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- W2068473490 abstract "The article on diffusion waves by Andreas Mandelis was a refreshing and interesting look at some applications of these waves, which are governed by a linear, parabolic partial differential equation. Readers may be interested in some other applications that arise from extensions of this governing equation in classical continuum mechanics. In porous media transport, for example, diffusion wave theories have variously been used to describe propagation in poroelastic media, 1 1. G. DeGrande, G. De Roeck, Transport in Porous Media 9, 85 (1992) https://doi.org/10.1007/BF01039628. the wave-driven dynamics of reacting solutes in homogeneous media 2 2. C. J. Van Duijn, P. Knabner, S. E. A. T. M. Van der Zee, Adv. Water Resour. 16, 97 (1993) https://doi.org/10.1016/0309-1708(93)90001-V. and in mixed media characterized by composite heterogeneity, or by interfaces at which discontinuities in the wave field are maintained. 3 3. M. G. Trefry, Transp. Porous Media 37, 183 (1999) https://doi.org/10.1023/A:1006562700905. In the related field of ground-water hydrology, the wave field is identified with hydraulic head and is typically forced by tidal effects in surface water bodies, by Earth tides or by seasonal effects. The governing equation ensures that high frequency modes are strongly damped in aquifers, while low frequency modes are passed.Of particular interest are nonlinear diffusion waves, which are often relevant for groundwaters near beaches, river banks, and so forth, and which display unusual characteristics. 4 4. R. Shepherd, R. J. Wiltshire, Transp. Porous Media 15, 175 (1994) https://doi.org/10.1007/BF00625515. Various examples of nonlinear diffusion waves are described in refs. 44. R. Shepherd, R. J. Wiltshire, Transp. Porous Media 15, 175 (1994) https://doi.org/10.1007/BF00625515. and 55. P. L.-F. Liu, J. Wen, J. Fluid Mech. 347, 119 (1997) https://doi.org/10.1017/S0022112097006472..Mandelis concentrated his discussion on applications close to modern physicists’ hearts, including materials science, photonics, and so forth. What I hope to have shown is that these peculiar waves are also important in other areas, reinforcing Mandelis’s conclusion that diffusive propagation is a topic worthy of further study.REFERENCESSection:ChooseTop of pageREFERENCES <<1. G. DeGrande, G. De Roeck, Transport in Porous Media 9, 85 (1992) https://doi.org/10.1007/BF01039628. Google ScholarCrossref, ISI2. C. J. Van Duijn, P. Knabner, S. E. A. T. M. Van der Zee, Adv. Water Resour. 16, 97 (1993) https://doi.org/10.1016/0309-1708(93)90001-V. Google ScholarCrossref, ISI3. M. G. Trefry, Transp. Porous Media 37, 183 (1999) https://doi.org/10.1023/A:1006562700905. Google ScholarCrossref, ISI4. R. Shepherd, R. J. Wiltshire, Transp. Porous Media 15, 175 (1994) https://doi.org/10.1007/BF00625515. Google ScholarCrossref, ISI5. P. L.-F. Liu, J. Wen, J. Fluid Mech. 347, 119 (1997) https://doi.org/10.1017/S0022112097006472. Google ScholarCrossref, ISI© 2001 American Institute of Physics." @default.
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- W2068473490 title "Many Uses for Diffusion Waves" @default.
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