A stochastic thermoelastic diffusion interaction in an infinitely long annular cylinder

Allam, Allam A.; Ramadan, Khaled T.; Omar, Mohamed

doi:10.1007/s00707-016-1569-6

Cited by 10 publications

(8 citation statements)

References 24 publications

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“…Now, a stochastic distribution of the temperature (thermal) at the boundary can be defined on the following form [ 32 , 33 ]: where , is a constant temperature, is the Heaviside unit function, and a stochastic process is which is based on the time-parameter and satisfies: …”

Section: Stochastic Main Physical Fieldsmentioning

confidence: 99%

“…6.1 , under the deterministic boundary condition Eqs. ( 24 ) and ( 21 ), the solution of the deterministic stress field can be described as [ 32 , 33 ]: …”

Section: Stochastic Main Physical Fieldsmentioning

confidence: 99%

“…( 30 ) by the same technique which is used in Sect. 6.1 , the mean displacement distribution can be written as [ 32 , 33 ]: where the mean of all the displacement field sample paths has the similar solution of the deterministic case.…”

Section: Stochastic Main Physical Fieldsmentioning

confidence: 99%

“…Sherief et al [ 30 ] developed a stochastic thermal shock problem according to the generalized thermoelasticity theory. Allam et al [ 31 , 32 ] studied a stochastic half-space problem under the effect of an internal heat source in the theory of generalized diffusion—thermoelasticity theory in an infinitely long annular cylinder. Gupta and Mukhopadhyay [ 33 ] investigated the stochastic thermoelastic interaction with random temperature distribution at the free surface of an elastic solid medium under a dual phase-lag model.…”

Section: Introductionmentioning

confidence: 99%

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A novel stochastic photo-thermoelasticity model according to a diffusion interaction processes of excited semiconductor medium

et al. 2022

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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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Section: Stochastic Main Physical Fieldsmentioning

confidence: 99%

“…6.1 , under the deterministic boundary condition Eqs. ( 24 ) and ( 21 ), the solution of the deterministic stress field can be described as [ 32 , 33 ]: …”

Section: Stochastic Main Physical Fieldsmentioning

confidence: 99%

Section: Stochastic Main Physical Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A novel stochastic photo-thermoelasticity model according to a diffusion interaction processes of excited semiconductor medium

et al. 2022

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show abstract

“…Sherief et al [24] developed a stochastic thermal shock problem according to the generalized thermoelasticity theory. Allam et al [25,26] studied a stochastic half-space problem under the effect of an internal heat source in the theory of generalized diffusion -thermoelasticity theory in an infinitely long annular cylinder. Gupta and Mukhopadhyay [27] investigated the stochastic thermoelastic interaction with random temperature distribution at the free surface of an elastic solid medium under a dual phase-lag model.…”

Section: Introductionmentioning

confidence: 99%

A Novel Stochastic Model of the Photo-Thermoelasticity Theory of the Non-Local Excited Semiconductor Medium

Lotfy

Ahmed

El-Bary

et al. 2022

Silicon

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A novel technique under the effect of stochastic heating due to the thermal effect of the photothermal theory is investigated. Realistically, stochastic processes are taken on the boundary of the non-local 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 dimension (1D) according to the elastic-electronic deformation. Laplace transforms with short-time approximation are used to analyze the main physical fields in linearity form. 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 simulation. The comparisons are carried out between the distributions of deterministic and stochastic (statistically, the mean and variance) of the main physical quantities along different sample paths graphically and discussed for the non-local silicon semiconductor material.

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Electro–magneto interaction in a two-dimensional generalized thermoelastic solid cylinder

Sherief

Allam

2017

Acta Mech

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A stochastic thermoelastic diffusion interaction in an infinitely long annular cylinder

Cited by 10 publications

References 24 publications

A novel stochastic photo-thermoelasticity model according to a diffusion interaction processes of excited semiconductor medium

A novel stochastic photo-thermoelasticity model according to a diffusion interaction processes of excited semiconductor medium

A Novel Stochastic Model of the Photo-Thermoelasticity Theory of the Non-Local Excited Semiconductor Medium

Electro–magneto interaction in a two-dimensional generalized thermoelastic solid cylinder

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