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.

Significance of a short-term test drive for prospective plug-in electric vehicle consumers: An exploratory study

The test drive is a well-known step in car buying. In the emerging plug-in electric vehicle (PEV) market, however, the influence of a pre-purchase test drive on a consumer's inclination to purchase is unknown. Policy makers and industry participants both are eager to understand what factors motivate vehicle consumers at the point-of-sale. A number of researchers have used choice models to shed light on consumer perceptions of PEVs, and others have investigated consumer change in disposition toward a PEV over the course of a trial, wherein test driving a PEV may take place over a number of consecutive days, weeks or months. However, there is little written on the impact of a short-term test drive - a typical experience at dealerships or public "ride-and-drive" events. The impact of a typical test drive, often measured in minutes of driving, is not well understood. This paper first presents a synthesis of the literature on the effect of PEV test drives as they relate to consumer disposition toward PEVs. An analysis of data obtained from an Australian case study whereby attitudinal and stated preference data were collected pre- and post- test drive at public "ride-and-drive" event held Brisbane, Queensland in March 2014 using a custom-designed iPad application. Motorists' perceptions and choice preferences around PEVs were captured, revealing the relative importance of their experience behind the wheel. Using the Australian context as a case-study, this paper presents an exploratory study of consumers' stated preferences toward PEVs both before and after a short test drive.

Critical test for Altshuler-Aronov theory: Evolution of the density of states singularity in double perovskite Sr2FeMoO6 with controlled disorder

With high-resolution photoemission spectroscopy measurements, the density of states (DOS) near the Fermi level (E-F) of double perovskite Sr2FeMoO6 having different degrees of Fe/Mo antisite disorder has been investigated with varying temperature. The DOS near E-F showed a systematic depletion with increasing degree of disorder, and recovered with increasing temperature. Altshuler-Aronov (AA) theory of disordered metals well explains the dependences of the experimental results. Scaling analysis of the spectra provides experimental indication for the functional form of the AA DOS singularity.

Digital Photography in the Diagnosis and Follow-up of Ocular Diseases

Purpose: The aim of the present study was to develop and test new digital imaging equipment and methods for diagnosis and follow-up of ocular diseases. Methods: The whole material comprised 398 subjects (469 examined eyes), including 241 patients with melanocytic choroidal tumours, 56 patients with melanocytic iris tumours, 42 patients with diabetes, a 52-year old patient with chronic phase of VKH disease, a 30-year old patient with an old blunt eye injury, and 57 normal healthy subjects. Digital 50° (Topcon TRC 50 IA) and 45° (Canon CR6-45NM) fundus cameras, a new handheld digital colour videocamera for eye examinations (MediTell), a new subtraction method using the Topcon Image Net Program (Topcon corporation, Tokyo, Japan), a new method for digital IRT imaging of the iris we developed, and Zeiss photoslitlamp with a digital camera body were used for digital imaging. Results: Digital 50° red-free imaging had a sensitivity of 97.7% and two-field 45° and 50° colour imaging a sensitivity of 88.9-94%. The specificity of the digital 45°-50° imaging modalities was 98.9-100% versus the reference standard and ungradeable images that were 1.2-1.6%. By using the handheld digital colour video camera only, the optic disc and central fundus located inside 20° from the fovea could be recorded with a sensitivity of 6.9% for detection of at least mild NPDR when compared with the reference standard. Comparative use of digital colour, red-free, and red light imaging showed 85.7% sensitivity, 99% specificity, and 98.2 % exact agreement versus the reference standard in differentiation of small choroidal melanoma from pseudomelanoma. The new subtraction method showed growth in four of 94 melanocytic tumours (4.3%) during a mean ±SD follow-up of 23 ± 11 months. The new digital IRT imaging of the iris showed the sphincter muscle and radial contraction folds of Schwalbe in the pupillary zone and radial structural folds of Schwalbe and circular contraction furrows in the ciliary zone of the iris. The 52-year-old patient with a chronic phase of VKH disease showed extensive atrophy and occasional pigment clumps in the iris stroma, detachment of the ciliary body with severe ocular hypotony, and shallow retinal detachment of the posterior pole in both eyes. Infrared transillumination imaging and fluorescein angiographic findings of the iris showed that IR translucence (p=0.53), complete masking of fluorescence (p=0.69), presence of disorganized vessels (p=0.32), and fluorescein leakage (p=1.0) at the site of the lesion did not differentiate an iris nevus from a melanoma. Conclusions: Digital 50° red-free and two-field 50° or 45° colour imaging were suitable for DR screening, whereas the handheld digital video camera did not fulfill the needs of DR screening. Comparative use of digital colour, red-free and red light imaging was a suitable method in the differentiation of small choroidal melanoma from different pseudomelanomas. The subtraction method may reveal early growth of the melanocytic choroidal tumours. Digital IRT imaging may be used to study changes of the stroma and posterior surface of the iris in various diseases of the uvea. It contributed to the revealment of iris atrophy and serous detachment of the ciliary body with ocular hypotony together with the shallow retinal detachment of the posterior pole as new findings of the chronic phase of VKH disease. Infrared translucence and angiographic findings are useful in differential diagnosis of melanocytic iris tumours, but they cannot be used to determine if the lesion is benign or malignant.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

