Validity and Regularization of Classical Half-Space Equations
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© 2016, Springer Science+Business Media New York.Recent result (Wu and Guo in Commun Math Phys 336(3):1473–1553, 2015) has shown that over the 2D unit disk, the classical half-space equation (CHS) for the neutron transport does not capture the correct boundary layer behaviour as long believed. In this paper we develop a regularization technique for CHS to any arbitrary order and use its first-order regularization to show that in the case of the 2D unit disk, although CHS misrepresents the boundary layer behaviour, it does give the correct boundary condition for the interior macroscopic (Laplace) equation. Therefore CHS is still a valid equation to recover the correct boundary condition for the interior Laplace equation over the 2D unit disk.
Published Version (Please cite this version)10.1007/s10955-016-1688-4
Publication InfoLi, Q; Lu, Jianfeng; & Sun, W (2017). Validity and Regularization of Classical Half-Space Equations. Journal of Statistical Physics, 166(2). pp. 398-433. 10.1007/s10955-016-1688-4. Retrieved from http://hdl.handle.net/10161/14105.
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Associate Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.More specifically, his current research focuses include:Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.