A novel stochastic photo-thermoelasticity model according to a diffusion interaction processes of excited semiconductor medium
Mathematics Department, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt
2 Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt
3 Department Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia
4 Department of Mathematics, Faculty of Science, Taibah University, P.O. Box 344, Madinah, Saudi Arabia
5 Basic & Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, 31441, Dammam, Saudi Arabia
6 Council of futuristic studies and risk management, Academy of Scientific Research and Technology, Cairo, Egypt
Accepted: 11 August 2022
Published online: 27 August 2022
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.
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