Moments of inertia for solids of revolution and variational methods

We present some formulae for the moments of inertia of homogeneous solids of revolution in terms of the functions that generate the solids. The development of these expressions exploits the cylindrical symmetry of these objects, and avoids the explicit use of multiple integration, providing an easy and pedagogical approach. The explicit use of the functions that generate the solid gives the possibility of writing the moment of inertia as a functional, which in turn allows us to utilize the calculus of variations to obtain a new insight into some properties of this fundamental quantity. In particular, minimization of moments of inertia under certain restrictions is possible by using variational methods.Comment: 6 pages, 6 figures, LaTeX2e. Two paragraphs added. Minor typos corrected. Version to appear in European Journal of Physic

About Gravitomagnetism

The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the electrodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms.Comment: 16 pages, a few amendments have been performed and a new section has been adde

Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame

The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivation which is based upon the behavior of free radiation fields and the assumption that the field correlation functions contain but a single correlation time in thermal equilibrium. The work has connections with the thermal effects of acceleration found in relativistic quantum field theory.Comment: 23 page

Method for fabricating a low stress x-ray mask using annealable amorphous refractory compounds

X‐ray masks have been fabricated by depositing a compressively stressed refractory material on a wafer, annealing to a zero stress state, and then forming the membrane. Amorphous TaSiN and TaSi alloys deposited with a magnetron sputter tool have been extensively characterized in terms of resistivity, composition, defectivity, surface roughness, and crystalline state. Optimization in terms of these parameters has resulted in base line selection of absorber films of the following compositions: Ta_(61)Si_(17)N_(21) and Ta_(75)Si_(23). The process is shown to be extendable to an entire class of amorphous annealable refractory materials. Careful studies of deposition and annealing conditions have resulted in a 4× reduction of image placement to the 30 nm maximum vector level. Finally, the importance of stress gradients is experimentally verified

Intermediate Tail Dependence: A Review and Some New Results

The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on intermediate tail dependence, and then we report new results to supplement the review. Intermediate tail dependence for elliptical, extreme value and Archimedean copulas are reviewed and further studied, respectively. For Archimedean copulas, we not only consider the frailty model but also the recently studied scale mixture model; for the latter, conditions leading to upper intermediate tail dependence are presented, and it provides a useful way to simulate copulas with desirable intermediate tail dependence structures.Comment: 25 pages, 1 figur

Charges and fields in a current-carrying wire

Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual consistency of classical electromagnetism and Special Relativity. Some consequences of the assumption that the net charge per unit length is zero in the electrons frame are also briefly discussed

Quantitative analysis of the anterolateral ossification mass in diffuse idiopathic skeletal hyperostosis of the thoracic spine

Diffuse idiopathic skeletal hyperostosis (DISH) is a systemic condition leading to ossification of spinal ligaments and has been shown to behave similarly to ankylosing spondylitis (AS) often leading to unstable hyperextension fractures. Currently, no quantitative data are available on the spatial relationship between the bridging anterolateral ossification mass (ALOM) and the vertebral body/intervertebral disc to explain the propensity in DISH to fracture through the vertebral body instead of through the intervertebral disc as more often seen in AS. Furthermore, no reasonable explanation is available for the typical flowing wax morphology observed in DISH. In the current study, a quantitative analysis of computed tomography (CT) data from human cadaveric specimens with DISH was performed to better understand the newly formed osseous structures and fracture biomechanics. Additionally, the results were verified using computed tomography angiography data from ten patients with DISH and ten controls. Transverse CT images were analyzed to obtain ALOM area and centroid angle relative to the anteroposterior axis; intervertebral disc and adjacent cranial and caudal levels. The ALOM area at the mid-vertebral body level averaged 57.9 ± 50.0 mm2; at the mid-intervertebral disc space level it averaged 246.4 ± 95.9 mm2. The mean ALOM area at the adjacent level caudal to the mid-vertebral body level was 169.6 ± 81.3 mm2; at the adjacent cranial level, it was 161.7 ± 78.2 mm2. The main finding was the significant difference between mean ALOM area at the mid-vertebral body level and other three levels (p < 0.0001). The subsequent verification study showed the presence of vertebral segmental arteries at the mid-vertebral body level in nearly all images irrespective of the presence of DISH. A larger area of ALOM seemed associated with increased counter-clockwise rotation (away from the aorta) of the centroid relative to the anteroposterior axis. The results from the present study suggest a predisposition for fractures through the vertebral body and a role for the arterial system in the inhibition of soft tissue ossification

Leading together, learning together: music education and music therapy students' perceptions of a shared practicum

The health benefits of musical engagement extend across the lifespan, with research documenting developmental and quality of life outcomes in senior adulthood. Whilst the psychological functions of music include three broad domains: cognitive, emotional and social, the social factors of music consumption have been, for the most part, ignored. This project is predicated on the understanding that students "construct" their own knowledge through engagement with others. It also reflects the belief that it is possible to link the world of learning with a world of action through a reflective process with small cooperative learning groups.This article reports on a collaborative creativity leadership project implemented by music therapy and music education students. In particular, it explores the perceptions of the students as they employed a teaching/therapeutic intervention with ageing participants from a local private retirement village. The project involved lyric rewriting and singing performance. Drawing on the students' reflective journals and interview transcripts, four themes emerged relating to students' perceptions of the learning experience. These themes were: learning about facilitating, learning about self, learning about the musical process, and learning about the context/ageing. Each of these themes is explored before conclusions about the process of leading a creative collaboration are drawn. The implications of this analysis extend beyond the context of a retirement village, and into various educational and therapeutic contexts where creative collaboration is facilitated

Continuity theorems for the M/M/1/nM/M/1/n queueing system

In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a certain sense from the exponential distribution, is approximated by that exponential distribution. Continuity theorems are obtained in the form of one or two-sided stochastic inequalities. The paper shows how the bounds of these inequalities are changed if further assumptions, associated with specific properties of the service time distribution (precisely described in the paper), are made. Specifically, some parametric families of service time distributions are discussed, and the paper establishes uniform estimates (given for all possible values of the parameter) and local estimates (where the parameter is fixed and takes only the given value). The analysis of the paper is based on the level crossing approach and some characterization properties of the exponential distribution.Comment: Final revision; will be published as i