Department of Biomedical Engineering and Mechanics
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A collaboration between School of Biomedical Engineering and Sciences and the Department of Engineering Science and Mechanics to form the Department of Biomedical Engineering and Mechanics.
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Browsing Department of Biomedical Engineering and Mechanics by Subject "2nd-sound shock-waves"
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- The Effect of Thermal Expansion on Nonlinear First And Second Sound in the Whole Temperature Region of He IiBraun, S.; Kluwick, A.; Cramer, Mark S. (AIP Publishing, 1996-09-01)We consider one-dimensional, weakly nonlinear first and second sound waves in He II. The first correction to the shock speed is computed for each sound mode. The expressions obtained are exact with respect to the coefficient of thermal expansion beta. It is shown that the commonly made assumption of negligible beta can lead to significant error in the shock speeds for first sound away from the lambda-line. This contrasts with the calculation of the linear sound speeds and the shock speed for second sound where the beta=0 approximation yields accurate results. Near the lambda-line, the exact expressions for both modes are seen to contain fundamentally different singularities than those found in the commonly employed beta=0 theory. (C) 1996 American Institute of Physics.
- Nonlinear second sound in solidsTarkenton, G. M.; Cramer, Mark S. (American Physical Society, 1994-05-01)We study the nonlinear propagation of thermal waves in rigid heat conductors using a model introduced by Ruggeri et al. We derive the lowest-order nonlinear corrections to the wave speed and show that the quadratic nonlinearity can be small for NaF and Bi. The smallness of the nonlinear steepening parameter complicates the wave dynamics, allowing for both forward and backward steepening waves within the same pulse. We show that this mixed condition places limits on the size of admissible discontinuities; we then argue that this limit on the size of shock waves limits the arrival times of thermal signals. Using this, we propose an experiment to measure arrival times to look for this limiting behavior.