An exact similarity solution in radiation-gas-dynamics

We have found an exact similarity solution of the point explosion problem in the case when the total energy of the shock wave that is produced is not constant but decreases with time and when the loss due to radiation escape is significant. We have compared the results of our exact solution with those of exact numerical solutions of Elliot and Wang and have explained the cause why our solution differs from theirs in certain aspects.

On the theory of the indentation test for the measurement of tensile strength of brittle materials

A theoretical solution has been obtained for the state of stress in a rectangular plate under a pair of symmetrically placed rigid indenters. The stress distributions along the two central axes have been calculated for a square plate assuming the pressure distribution under the indenters as uniform, parabolic and one resulting from 'constant displacement' on a semiinfinite boundary, for different ratios of indenter-width to side of square. The results are compared with those of photoelastic analysis of Berenbaum and Brodie and the validity of the solution is discussed. The solution has been extended to orthotropic materials and numerical results for one type of coal are given.

An exact analysis of free vibrations of simply-supported viscoelastic plates

In this paper an exact three-dimensional analysis for free vibrations of a class of simply-supported viscoelastic rectangular plates is given. The characteristic equation defining the eigenvalues is of closed form. Some numerical results are presented for standard linear solids. Results from thin plate and Mindlin theories are also given for the purpose of comparison.

Effect of directionality of unidirectional grinding marks on friction and transfer layer formation of Mg on steel using inclined scratch test

Surface topography has been known to play an important role in the friction and transfer layer formation during sliding. In the present investigation, EN8 steel flats were ground to attain different surface roughness with unidirectional grinding marks. Pure Mg pins were scratched on these surfaces using an Inclined Scratch Tester to study the influence of directionality of surface grinding marks on coefficient of friction and transfer layer formation. Grinding angle (i.e., the angle between direction of scratch and grinding marks) was varied between 0 degrees and 90 degrees during the tests. Experiments were conducted under both dry and lubricated conditions. Scanning electron micrographs of the contact surfaces of pins and flats were used to reveal the surface features that included the morphology of the transfer layer. It was observed that the average coefficient of friction and transfer layer formation depend primarily on the directionality of the grinding marks but were independent of surface roughness on the harder mating surface. In addition, a stick-slip phenomenon was observed, the amplitude of which depended both on the directionality of grinding marks and the surface roughness of the harder mating surface. The grinding angle effect on the coefficient of friction, which consists of adhesion and plowing components, was attributed to the variation of plowing component of friction. (c) 2006 Elsevier B.V. All rights reserved.

