Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: The excellent mechanical properties of carbon-nanotubes are driving research into the creation of new strong, tough nanocomposite systems. Here, the first evidence of toughening mechanisms operating in carbon-nanotube-reinforced ceramic composites is presented. A highly-ordered array of parallel multiwall carbon-nanotubes (CNTs) in an alumina matrix was fabricated. Nanoindentation introduced controlled cracks and the damage was examined by SEM. These nanocomposites exhibit the three hallmarks of toughening in micron-scale fiber composites: crack deflection at the CNT/matrix interface; crack bridging by CNTs; and CNT pullout on the fracture surfaces. Interface debonding and sliding can thus occur in materials with microsctructures approaching the atomic scale. Furthermore, for certain geometries a new mechanism of nanotube collapse in "shear bands" occurs, rather than crack formation, suggesting that these materials can have multiaxial damage tolerance. Evidence for a novel nanotube fracture mode is also presented. The quantitative indentation data and computational models are used to determine the multiwall CNT axial Young's modulus as 200-570 GPa, depending on the nanotube geometry and quality. 3d FEM analysis indicates that matrix residual stresses on the order of 300 MPa are sustained in these materials without spontaneous cracking. Preliminary analysis of the indentation cracking using a 3d cohesive zone model indicates that the toughening due to nanotube bridging is about 5 MPa-m^1/2, and that the nanotube tensile strengths are in the range of 15-25 GPa. Overall, these results show that careful tailoring of the nanotube geometry (diameter, wall thickness), matrix properties, and residual stresses, may permit engineering of these materials for multiaxial hardness and damage tolerance at submicron scales, making them excellent candidates for wear-resistant coatings.
Brown University Center for Statistical Sciences Seminar
Center for Statistical Sciences, Brown University | |
Abstract: Many biomedical datasets are concerned with relating the result of screening procedure(s) for a clinical event to the occurrence of that event. The effect of risk factors on the measures of accuracy such as sensitivity and specificity is of great interest for clinicians. In this paper we propose a generic approach to estimate these measures of accuracy when information on one or more risk factors is not available. We refer to these as conditional rates, i.e., rates conditioned on only a subset of risk factors. We argue that, based upon the joint distribution of the event outcome, the screening result and the risk factor occurrence, a formal expression for such a rate can be obtained. This expression is a function of model parameters and thus can be estimated once the model has been fitted. Inference with the Bayesian framework is particularly attractive since simulation based model fitting straightforwardly yields samples from the posterior distribution of the conditional rate. We perform a simulation study to compare these estimated conditional rates with frequently used ad hoc estimates. The proposed approach is extended for multiple test outcomes and for random effects model.
Brown Analysis Seminar
Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: Natural composite materials are renowned for their mechanical strength and toughness; despite being highly mineralized, with the organic component constituting not more than a few percent of the composite material, the fracture toughness exceeds that of single crystals of the pure mineral by two to three orders of magnitude. The judicious placement of the organic matrix, relative to the mineral phase, and the hierarchical structural architecture extending over several distinct length scales both play crucial roles in the mechanical response of natural composites to external loads. In this talk the results of transmission electron microscopy studies, beam bending experiments, and theoretical modeling are used to show that the resistance of the shell of the conch {\it Strombus Gigas} to catastrophic fracture can be understood quantitatively by invoking two energy-dissipating mechanisms: multiple cracking in the outer layers at low mechanical loads, and crack bridging in the shell's tougher middle layers at higher loads. Both mechanisms are intimately associated with the so-called crossed lamellar microarchitecture of the shell, which provides for tunnel cracking in the outer layers and uncracked structural features that bridge crack surfaces, thereby significantly increasing the work of fracture, and hence the toughness, of the material. Despite a high mineral content of about 99% (by volume) of aragonite, the shell of {\it Strombus Gigas} can thus be considered `ceramic plywood' (albeit plywood fails in a different manner than the shell), and can guide the bioinspired design of tough, lightweight structures.
PDE Seminar
Abstract: We consider a one dimensional hyperbolic system for chemosenstive movement, especially for chemotactic behavior. The model consists of two hyperbolic differential equations for the chemotactic species and is coupled with either a parabolic or an elliptic equation for the dynamics of the external chemical signal. The speed of the chemotactic species is allowed to depend on the external signal and turning rates may depend on the signal and its gradients in space and time, as observed in experiments. Global classical solutions are established for regular initial data and its parabolic limit is proved.
Department of Mathematics Colloquium
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