Research Paper#Thermal Physics, Inverse Problems, Nanoscale Heat Transfer🔬 ResearchAnalyzed: Jan 3, 2026 17:01
Stability of Heat Reflection Coefficient Reconstruction
Published:Dec 30, 2025 18:23
•1 min read
•ArXiv
Analysis
This paper investigates the stability of an inverse problem related to determining the heat reflection coefficient in the phonon transport equation. This is important because the reflection coefficient is a crucial thermal property, especially at the nanoscale. The study reveals that the problem becomes ill-posed as the system transitions from ballistic to diffusive regimes, providing insights into discrepancies observed in prior research. The paper quantifies the stability deterioration rate with respect to the Knudsen number and validates the theoretical findings with numerical results.
Key Takeaways
- •The paper focuses on the stability of reconstructing the heat reflection coefficient.
- •The inverse problem becomes ill-posed as the system transitions to the diffusive regime.
- •The study quantifies the rate of stability deterioration with respect to the Knudsen number.
- •Numerical evidence supports the theoretical findings.
Reference
“The problem becomes ill-posed as the system transitions from the ballistic to the diffusive regime, characterized by the Knudsen number converging to zero.”