In this paper we present the convergence analysis of iterative schemes for solving linear systems resulting from discretizing multidimensional linear second-order elliptic partial differential equations (PDEs) defined in a hyperparallelepiped $\Omega$ and subject to Dirichlet boundary conditions on some faces of $\Omega$ and Neumann on the others, using line cubic spline collocation (LCSC) methods. Specifically, we derive analytic expressions or obtain sharp bounds for the spectral radius of the corresponding Jacobi iteration matrix and from this we determine the convergence ranges and compute the optimal parameters for the extrapolated Jacobi and successive overrelaxation (SOR) methods. Experimental results are also presented.
We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.
Abstract : The overall objectives of the AASERT project are to develop an approach for the controlled synthesis of single crystal, one-dimensional (1D) nanowires of the Bi2Te3 family of thermoelectric materials, and to characterize the potentially unique electronic properties of these 1D systems. To achieve these goals we will (1) develop synthetic procedures, which were initiated as part of our current ONR project on nanorod- superconductor composites, to prepare Bi2Te3 nanowires and (2) exploit existing scanning tunneling microscopy facilities and expertise to characterize the nanowire density of electronic states. The combination of systematic synthesis with high-resolution structural and electronic characterization will elucidate the basic factors that control the diameter, aspect ratio, and crystallographic growth direction of Bi2Te3 nanowires, and define the variation and potential enhancements in valence and conduction band edge density of states with nanowire diameter. These studies will thus provide a critical assessment of the possibility of obtaining enhanced thermoelectric figures of merit through material dimensional control.
As idiopathic pulmonary fibrosis emerges as an important public health problem, there is a need to coordinate data on incidence and mortality globally. This study aims to systematically assess all available studies to investigate the global burden of disease. Medline and Embase databases were searched systematically for all population-based studies of incidence or mortality of idiopathic pulmonary fibrosis. Clinical case series and prevalence studies were excluded. The search was supplemented using the Google search engine, hand-searching of references and conference abstracts. Data were extracted independently by two authors using a pre-specified proforma, with assessment of methodological quality. 34 studies were identified, providing data from 21 countries from 1968–2012. 28 studies reported incidence data and eight reported mortality data. In studies from the year 2000 onwards, we estimated a conservative incidence range of 3–9 cases per 100 000 per year for Europe and North America. Incidence was lower in East Asia and South America. The majority of studies showed an increase in incidence over time. The incidence of idiopathic pulmonary fibrosis is increasing worldwide and rates are coming together across countries. Current data suggest incidence is similar to that of conditions such as stomach, liver, testicular and cervical cancers.
For some multilayer systems that experience compression, buckling of the film in an initially debonded region may release energy that becomes available to drive the interface crack and increase the size of the debonded region. This phenomenon, called buckling delamination, occurs in structural composites where a compressed surface layer has debonded from its adjacent layers and buckles when the applied compression is sufficiently large. This surface layer may then delaminate if the interface toughness is not large enough to keep the interface crack from propagating. Buckling delamination is one of the most widely observed failure mechanisms in thin films and coatings on substrates when the stress is compressive. Buckling delamination involves the simultaneous interaction of buckling and interface cracking.
ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThe chemistry of carbanions. XIII. The nuclear magnetic resonance spectra of various methylmagnesium derivatives and related substancesHerbert O. House, Roger A. Latham, and George M. WhitesidesCite this: J. Org. Chem. 1967, 32, 8, 2481–2496Publication Date (Print):August 1, 1967Publication History Published online1 May 2002Published inissue 1 August 1967https://pubs.acs.org/doi/10.1021/jo01283a028https://doi.org/10.1021/jo01283a028research-articleACS PublicationsRequest reuse permissionsArticle Views331Altmetric-Citations48LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts
The role of the substrate in determining heat dissipation in high power electronics is calculated, subject to convective cooling in the small Biot number regime. Analytical models that exploit the large aspect ratio of the substrate to justify approximations are shown to predict the behavior with good accuracy over a wide range of configurations. The solutions distinguish heat spreading effects’ that enable high chip-level power densities from insulation effects that arise at large chip densities. In the former, the attributes of high thermal conductivity are apparent, especially when the substrate dimensions are optimized. Additional benefits that derive from a thin layer of a high thermal conductivity material (such as diamond) are demonstrated. In the insulating region, which arises at high overall power densities, the substrate thermal conductivity has essentially no effect on the heat dissipation. Similarly, for compact multichip module designs, with chips placed on both sides of the substrate, heat dissipation is insensitive to the choice of the substrate material, unless advanced cooling mechanisms are used to remove heat around the module perimeter.
