Analysis of one-dimensional wave scattering by the random walk method

2002 ◽  
Vol 111 (6) ◽  
pp. 2555-2560 ◽  
Author(s):  
B. V. Budaev ◽  
D. B. Bogy
Keyword(s):  
Random Walk ◽  
Wave Scattering ◽  
One Dimensional ◽  
Random Walk Method ◽  
Dimensional Wave

A note on random walks at constant speed

1978 ◽  
Vol 10 (04) ◽  
pp. 704-707 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Random Walks ◽  
Constant Speed ◽  
Position Vector ◽  
Biological Models ◽  
Motion Equations ◽  
One Dimensional ◽  
Motion Models ◽  
Dimensional Wave

While the general principles involved in the formulation of random walk and Brownian motion equations (whether the random changes are directly on the position of a particle or individual, or on the velocity) are well-known, there are various situations considered in the literature involving the assumption of a constant speed (in magnitude). Thus the derivation by Goldstein (1951) of a one-dimensional wave-like equation involved the tacit assumption Ut = ± a, where Ut is the vector velocity dRt /dt, Rt being the (column) position vector (Bartlett (1957)). Biological models may involve the assumption of individuals moving at constant speed (cf. Kendall (1974)). Finally, the derivation of Schrodinger-type equations from Brownian motion models has sometimes involved the assumption U′t Ut = c 2, where c is the velocity of light (Cane (1967), (1975)).

A note on random walks at constant speed

1978 ◽  
Vol 10 (4) ◽  
pp. 704-707 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Random Walks ◽  
Constant Speed ◽  
Position Vector ◽  
Biological Models ◽  
Motion Equations ◽  
One Dimensional ◽  
Motion Models ◽  
Dimensional Wave

While the general principles involved in the formulation of random walk and Brownian motion equations (whether the random changes are directly on the position of a particle or individual, or on the velocity) are well-known, there are various situations considered in the literature involving the assumption of a constant speed (in magnitude). Thus the derivation by Goldstein (1951) of a one-dimensional wave-like equation involved the tacit assumption Ut = ± a, where Ut is the vector velocity dRt/dt,Rt being the (column) position vector (Bartlett (1957)). Biological models may involve the assumption of individuals moving at constant speed (cf. Kendall (1974)). Finally, the derivation of Schrodinger-type equations from Brownian motion models has sometimes involved the assumption U′tUt = c2, where c is the velocity of light (Cane (1967), (1975)).

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

Some differential equations for problems of wave scattering in a one-dimensional medium

Astrophysics ◽  
1999 ◽  
Vol 42 (3) ◽  
pp. 316-321 ◽  
Author(s):  
D. M. Sedrakian ◽  
A. Zh. Khachatrian
Keyword(s):  
Differential Equations ◽  
Wave Scattering ◽  
One Dimensional
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