A brief overview of existence results and decay time estimates for a mathematical modeling of scintillating crystals
A brief overview of existence results and decay time estimates for a mathematical modeling of scintillating crystals
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DOI：
10.1002/mma.7660
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发表时间：
2021-07-26
影响因子：
2.9
通讯作者：
Davi，Fabrizio
中科院分区：
文献类型：
--
作者：
Davi，Fabrizio
无机闪烁晶体可以建模为具有微观结构的连续体。对于刚性和等温晶体，载流子的演化可以用反应-扩散-漂移方程和静电泊松方程来描述。在这里，我们给出了可用的存在性和渐近衰减结果的调查所得的边值问题，后者是闪烁衰减时间的直接估计。我们还展示了如何恢复各种近似模型，这些模型也包含了闪烁体的两种最常用的现象学模型，即动力学模型和扩散模型。同样，对于这些情况，我们表明，只要可能，哪些存在性和渐近衰减估计结果是已知的。
Inorganic scintillating crystals can be modelled as continua with microstructure. For rigid and isothermal crystals, the evolution of charge carriers becomes in this way described by a reaction‐diffusion‐drift equation coupled with the Poisson equation of electrostatic. Here, we give a survey of the available existence and asymptotic decays results for the resulting boundary value problem, the latter being a direct estimate of the scintillation decay time. We also show how to recover various approximated models which encompass also the two most used phenomenological models for scintillators, namely, the kinetic and diffusive ones. Also for these cases, we show, whenever it is possible, which existence and asymptotic decays estimate results are known to date.