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Yan Guo - One of the best experts on this subject based on the ideXlab platform.
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Geometric Correction in diffusive limit of neutron transport equation in 2d convex domains
Archive for Rational Mechanics and Analysis, 2017Co-Authors: Yan GuoAbstract:Consider the steady neutron transport equation with diffusive boundary condition. In Wu and Guo (Commun Math Phys 336:1473–1553, 2015) and Wu et al. (J Stat Phys 165:585–644, 2016), it was discovered that Geometric Correction is necessary for the Milne problem of Knudsen-layer construction in a disk or annulus. In this paper, we establish the diffusive limit for a 2D convex domain. Our contribution relies on novel weighted \({W^{1,\infty}}\) estimates for the Milne problem with Geometric Correction in the presence of a convex domain, as well as an \({L^{2m}-L^{\infty}}\) framework which yields stronger remainder estimates.
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Regularity of Milne problem with Geometric Correction in 3D
Mathematical Models and Methods in Applied Sciences, 2017Co-Authors: Yan GuoAbstract:Consider the Milne problem with Geometric Correction in a 3D convex domain. Via bootstrapping arguments, we establish W1,∞-regularity for its solutions. Combined with a uniform L6-estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.
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Regularity of Milne problem with Geometric Correction in 3D
Mathematical Models and Methods in Applied Sciences, 2017Co-Authors: Yan GuoAbstract:Consider the Milne problem with Geometric Correction in a 3D convex domain. Via bootstrapping arguments, we establish [Formula: see text]-regularity for its solutions. Combined with a uniform [Formula: see text]-estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.
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Geometric Correction for diffusive expansion of steady neutron transport equation
Communications in Mathematical Physics, 2015Co-Authors: Yan GuoAbstract:We revisit the diffusive limit of a steady neutron transport equation in a two-dimensional unit disk with one-speed velocity. A classical theorem by Bensoussan et al. (Publ Res Inst Math Sci 15(1):53–157, 1979) states that its solution can be approximated in L∞ by the leading order interior solution plus the Knudsen layer in the diffusive limit. In this paper, we construct a counterexample to this result via a different boundary layer expansion with Geometric Correction.
Lei Wu - One of the best experts on this subject based on the ideXlab platform.
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hydrodynamic limit with Geometric Correction of stationary boltzmann equation
Journal of Differential Equations, 2016Co-Authors: Lei WuAbstract:Abstract We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier–Stokes–Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in L ∞ both for its proof and result. Also, we show the hydrodynamic limit with a different boundary layer expansion with Geometric Correction.
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hydrodynamic limit with Geometric Correction of stationary boltzmann equation
arXiv: Analysis of PDEs, 2014Co-Authors: Lei WuAbstract:We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with Geometric Correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.
D L Chen - One of the best experts on this subject based on the ideXlab platform.
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Geometric Correction factors for center cracked specimens subjected to nonlinear bridging stresses in the shear lag model
Engineering Fracture Mechanics, 2003Co-Authors: S X Xu, D L ChenAbstract:Fiber bridging plays an important role in the fracture mechanism of fiber-reinforced composites. The determination of the Geometric Correction factors for finite-width specimens subjected to complex bridging stresses is vital for the practical application of various bridging models. An approximate approach named the force balance method (FBM) was recently reported in the literature to evaluate such Geometric factors. The main purpose of this study is to assess the effectiveness of the FBM by using the well-established boundary element method. The case of a center cracked specimen subjected to a nonlinear fiber bridging stress in the shear lag model in fiber-reinforced composites is considered. The Geometric Correction factors computed by the boundary element method are compared with those deduced by the FBM.
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Geometric Correction factors determined by force balance method for center cracked specimens xii subjected to a nonlinear bridging stress in shear lag model in fiber reinforced composites
International Journal of Fracture, 1997Co-Authors: D L Chen, M C Chaturvedi, B Weiss, Roland SticklerAbstract:The improvement in fatigue and fracture resistance in composite materials is directly related to the toughening mechanisms. To understand better the shielding/bridging effect close to the crack tip, it is necessary to evaluate the Geometric Correction factor, induced by the bridging stresses existing on the fracture surfaces, for finite-width specimens. Force balance method was applied to determine the Geometric Correction factor for a center cracked specimen subjected to a nonlinear bridging stress in the shear lag model in fiber-reinforced composites.
Luis Cortereal - One of the best experts on this subject based on the ideXlab platform.
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measures for an objective evaluation of the Geometric Correction process quality
IEEE Geoscience and Remote Sensing Letters, 2009Co-Authors: Hernâni Goncalves, J A Goncalves, Luis CorterealAbstract:The Geometric Correction process is a crucial step in remote sensing applications. This process is frequently manually performed-which is a laborious task in many situations-as automatic image registration methods are still far from being broadly applied. One of the reasons that justify the absence of a broad application of automatic image registration methods is the lack of measures for an objective and automated analysis of the image registration process quality. The root mean square (RMS) of the residuals is the only quantitative evaluation which is generally used in this process, with the final validation of the Geometric Correction process being a qualitative analysis. Therefore, in both ldquohumanrdquo and automatic image registration processes, an objective evaluation of its quality is required. In this letter, we propose several measures for an objective evaluation of the Geometric Correction process, as a complement to the traditional RMS of the residuals and visual inspection. Two scenarios of control point distribution and the most common residual distributions were considered. With the proposed measures, we intend to cover the most common qualitative analysis aspects. This has particular importance under the scope of automatic image registration methods, where an automatic evaluation of the results is also required.
Mikio Takagi - One of the best experts on this subject based on the ideXlab platform.
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precise Geometric Correction for noaa and gms images considering elevation effects using gcp template matching and affine transform
Remote Sensing, 2004Co-Authors: Mikio TakagiAbstract:This paper describes a precise Geometric Correction method considering elevation effects for NOAA/AVHRR of GMS images, which is mandatory for long-term global environmental monitoring studies. First, using the so-called systematic Geometric Correction, the correspondences of sub-sampled image pixels to their map coordinates are calculated. And, the correspondences of sub-sampled map locations, which are the corner points of blocks, to image pixels are calculated to speed up the inverse transform to find for a pixel on the map coordinates to the corresponding pixel in the image coordinates using the bilinear interpolation of the four corner points of a block. For precise Geometric Correction, the residual errors of the systematic Correction are measured using many GCP templates. GCP templates in the map coordinates are provide using DCW. Templates in the image coordinates are generated using the bilinear Interpolation. Also, the templates of high elevation areas are modified to include the elevation effects, using the height from GTOPO30 and satellite sensor geometry. Then, the residual errors are acquired by template matching and affine transform coefficients are calculated to remove the residual errors. And if the difference between the average error and each GCP is more than one pixel, these GCP’s are removed and new affine transform coefficients are recalculated iteratively until all errors reach within one pixel. Then, mapping of each pixel is done using the correspondence of four corner block points and image coordinates modified by affine transform, but for high elevation areas blocks are divided into pixels according to their elevation. The accuracy of within one pixel; i.e. 0.01 degree for NOAA/AVHRR and GMS/VIS and 0.04 degrees for GMS/IR is obtained for NOAA images received at Tokyo and the stitched ones received at Tokyo and Bangkok and also GMS full disk images.