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The steady-state fully resonant wave system, consisting of two progressive primary waves in finite water depth and all components due to nonlinear interaction, is investigated in detail by means of analytically solving the fully nonlinear wave equations as a nonlinear boundary-value problem. It is found that multiple steady-state fully resonant waves exist in some cases which have no exchange of wave energy at all, so that the energy spectrum is time-independent. Further, the steady-state resonant wave component may contain only a small proportion of the wave energy. However, even in these cases, there usually exist time-dependent periodic exchanges of wave energy around the time-independent energy spectrum corresponding to such a steady-state fully resonant wave, since it is hard to be exactly in such a balanced state in practice. This view serves to deepen and enrich our understanding of the resonance of gravity waves.
A poly(acrylic acid)/gelatin interpenetrating network hydrogel was synthesized by aqueous solution polymerization. The influences of preparation conditions including cross-linker, initiator, gelatin content, and neutralization degree on the swelling ratios of the hydrogels are investigated. The swelling, mechanical strength, biodegradability, and drug-release properties of poly(acrylic acid)/gelatin hydrogel are evaluated. The hydrogel has excellent mechanical properties; tensile strength is 1500 kPa, and elongation at break is 887%, respectively. The in vitro biodegradation shows that an interpenetrating network structure exists in the poly(acrylic acid)/gelatin hybrid hydrogel. A release study indicates that the theophylline release from the hydrogel depends on the cross-linking density of the hydrogel and pH of the medium, and the drug diffusion obeys an anomalous transport model.
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