arXiv subjects

Andreas Mandelis

Publications and source records attributed to Andreas Mandelis.

4 recordsLinked to original sources

arXiv2026

The Spectral Domain Snell Law in Diffusion-Wave Fields

Snell law is traditionally regarded as a hallmark of phase-propagating phenomena such as optical, acoustic, elastic, electromagnetic, and quantum waves. In contrast, purely diffusive processes, such as Fourier heat conduction and chemical diffusion, are generally considered incapable of exhibiting refractive/reflective behavior. In this letter, we demonstrate that although diffusion waves including thermal diffusion, mass diffusion, Lindblad quantum diffusion, and electromagnetic diffusion do not follow Snell law in either time or frequency-domain, nevertheless they obey a spectral form of Snell law which reveals a hidden analog of wave refraction/reflection within the mathematical structure of diffusion dynamics. Remarkably, the spectral refraction ratio is governed not by the diffusion coefficient itself but by the constitutive relations of the media across the interface, establishing a new physical paradigm for diffusion-wave fields. Importantly, while each spectral eigenmode satisfies a rigorous Snell-type refraction relation, the inverse Fourier-Laplace transformation mixes these modes and suppresses any persistent real-space refraction angle, thereby reconciling the modal-level directionality with the long-standing absence of geometric refraction in diffusive systems.

physics.optics↗

arXiv2025

Real-Time Super-Resolution Imaging System Based on Zero-Shot Learning for Infrared Non-Destructive Testing

Infrared thermography (IRT) and photothermal coherence tomography (PCT) exhibit potential in non-destructive testing and biomedical fields. However, the inevitable heat diffusion significantly affects the sensitivity and resolution of IRT and PCT. Conventional image processing techniques rely on capturing complete thermal sequences, which limits their ability to achieve real-time processes. Here, we construct a real-time super-resolution imaging system based on zero-shot learning strategy for the non-invasive infrared thermography and photothermal coherence tomography techniques. To validate the feasibility and accuracy of this super-resolution imaging system, IRT systems were employed to test several industrial samples and one biomedical sample. The results demonstrated high contrast in the region of interest (ROI) and uncovered valuable information otherwise obscured by thermal diffusion. Furthermore, three-dimensional photothermal coherence tomography was used to validate the excellent denoising and deconvolution capabilities of the proposed real-time super-resolution imaging system.

physics.app-ph↗

arXiv2025

Making neural networks understand internal heat transfer using Fourier-transformed thermal diffusion wave fields

Heat propagation is governed by phonon interactions and mathematically described by partial differential equations (PDEs), which link thermal transport to the intrinsic properties of materials. Conventional experimental techniques infer thermal responses based on surface emissions, limiting their ability to fully resolve subsurface structures and internal heat distribution. Additionally, existing thermal tomographic techniques can only shoot one frame from each layer. Physics-informed neural networks (PINNs) have recently emerged as powerful tools for solving inverse problems in heat transfer by integrating observational data with physical constraints. However, standard PINNs are primarily focused on fitting the given external temperature data, without explicit knowledge of the unknown internal temperature distribution. In this study, we introduce a Helmholtz-informed neural network (HINN) to predict internal temperature distributions without requiring internal measurements. The time-domain heat diffusion equation was converted to the frequency-domain and becomes the pseudo-Helmholtz equation. HINN embeds this pseudo-Helmholtz equation into the learning framework, leveraging both real and imaginary components of the thermal field. Finally, an inverse Fourier transform brings real-part and imagery-part back to the time-domain and can be used to map 3D thermal fields with interior defects. Furthermore, a truncated operation was conducted to improve computational efficiency, and the principle of conjugate symmetry was employed for repairing the discarded data. This approach significantly enhances predictive accuracy and computational efficiency. Our results demonstrate that HINN outperforms state-of-the-art PINNs and inverse heat solvers, offering a novel solution for non-invasive thermography in applications spanning materials science, biomedical diagnostics, and nondestructive evaluation.

physics.app-ph↗

arXiv2025

Thermal diffusivity measurement based on evaporative cryocooling excitation: Theory and experiments

Photo-thermal methods for measuring thermal diffusivity inherently pose an ill-posed inverse problem, affected by factors such as sample thickness, heating or cooling time, and excitation energy. Measurement accuracy becomes particularly challenging under non-impulsive pulsed excitation when the observation timescale is comparable to the pulse duration. This is often due to poorly defined pulse shapes, broadened thermal responses, and the absence of clear boundary conditions, especially under significant interfacial temperature gradients where natural convection dominates. The classic Parker solution, while widely used, is physically unrealistic as it assumes adiabatic heat flux and shallow-region heat absorption. In this study, we prove that Parker's assumption is equivalent to the Dirac pulse boundary condition in mathematics. Then, we present comprehensive analytical solutions for thermal/cooling responses under Dirac and rectangular pulse excitations. By comparing with eigenfunction-based solutions for well-posed boundary conditions, we show that Parker's solution is only valid before the thermal peak. Through dimensionless processing, we further demonstrate that Parker's solution can be regarded as a limiting case of the rectangular pulse solution as the heating duration approaches zero. Furthermore, we propose a novel excitation approach, evaporative cryocooling, for thermal diffusivity measurement. This method offers a compact, low-cost, and easy-to-implement alternative to conventional excitation schemes. The theoretical model was further validated through comparison with experimental results.

physics.app-ph↗