The periodic unfolding method for the heat equation in perforated domains

We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).

Calibration and Unfolding of the Pulse Height Spectra of Liquid Scintillator-Based Neutron Detectors Using Photon Sources

An accurate energy calibration of a 5＂× 2＂ BC501A liquid scintillator-based neutron detector by means of photon sources and the unfolding of pulse height spectra are described. The photon responses were measured with 22Na, 137Cs and 54Mn photon sources and simulated using the GRESP code, which was developed at the Physiknlisch Technische Bundesanstalt in Germany. Pulse height spectra produced by three different photon sources were employed to investigate the effects of the unfolding techniques. It was found that the four unfolding codes of the HEPRO and UMG3.3 packages, including GRAVEL, UNFANA, MIEKE and MAXED, performed well with the test spectra and produced generally consistent results. They could therefore be used to obtain neutron energy spectra in toknmak experiments.

Manufacturing of ultra-large plate forgings by unfolding and flattening of thick cylinders

Ultra-large plate forgings are foundation of heavy machinery,but many parts of the type cannot be made by conventional technologies due to the characters of extreme manufacturing in terms of size and quality requirements.This paper introduced a systematically method called cylinder unfolding method(CUM)for producing large plate forgings,by using a serial of operations including“splitting”,“unfolding”,and“flattening”of a thick cylinder obtained from saddle forging.The technological route of CUM was presented in detail with an example of plate forging with the horizontal sizes of 6100 mm and thickness of 300 mm.The deformation features of saddle forging for fabricating transitional cylinders were analyzed,and then the subsequent handling steps including splitting,unfolding and flattening of the cylinder,as well as the auxiliary processing,were addressed.The practice proved that CUM can provide an efficient way for manufacturing ultra-large plate forgings and meet the strict requirements in geometry and mechanical performance,without highly increasing the investments of forming equipment and tooling.

A Note on Homogenization of Parabolic Equation in Perforated Domains

We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes.By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh（Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci.（Math. Sci.）, 2002, 112（1）： 195–207）. Moreover,these results generalize those obtained by Donato and Nabil（Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50： 115–144）.

Periodic Homogenization for Inner Boundary Conditions with Equi-valued Surfaces:the Unfolding Approach

Making use of the periodic unfolding method,the authors give an elementary proof for the periodic homogenization of the elastic torsion problem of an infinite 3dimensional rod with a multiply-connected cross section as well as for the general electroconductivity problem in the presence of many perfect conductors(arising in resistivity well-logging).Both problems fall into the general setting of equi-valued surfaces with corresponding assigned total fluxes.The unfolding method also gives a general corrector result for these problems.