918 resultados para Eigenfunctions and fundamental solution


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Diffusion couple experiments are conducted in Co-Ni-Pt system at 1200 degrees C and in Co-Ni-Fe system at 1150 degrees C, by coupling binary alloys with the third element. Uphill diffusion is observed for both Co and Ni in Pt rich corner of the Co-Ni-Pt system, whereas in the Co-Ni-Fe system, it is observed for Co. Main and cross interdiffusion coefficients are calculated at the composition of intersection of two independent diffusion profiles. In both the systems, the main interdiffusion coefficients are positive over the whole composition range and the cross interdiffusion coefficients show both positive and negative values at different regions. Hardness measured by performing the nanoindentations on diffusion couples of both the systems shows the higher values at intermediate compositions.

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Diffusion couple experiments are conducted in Co-Ni-Pt system at 1200 degrees C and in Co-Ni-Fe system at 1150 degrees C, by coupling binary alloys with the third element. Uphill diffusion is observed for both Co and Ni in Pt rich corner of the Co-Ni-Pt system, whereas in the Co-Ni-Fe system, it is observed for Co. Main and cross interdiffusion coefficients are calculated at the composition of intersection of two independent diffusion profiles. In both the systems, the main interdiffusion coefficients are positive over the whole composition range and the cross interdiffusion coefficients show both positive and negative values at different regions. Hardness measured by performing the nanoindentations on diffusion couples of both the systems shows the higher values at intermediate compositions.

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The relationship is determined between saturated duration of rectangular pressure pulses applied to rigid, perfectly plastic structures and their fundamental periods of elastic vibration. It is shown that the ratio between the saturated duration and the fundamental period of elastic vibration of a structure is dependent upon two factors: the first one is the slenderness or thinness ratio of the structure; and the second one is the square root of ratio between the Young's elastic modulus and the yield stress of the structural material. Dimensional analysis shows that the aforementioned ratio is one of the basic similarity parameters for elastic-plastic modeling under dynamic loading.

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Both a real time optical interferometric experiment and a numerical simulation of two-dimension non-steady state model were employed to study the growth process of aqueous sodium chlorate crystals. The parameters such as solution concentration distribution, crystal dimensions, growth rate and velocity field were obtained by both experiment and numerical simulation. The influence of earth gravity during crystal growth process was analyzed. A reasonable theory model corresponding to the present experiment is advanced. The thickness of concentration boundary layer was investigated especially. The results from the experiment and numerical simulation match well.

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The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

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The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

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The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.

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As a means of characterizing the diffusion parameters of fiber reinforced polymer (FRP) composites within a relatively short time frame, the potential use of short term tests on epoxy films to predict the long-term behavior is investigated. Reference is made to the literature to assess the effectiveness of Fickian and anomalous diffusion models to describe solution uptake in epoxies. The influence of differing exposure conditions on the diffusion in epoxies, in particular the effect of solution type and temperature, are explored. Experimental results, where the solution uptake in desiccated (D) or undesiccated (U) thin films of a commercially available epoxy matrix subjected to water (W), salt water (SW), or alkali concrete pore solution (CPS) at either 20 or 60°C, are also presented. It was found that the type of solution did not significantly influence the diffusion behavior at 20°C and that the mass uptake profile was anomalous. Exposure to 60°C accelerated the initial diffusion behavior and appeared to raise the level of saturation. In spite of the accelerated approach, conclusive values of uptake at saturation remained elusive even at an exposure period of 5 years. This finding questions the viability of using short-term thin film results to predict the long-term mechanical performance of FRP materials. © 2013 Wiley Periodicals, Inc.

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A solution processed aluminum-doped zinc oxide (AZO)/multi-walled carbon nanotube (MWCNT) nanocomposite thin film has been developed offering simultaneously high optical transparency and low electrical resistivity, with a conductivity figure of merit (σDC/σopt) of ~75-better than PEDOT:PSS and many graphene derivatives. The reduction in sheet resistance of thin films of pristine MWCNTs is attributed to an increase in the conduction pathways within the sol-gel derived AZO matrix and reduced inter-MWCNT contact resistance. Films have been extensively characterized by scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), transmission electron microscopy (TEM), X-ray diffractometry (XRD), photoluminescence (PL), and ultraviolet-visible (UV-vis) spectroscopy. © 2013 Elsevier Ltd and Techna Group S.r.l. All rights reserved.