Lotfy Kh, Ahmed Abdelaala, El-Bary A, El-Shekhipy Abdelhafeez, Tantawi Ramdan S
Mathematics Department, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt.
Department of Mathematics, Faculty of Science, Taibah University, P.O. Box 344, Madinah, Saudi Arabia.
Eur Phys J Plus. 2022;137(8):972. doi: 10.1140/epjp/s13360-022-03185-6. Epub 2022 Aug 27.
A novel technique under the impact of stochastic heating due to the thermal effect of photothermal theory is investigated. Realistically, stochastic processes are taken on the boundary of the semiconductor medium. The interactions between optical, thermal, and mechanical waves in a half-space of the medium are studied according to the photo-thermoelasticity theory. The governing equations are described in one-dimensional elastic-electronic deformation. Laplace transforms with short-time approximation are used to analyze the main physical fields. To study the problem more realistically, some conditions are taken as random with white noise on the free surface of the elastic medium. The deterministic physical quantities are obtained with a stochastic calculus when a numerical inversion of the Laplace transform is applied. The silicon material is utilized to make the stochastic numerical simulation. The comparisons are carried out between the distributions of deterministic and stochastic (statistically, the mean and variance) the main physical quantities along different sample paths graphically and discussed.
研究了一种受光热理论热效应影响的随机加热作用下的新技术。实际情况是，在半导体介质边界上考虑随机过程。根据光热弹性理论，研究了介质半空间中光波、热波和机械波之间的相互作用。控制方程用一维弹性 - 电子变形来描述。采用具有短时近似的拉普拉斯变换来分析主要物理场。为了更实际地研究该问题，在弹性介质自由表面上，将一些条件视为具有白噪声的随机条件。当应用拉普拉斯变换的数值反演时，通过随机微积分获得确定性物理量。利用硅材料进行随机数值模拟。以图形方式对沿不同样本路径的主要物理量的确定性分布和随机分布（统计上，均值和方差）进行了比较并讨论。
