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Phaseless uniqueness for determining internal source in photo-thermal effect
Analysis of PDEs · Submitted 13 Sep 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Based on the potential theory and asymptotic analysis, we prove that the internal source can be uniquely determined up to sign by the external temperature field.
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The abstract, sentence by sentence
The paper investigates an inverse problem of recovering the internal source from external temperature measurements in photo-thermal effect. The photo-thermal effect actually involves two physical processes: electromagnetic scattering and heat transfer, described by a nonlinear coupled system of Maxwell's equation and the heat transfer equation. The nonlinear coupling term in the system is represented by the square of the modulus of the electromagnetic (missing the phase information of the electromagnetic field), and the absence of this phase information poses a significant challenge to the reconstruction of the internal source. In addition, the interaction and mutual influence of multiple physical fields, including electric field, magnetic field and temperature field, add to the complexity involved in the inversion of the internal source. Based on the potential theory and asymptotic analysis, we prove that the internal source can be uniquely determined up to sign by the external temperature field. This provides a solid theoretical basis for designing the internal source inversion algorithm and further exploring the theoretical aspects of photo-thermal effect.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The paper investigates an inverse problem of recovering the internal source from external temperature measurements in photo-thermal effect. | contribution 0.61 | 0.78 | 0.04 | asserted 0.96 |
| s1 | The photo-thermal effect actually involves two physical processes: electromagnetic scattering and heat transfer, described by a nonlinear coupled system of Maxwell's equation and the heat transfer equation. | background 1.00 | 0.10 | 0.02 | asserted 1.00 |
| s2 | The nonlinear coupling term in the system is represented by the square of the modulus of the electromagnetic (missing the phase information of the electromagnetic field), and the absence of this phase information poses a significant challenge to the reconstruction of the internal source. | background 0.48 | 0.20 | 0.03 | asserted 1.00 |
| s3 | In addition, the interaction and mutual influence of multiple physical fields, including electric field, magnetic field and temperature field, add to the complexity involved in the inversion of the internal source. | background 0.92 | 0.10 | 0.02 | asserted 0.99 |
| s4 | Based on the potential theory and asymptotic analysis, we prove that the internal source can be uniquely determined up to sign by the external temperature field. | result 0.96 | 0.95 | 0.95 | asserted 1.00 |
| s5 | This provides a solid theoretical basis for designing the internal source inversion algorithm and further exploring the theoretical aspects of photo-thermal effect. | interpretation 0.95 | 0.33 | 0.07 | asserted 0.98 |
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Original abstract
The paper investigates an inverse problem of recovering the internal source from external temperature measurements in photo-thermal effect. The photo-thermal effect actually involves two physical processes: electromagnetic scattering and heat transfer, described by a nonlinear coupled system of Maxwell's equation and the heat transfer equation. The nonlinear coupling term in the system is represented by the square of the modulus of the electromagnetic (missing the phase information of the electromagnetic field), and the absence of this phase information poses a significant challenge to the reconstruction of the internal source. In addition, the interaction and mutual influence of multiple physical fields, including electric field, magnetic field and temperature field, add to the complexity involved in the inversion of the internal source. Based on the potential theory and asymptotic analysis, we prove that the internal source can be uniquely determined up to sign by the external temperature field. This provides a solid theoretical basis for designing the internal source inversion algorithm and further exploring the theoretical aspects of photo-thermal effect.
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Cites as background 2 papers
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Moreover, there is a lot of literature available on relevant stability estimates and algorithmic research [ref] .
Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data · Related results and discussion · 1.00
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This remarkable phenomenon has diverse applications across various fields, such as photothermal energy conversion [ref] , photothermal therapy [ref] , medical imaging [ref] , thermoplasmonics [ref] and photothermal materials [ref] .
Heat Generation Using Lorentzian Nanoparticles. The Full Maxwell System · Mathematical setup and statement of main results · 0.97
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