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Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially. 相似文献
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Alves GA Amato S Anjos JC Appel JA Astorga J Bernard T Bracker SB Cremaldi LM Darling CL Dixon RL Errede D Gay C Green DR Jedicke R Karchin PE Kwan S Lueking LJ de Mello Neto JR Metheny J Milburn RH de Miranda JM da Motta Filho H Napier A Passmore D Rafatian A dos Reis AC Ross WR Santoro AF Sheaff M Souza MH Spalding WJ Stoughton C Streetman ME Summers DJ Takach SF Wallace A Wu Z 《Physical review letters》1994,72(6):812-815
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Steven H. Izen 《Proceedings of the American Mathematical Society》2007,135(1):269-276
In the context of helical cone-beam CT, Danielsson et al. discovered that for each point interior to the cylindrical surface containing a given helix, there is exactly one line segment passing through the point which intersects two points less than one turn apart on the helix. This segment is called a -line. A new constructive algebraic proof of this result is presented along with a fast algorithm to compute the endpoints of the -line through an arbitrary point in the interior of the helix cylinder. This proof exposes the geometry of the decomposition of a cylinder interior as a disjoint union of -lines.
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