario trees generated by scenario reduction are arbitrage-free, the solutions to the approximate optimization problem represented by the reduced tree are biased and highly variable. These results hold for correlated and uncorrelated asset returns, as well as for normal and non-normal returns. (authors' abstract)

The purpose of this study was to compare the shoulder resultant joint moment (RJM) during a shoulder internal rotator exercise using elastic resistance employing four different movement strategies and two different starting elastic strains. Methods: Ten subjects aged 27.4 ± 2.6 yr (5 female and 5 male) with no previous shoulder pathology performed four sets of six repetitions of shoulder rotation though 180° using elastic resistance (Thera-Band® elastic band, blue) during two acceleration (medium and low) and two cadence (2s:2s, <1s:1s) strategies at 0% elastic starting strain. The acceleration movement strategies were also performed with starting strain of 30%. A mathematical model using Newtonian mechanics was used to compute the RJM. Elastic band recoil force was measured with a force transducer. Forearm acceleration was determined by a miniature uniaxial accelerometer secured at the wrist. Electrogoniometer data were collected to determine the range of motion (ROM) as well as the angle between the forearm and band which was used to determine elastic moment arm. Paired t-tests were used to identify joint angle specific RJM differences between conditions. Results: Angle specific comparisons revealed that RJM in the moderate acceleration movement strategy was significantly different from RJM in the low acceleration movement strategy through 150° (83%) of range of motion (p<0.05). Shoulder RJM was up to 111% higher in the moderate acceleration strategy (P < 0.01). Angle specific comparisons revealed RJM in the <1:1 cadence strategy was significantly different from RJM in the 2:2 cadence through 108° (60%) of the range of motion (p<0.05). RJM was up to 47% higher in the <1:1 cadence (p<0.01). RJM in the low acceleration strategy was significantly greater with 30% elastic start strain relative to 0% elastic start strain through 180º of angular excursion (p<0.001). The pattern and magnitude of neuromuscular loading was significantly different in higher acceleration movement strategies (moderate acceleration and fast cadence). Conclusions: These findings indicate that differential limb acceleration as a result of movement strategy significantly affects shoulder load during elastic resistance exercise. The pattern and magnitude of load was different in each movement strategy and could result in differential neuromuscular adaptation through training. Clinicians and exercise professionals should consider movement strategy/acceleration as an important factor when prescribing elastic resistance exercise for safety and efficacy.

Die vorliegende Arbeit beschäftigt sich mit den finiten matriziellen Momentenproblemen von Stieltjes-Typ und beschreibt unter Verwendung der Methode der Fundamentalen Matrixungleichungen die Lösungsmenge durch gebrochen lineare Transformationen.

The purpose of this study was to compare the shoulder resultant joint moment (RJM) during a shoulder internal rotator exercise using elastic resistance employing four different movement strategies and two different starting elastic strains. Methods: Ten subjects aged 27.4 ± 2.6 yr (5 female and 5 male) with no previous shoulder pathology performed four sets of six repetitions of shoulder rotation though 180° using elastic resistance (Thera-Band® elastic band, blue) during two acceleration (medium and low) and two cadence (2s:2s, <1s:1s) strategies at 0% elastic starting strain. The acceleration movement strategies were also performed with starting strain of 30%. A mathematical model using Newtonian mechanics was used to compute the RJM. Elastic band recoil force was measured with a force transducer. Forearm acceleration was determined by a miniature uniaxial accelerometer secured at the wrist. Electrogoniometer data were collected to determine the range of motion (ROM) as well as the angle between the forearm and band which was used to determine elastic moment arm. Paired t-tests were used to identify joint angle specific RJM differences between conditions. Results: Angle specific comparisons revealed that RJM in the moderate acceleration movement strategy was significantly different from RJM in the low acceleration movement strategy through 150° (83%) of range of motion (p<0.05). Shoulder RJM was up to 111% higher in the moderate acceleration strategy (P < 0.01). Angle specific comparisons revealed RJM in the <1:1 cadence strategy was significantly different from RJM in the 2:2 cadence through 108° (60%) of the range of motion (p<0.05). RJM was up to 47% higher in the <1:1 cadence (p<0.01). RJM in the low acceleration strategy was significantly greater with 30% elastic start strain relative to 0% elastic start strain through 180º of angular excursion (p<0.001). The pattern and magnitude of neuromuscular loading was significantly different in higher acceleration movement strategies (moderate acceleration and fast cadence). Conclusions: These findings indicate that differential limb acceleration as a result of movement strategy significantly affects shoulder load during elastic resistance exercise. The pattern and magnitude of load was different in each movement strategy and could result in differential neuromuscular adaptation through training. Clinicians and exercise professionals should consider movement strategy/acceleration as an important factor when prescribing elastic resistance exercise for safety and efficacy.

