# Browsing by Subject "size effect"

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Item Monte Carlo simulations of solid walled proportional counters with different site size for HZE radiation(2009-05-15) Wang, XudongShow more Characterizing high z high energy (HZE) particles in cosmic radiation is of importance for the study of the equivalent dose to astronauts. Low pressure, tissue equivalent proportional counters (TEPC) are routinely used to evaluate radiation exposures in space. A multiple detector system composed of three TEPC of different sizes was simulated using the Monte-Carlo software toolkit GEANT4. The ability of the set of detectors to characterize HZE particles, as well as measure dose, was studied. HZE particles produce energetic secondary electrons (-rays) which carry a significant fraction of energy lost by the primary ion away from its track. The range and frequency of these delta rays depends on the velocity and charge of the primary ion. Measurements of lineal energy spectra in different size sites will differ because of these delta ray events and may provide information to characterize the incident primary particle. Monte Carlo calculations were accomplished, using GEANT4, simulating solid walled proportional detectors with unit density site diameter of 0.1, 0.5 and 2.5 ?m in a uniform HZE particle field. The simulated spherical detectors have 2 mm thick tissue equivalent walls. The uniform beams of 1 GeV/n, 500 MeV/n and 100 MeV/n 56Fe, 28Si, 16O, 4He and proton particles were used to bombard the detector. The size effect of such a detector system was analyzed with the calculation results. The results show that the y vs. yf(y) spectrum differs significantly as a function of site size. From the spectra, as well as the calculated mean lineal energy, the simulated particles can be characterized. We predict that the detector system is capable of characterizing HZE particles in a complex field. This suggests that it may be practical to use such a system to measure the average particle velocity as well as the absorbed dose delivered by HZE particles in space. The parameters used in the simulation are also good references for detector construction. characterizing HZE particles in a complex field. This suggests that it may be practical to use such a system to measure the average particle velocity as well as the absorbed dose delivered by HZE particles in space. The parameters used in the simulation are also good references for detector construction.Show more Item Strain Gradient Solutions of Eshelby-Type Problems for Polygonal and Polyhedral Inclusions(2012-02-14) Liu, MengqiShow more The Eshelby-type problems of an arbitrary-shape polygonal or polyhedral inclusion embedded in an infinite homogeneous isotropic elastic material are analytically solved using a simplified strain gradient elasticity theory (SSGET) that contains a material length scale parameter. The Eshelby tensors for a plane strain inclusion with an arbitrary polygonal cross section and for an arbitrary-shape polyhedral inclusion are analytically derived in general forms in terms of three potential functions. These potential functions, as area integrals over the polygonal cross section and volume integrals over the polyhedral inclusion, are evaluated. For the polygonal inclusion problem, the three area integrals are first transformed to three line integrals using the Green's theorem, which are then evaluated analytically by direct integration. In the polyhedral inclusion case, each of the three volume integrals is first transformed to a surface integral by applying the divergence theorem, which is then transformed to a contour (line) integral based on Stokes' theorem and using an inverse approach. In addition, the Eshelby tensor for an anti-plane strain inclusion with an arbitrary polygonal cross section embedded in an infinite homogeneous isotropic elastic material is analytically solved. Each of the newly derived Eshelby tensors is separated into a classical part and a gradient part. The latter includes the material length scale parameter additionally, thereby enabling the interpretation of the inclusion size effect. For homogenization applications, the area or volume average of each newly derived Eshelby tensor over the polygonal cross section or the polyhedral inclusion domain is also provided in a general form. To illustrate the newly obtained Eshelby tensors and their area or volume averages, different types of polygonal and polyhedral inclusions are quantitatively studied by directly using the general formulas derived. The numerical results show that the components of the each SSGET-based Eshelby tensor for all inclusion shapes considered vary with both the position and the inclusion size. It is also observed that the components of each averaged Eshelby tensor based on the SSGET change with the inclusion size.Show more