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Shock experiments are widely used to understand the mechanical and electronic properties of matter under extreme conditions. However, after shock loading to a Hugoniot state, a clear description of the post-shock thermal state and its impacts on materials is still lacking. We used diffraction patterns from 100-fs x-ray pulses to investigate the temperature evolution of laser-shocked Al–Zr metal film composites at time delays ranging from 5 to 75 ns driven by a 120-ps short-pulse laser. We found significant heating of both Al and Zr after shock release, which can be attributed to heat generated by inelastic deformation. A conventional hydrodynamic model that employs (i) typical descriptions of Al and Zr mechanical strength and (ii) elevated strength responses (which might be attributed to an unknown strain rate dependence) did not fully account for the measured temperature increase, which suggests that other strength-related mechanisms (such as fine-scale void growth) could play an important role in thermal responses under shock wave loading/unloading cycles. Our results suggest that a significant portion of the total shock energy delivered by lasers becomes heat due to defect-facilitated plastic work, leaving less converted to kinetic energy. This heating effect may be common in laser-shocked experiments but has not been well acknowledged. High post-shock temperatures may induce phase transformation of materials during shock release. Another implication for the study is the preservability of magnetic records from planetary surfaces that have a shock history from frequent impact events.
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Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model
We consider a hyperbolic–parabolic system arising from a chemotaxis model in tumor angiogenesis, which is described by a Keller–Segel equation with singular sensitivity. It is known to allow viscous shocks (so-called traveling waves). We introduce a relative entropy of the system, which can capture how close a solution at a given time is to a given shock wave in almost [Formula: see text]-sense. When the shock strength is small enough, we show the functional is non-increasing in time for any large initial perturbation. The contraction property holds independently of the strength of the diffusion.
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- Award ID(s):
- 1614918
- PAR ID:
- 10209739
- Date Published:
- Journal Name:
- Mathematical Models and Methods in Applied Sciences
- Volume:
- 30
- Issue:
- 02
- ISSN:
- 0218-2025
- Page Range / eLocation ID:
- 387 to 437
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0218202520500104