In the operation of CMGs there exists a concept called “back drive,” which represents a case where the coupling effects of the angular velocity of the body and the angular momentum of the CMG overwhelm the input torque and result in a lack of control. This effect is known but not well documented or studied in the literature. Starting from first principles, this thesis derives the full nonlinear dynamical equations for CMGs. These equations contain significantly more terms than are found in the literature. As a means to understand the implications of these terms, a reduced order model is derived. The full and reduced models are then validated by means of extensive simulations. Finally, experimental verification of the models confirms the finding that the reduced order model provides a reasonably high fidelity for dynamics.

The generalized moment of order k of a mass distribution sigma for a natural number k is given by integral of lambda to the power k with respect to mass distribution sigma and variable lambda. In extended moment problem, given a sequence of real numbers, it is required to find a mass distribution whose generalized moment of order k is k&#039 / th term of the sequence. The conditions of existence and uniqueness of the solution obtained by Hamburger are studied in this thesis by the use of orthogonal polynomials determined by a measure on real line. A chapter on the study of asymptotic behaviour of orthogonal functions on compact subsets of complex numbers is also included.

This practice-based project explores the photographic phenomenon of ‘moment beyond moment’, which refers to the combined representations of an existing image in an environment, together with the real-life situation at the moment the photograph is taken. I call this photograph an ‘extended photograph’. Employing practical works of extended photographs and focusing on interactions between the moment in real-life and the moment in an existing image, the research explores the transformation of meanings caused by the interactions of these moments in an extended photograph. The research owes its approach to grounded theory, contrary thinking and Chinese Buddhist ‘Sudden Enlightenment’ to further its aim of exploring the unpredictable interaction of these moments, and to disclose the potentials of meaning transformation. My research outcome intends to initiate a discourse with photographic practitioners and theorists on the phenomenon of moment beyond moment in a working environment that is encaged by the excessive existence of displayed images. The thesis is composed as a creative work that consists of a series of photographic images accompanied by an exegesis component. The images represent a nominal 80%, and the exegesis 20% of the final submission.

This thesis describes the implementation of the conditional moment closure (CMC) combustion model in a numerical scheme and its application to the modelling of enclosure fires. Prediction of carbon monoxide (CO) in the upper smoke layer of enclosure fires is of primary interest because it is a common cause of death. The CO concentration cannot be easily predicted by empirical means, so a method is needed which models the chemistry of a quenched, turbulent fire plume and subsequent mixing within an enclosed space. CMC is a turbulent combustion model which has been researched for over a decade. It has provided predictions of major and minor species in jet diffusion flames. The extension to enclosure fires is a new application for which the flow is complex and temperatures are well below adiabatic conditions. Advances are made in the numerical implementation of CMC. The governing combustion equations are cast in a conserved, finite volume formulation for which boundary conditions are uniquely defined. Computational efficiency is improved through two criteria which allow the reduction in the size of the computational domain without any loss of accuracy. Modelling results are compared to experimental data for natural gas fires burning under a hood. Comparison is made in the recirculating, post-flame region of the flow where temperatures are low and reactions are quenched. Due to the spatial flux terms contained in the governing equations, CMC is able to model the situation where chemical species are produced in the high temperature fire-plume and then transported to non-reacting regions. Predictions of CO and other species are in reasonable agreement with the experimental data over a range of lean and rich hood-fire conditions. Sensitivity of results to chemistry, temperature and modelling closures is inves- tigated. Species predictions are shown to be quite different for the two detailed chemical mechanisms used. Temperature conditions within the hood effect the for- mation of species in the plume prior to quenching and subsequently species predic- tions in the post-flame region are also effected. Clipped Gaussian and ß-function probability density functions (PDFs) are used for the stochastic mixture fraction. Species predictions in the plume are sensitive to the form of the PDF but in the post-flame region, where the ß-function approaches a Gaussian form, predictions are relatively insensitive. Two models are used for the conditional scalar dissipation: a uniform model, where the conditional quantity is set equal to the unconditional scalar dissipation across all mixture fraction space; and a model which is consistent with the PDF transport equation. In the plume, predictions of minor species are sensitive to the modelling used, but in the recirculating, post-flame region species are not significantly effected.

Zugl.: Braunschweig, Techn. Univ., Diss., 2008