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In this paper, we observe how the heat equation in a noncylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as a parabolic version of a previous work by the first and last authors, concerning the stationary case [Alvarez-Caudevilla and Lemenant, Adv. Differ. Equ.15 (2010) 649-688]. We provide a strong convergence result for the solution by use of energetic methods and Gamma -convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon.

Photoluminescence (PL) quantum efficiency (QE) is one of the important parameters to characterize photoluminescent materials especially for lighting and display applications. Under a few assumptions, IEC standard (IEC62607-3-1) provides two methods of high simplicity and moderate accuracy with an integrating sphere for absolute measurement of QE named 'collimated incident light method (CILM)' and 'diffuse incident light method (DILM)', respectively (International standard IEC 62607-3-1 2014 Nanomanufactureing-Key Control Characteristics Part3-1: Luminescent Nanomaterials-Quantum Efficiency 1st edn (Geneva: International Electrotechnical Commission); de Mello et al 1997 Adv. Mater. 9 230-2). However, the simplification unavoidably causes systematic errors, which could be significant in certain cases of sphere reflectance or material properties. In this paper, we numerically investigate the systematic errors that can occur in the standardised methods when employing a Monte Carlo ray-tracing simulation and also present the correction method based on additional measurement to estimate the diffusivity of the sample reflectance at excitation wavelength and absorption of the sample at PL emission wavelength.