Relationship between Low Strain Shear Modulus and Standard Penetration Test N Values

A low strain shear modulus plays a fundamental role in the estimation of site response parameters In this study an attempt has been made to develop the relationships between standard penetration test (SPT) N values with the low strain shear modulus (G(max)) For this purpose, field experiments SPT and multichannel analysis of surface wave data from 38 locations in Bangalore, India, have been used, which were also used for seismic microzonation project The in situ density of soil layer was evaluated using undisturbed soil samples from the boreholes Shear wave velocity (V-s) profiles with depth were obtained for the same locations or close to the boreholes The values for low strain shear modulus have been calculated using measured V-s and soil density About 215 pairs of SPT N and G(max) values are used for regression analysis The differences between fitted regression relations using measured and corrected values were analyzed It is found that an uncorrected value of N and modulus gives the best fit with a high regression coefficient when compared to corrected N and corrected modulus values This study shows better correlation between measured values of N and G(max) when compared to overburden stress corrected values of N and G(max)

Exact energy eigenvalues for an attractive Coulomb potential with zero-radius hard core

Following a peratization procedure, the exact energy eigenvalues for an attractive Coulomb potential, with a zero-radius hard core, are obtained as roots of a certain combination of di-gamma functions. The physical significance of this entirely new energy spectrum is discussed.

A Hardware Grid Simulator to Test Grid-Connected Inverter Systems.

Grid-connected systems when put to use at the site would experience scenarios like voltage sag, voltage swell, frequency deviations and unbalance which are common in the real world grid. When these systems are tested at laboratory, these scenarios do not exist and an almost stiff voltage source is what is usually seen. But, to qualify the grid-connected systems to operate at the site, it becomes essential to test them under the grid conditions mentioned earlier. The grid simulator is a hardware that can be programmed to generate some of the typical conditions experienced by the grid-connected systems at site. It is an inverter that is controlled to act like a voltage source in series with a grid impedance. The series grid impedance is emulated virtually within the inverter control rather than through physical components, thus avoiding the losses and the need for bulky reactive components. This paper describes the design of a grid simulator. Control implementation issues are highlighted in the experimental results.

Topics in Spatial Econometrics - With Applications to House Prices

Topics in Spatial Econometrics — With Applications to House Prices Spatial effects in data occur when geographical closeness of observations influences the relation between the observations. When two points on a map are close to each other, the observed values on a variable at those points tend to be similar. The further away the two points are from each other, the less similar the observed values tend to be. Recent technical developments, geographical information systems (GIS) and global positioning systems (GPS) have brought about a renewed interest in spatial matters. For instance, it is possible to observe the exact location of an observation and combine it with other characteristics. Spatial econometrics integrates spatial aspects into econometric models and analysis. The thesis concentrates mainly on methodological issues, but the findings are illustrated by empirical studies on house price data. The thesis consists of an introductory chapter and four essays. The introductory chapter presents an overview of topics and problems in spatial econometrics. It discusses spatial effects, spatial weights matrices, especially k-nearest neighbours weights matrices, and various spatial econometric models, as well as estimation methods and inference. Further, the problem of omitted variables, a few computational and empirical aspects, the bootstrap procedure and the spatial J-test are presented. In addition, a discussion on hedonic house price models is included. In the first essay a comparison is made between spatial econometrics and time series analysis. By restricting the attention to unilateral spatial autoregressive processes, it is shown that a unilateral spatial autoregression, which enjoys similar properties as an autoregression with time series, can be defined. By an empirical study on house price data the second essay shows that it is possible to form coordinate-based, spatially autoregressive variables, which are at least to some extent able to replace the spatial structure in a spatial econometric model. In the third essay a strategy for specifying a k-nearest neighbours weights matrix by applying the spatial J-test is suggested, studied and demonstrated. In the final fourth essay the properties of the asymptotic spatial J-test are further examined. A simulation study shows that the spatial J-test can be used for distinguishing between general spatial models with different k-nearest neighbours weights matrices. A bootstrap spatial J-test is suggested to correct the size of the asymptotic test in small samples.