A theoretical analysis on crack formation and propagation was performed based on the coupling between the electrochemical process, classical elasticity, and fracture mechanics. The chemical potential of oxygen, thus oxygen partial pressure, at the oxygen electrode-electrolyte interface ( ) was investigated as a function of transport properties, electrolyte thickness and operating conditions (e.g., steam concentration, constant current, and constant voltage). Our analysis shows that: a lower ionic area specific resistance (ASR), and a higher electronic ASR ( ) of the oxygen electrode/electrolyte interface are in favor of suppressing crack formation. The thus local pO2, are sensitive towards the operating parameters under galvanostatic or potentiostatic electrolysis. Constant current density electrolysis provides better robustness, especially at a high current density with a high steam content. While constant voltage electrolysis leads to greater variations of Constant current electrolysis, however, is not suitable for an unstable oxygen electrode because can reach a very high value with a gradually increased A crack may only occur under certain conditions when
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On the simultaneous reconstruction of the nonlinearity coefficient and the sound speed in the Westervelt equation
Abstract This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importance from time-trace boundary measurements. Specifically, these are the nonlinearity parameter often referred to as in the acoustics literature and the wave speed . The determination of the spatial change in these quantities can be used as a means of imaging. We consider identifiability from one or two boundary measurements as relevant in these applications. For a reformulation of the problem in terms of the squared slowness and the combined coefficient we devise a frozen Newton method and prove its convergence. The effectiveness (and limitations) of this iterative scheme are demonstrated by numerical examples.
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- Award ID(s):
- 2111020
- PAR ID:
- 10504167
- Publisher / Repository:
- IOP
- Date Published:
- Journal Name:
- Inverse Problems
- Edition / Version:
- 1.0
- Volume:
- 39
- Issue:
- 10
- ISSN:
- 0266-5611
- Page Range / eLocation ID:
- 105001
- Subject(s) / Keyword(s):
- nonlinearity parameter tomography, damped nonlinear wave equation, ultrasound
- Format(s):
- Medium: X Size: 256Kb Other: .pdf
- Size(s):
- 256Kb
- Sponsoring Org:
- National Science Foundation
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