An investigation of irregular crack path effects on fracture mechanics parameters using a grain microstructure meshing technique

Electronic version of an article published as Journal of Multiscale Modeling, Vol. 4, Iss. 1, atricle 1250001, 2012, http://dx.doi.org/10.1142/S1756973712500011 © World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/jmmA sub-grain size finite element modelling approach is presented in this paper to investigate variations in fracture mechanics parameters for irregular crack paths. The results can be used when modelling intergranular and transgranular crack growth where creep and fatigue are the dominant failure mechanisms and their crack paths are irregular. A novel method for sub-grain scale finite element mesh consisting of multiple elements encased in ~50–150 μm-sized grains has been developed and implemented in a compact tension, C(T), mesh structure. The replicated shapes and dimensions were derived from an isotropic metallic grain structure using representative random sized grain shapes repeated in sequence ahead of the crack tip. In this way the effects of crack tip angle ahead of the main crack path can be considered in a more realistic manner. A comprehensive sensitivity analysis has been performed for elastic and elastic-plastic materials using ABAQUS and the stress distributions, the stress intensity factor and the J-integral have been evaluated for irregular crack paths and compared to those of obtained from analytical solutions. To examine the local and macroscopic graph path effects on fracture mechanics parameters, a few extreme cases with various crack-tip angles have been modelled by keeping the macroscopic crack path parallel to the axis of symmetry. The numerical solutions from these granular mesh structures have been found in relatively good agreement with analytical solutions

An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs. This integral representation is a suitable starting point for a detailed analysis of the long-time dynamics of scalar waves in the Kerr geometry.Comment: 41 pages, 4 figures, minor correction

Correlation of Atrial Fibrillation with Left Atrial Volume in Patients with Mitral Stenosis. a Single Centre Study From Pakistan

Background: Rheumatic heart disease has a strong association with mitral valve stenosis. Atrial fibrillation is one of the most common complications of this condition and is a poor prognostic factor. Early detection and prompt management of atrial fibrillation can help to improve the quality of life and increase the life expectancy of the patients. We carried out this study to investigate the significance of left atrial volumetric changes in mitral stenosis and its correlation with atrial fibrillation. Methodology: We audited the data of 60 patients of rheumatic heart disease who had mitral valve stenosis. The patients were randomized into atrial fibrillation (Group A) and normal sinus rhythm (Group B). We conducted this cross-sectional analytical study at Cardiology Department, Mayo Hospital, Lahore, from 1st February 2017 to 31st January 2018. We only included those patients who consented to be a part of this study and fulfilled our predefined inclusion criteria. Left atrial volume was measured by prolate ellipse method and biplane methods on echocardiography. The Data was analyzed on SPSS v20. Results: Sixty patients were included in the study. Among the subjects, thirty-six (60%) were males, and twenty-four (40%) were females. Atrial fibrillation was noted in 43.33% of the patients of mitral valve stenosis. There was a marked difference in the mean volume of the left atrium among the two groups. We observed that the mean area of the mitral valve for Group A patients was larger than that of patients in Group B. Our study showed an inverse correlation between left atrial volume and mitral valve area among Group A patients. Conclusion: Patients of mitral stenosis are at an increased risk of developing atrial fibrillation if the left atrial volume is increasing. All patients with mitral stenosis should have routine echocardiography & measurement of left atrial volumes, so that proper treatment can be started if the left atrial volume is increasing, to prevent atrial fibrillation

A preliminary study of factors affecting the calibration stability of the iridium versus iridium-40 percent rhodium thermocouple

An iridium versus iridium-40% rhodium thermocouple was studied. Problems associated with the use of this thermocouple for high temperature applications (up to 2000 C) were investigated. The metallurgical studies included X-ray, macroscopic, resistance, and metallographic studies. The thermocouples in the as-received condition from the manufacturer revealed large amounts of internal stress caused by cold working during manufacturing. The thermocouples also contained a large amount of inhomogeneities and segregations. No phase transformations were observed in the alloy up to 1100 C. It was found that annealing the thermocouple at 1800 C for two hours, and then at 1400 C for 2 to 3 hours yielded a fine grain structure, relieving some of the strains, and making the wire more ductile. It was also found that the above annealing procedure stabilized the thermal emf behavior of the thermocouple for application below 1800 C (an improvement from + or - 1% to + or - 0.02% within the range of the test parameters used)

Chiral symmetry breaking in QED3{\rm QED}_{3} in presence of irrelevant interactions: a renormalization group study

Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three dimensional quantum electrodynamics ${\rm QED}_{3}$) in presence of irrelevant four-fermion quartic terms. The problem is reformulated in terms of the renormalization group flows of certain four-fermion couplings and charge, and then studied in the limit of large number of fermion flavors $N$. We find that the critical number of fermions $N_c$ below which the mass becomes dynamically generated depends continuously on a weak chiral-symmetry-breaking interaction. One-loop calculation in our gauge-invariant approach yields $N_{c0} = 6$ in pure ${\rm QED}_3$. We also find that chiral-symmetry-preserving mass cannot become dynamically generated in pure ${\rm QED}_{3}$.Comment: 7 pages, 7 figure

Two novel classes of solvable many-body problems of goldfish type with constraints

Two novel classes of many-body models with nonlinear interactions "of goldfish type" are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints): i. e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited: i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.Comment: 30 pages, 2 figure

A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou's result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator.Comment: 19 pages, LaTeX, proof of Propositions 2.3 and 3.1 given in more detai

Estimation of conservation value of myrtle (Myrtus communis) using a contingent valuation method: a case study in a Dooreh forest area, Lorestan Province, Iran

Background: Around 2000 plant species occur naturally in Lorestan Province of which 250 species are medicinal and myrtle is one of them. Myrtle is a shrub whose leaves and fruits have medicinal value and thus, if managed and harvested properly, could produce sustained economic benefits. In recent years, however, over half of the myrtle site areas was destroyed, due to inappropriate management and excessive harvesting practices. Thus, coming up with a practical harvesting approach along with identifying those factors damaging the sites, seems to be very crucial. Methods: In our investigation, we calculated the conservation value per hectare of myrtle in the Dooreh forest area in Lorestan Province. Using the Contingent Valuation (CV) and Double Bounded Dichotomous Choice (DBDC) methods, we determined the willingness to pay (WTP) for myrtle conservation. The WTP was estimated with a logit model for which indices were obtained based on a maximum precision criterion. Results: The results showed that 86.67 per cent of people were willing to pay for the conservation of these myrtle sites. Average monthly WTP per family was calculated as $0.79. The annual conservation value in terms of WTP for the preservation of the myrtle sites in Dooreh was estimated as$102,525. Among the variables of the model presented, education had a positive impact, while the amount proposed for payment and family size had a negative impact on the WTP. Conclusions: Our estimate of the value of myrtle conservation should provide justification for policy makers and decision making bodies of natural resources to implement policies in order to conserve the natural sites of this species more effectively. Keywords: Conservation value, Myrtle, Contingent valuation method, Double Bounded Dichotomous method, Logit mode