Cyril Caliot

Monte Carlo methods are highly capable at solving complex radiative transfer and coupled-physics problems and are used as reference solutions in many fields (e.g. solar processes,astrophysics and climate research). However, computing sensitivities of observables to geometricparameters, or computing spatial and angular derivatives of the radiative intensity, are difficultwhen employing Monte Carlo methods. Starting from the radiative transfer equation and its usualboundary conditions, this work aims to derive two new Monte Carlo algorithms for estimatingarbitrary spatial and angular derivatives of the radiative intensity. We apply the new estimatorsfor the spatial and angular derivatives in several test configurations involving homogeneousand non-homogeneous scattering and absorbing media, as well as black, diffuse and specularboundaries. Our approach provides direct access to spatial and angular derivatives of radiativeintensity, which are critical for applications such as analyzing inhomogeneous solar radiancein photovoltaic systems or optimizing satellite camera angles. By enabling these derivativecalculations, our work expands the utility of Monte Carlo methods, paving the way for advancedoptimization and inversion techniques in radiative transfer applications.

Compact hybrid photovoltaic-concentrating solar thermal (PV-CST) systems have emerged as a promising strategy to enhance solar energy utilization by simultaneously delivering electricity and heat. Despite their potential, their assessment remains challenging due to the lack of consistent metrics capable of capturing the relative value of these distinct energy outputs. To address this gap, we introduce a unified benchmarking framework for hybrid PV-CST systems that explicitly accounts for the relative value of heat to electricity. Within this framework, we introduce the Effective Improvement Range (EIR), a novel metric that quantifies the resilience and competitiveness of hybrid configurations under varying heat-to-electricity value ratios. We apply this framework to three spectral-splitting hybrid architectures, named semitransparent-thermal, semitransparent-photovoltaic, and PV-mirror, each evaluated considering four photovoltaic materials (Ge, Si, GaAs, and GaP). The benefit of hybridization is assessed by benchmarking each configuration against its standalone photovoltaic and thermal counterparts, as well as against state-of-the-art reference technologies. Our analysis reveals that each hybrid architecture exhibits a well-defined optimal heat-to-electricity value ratio. Among the designs considered, GaAs-based PV-mirror systems emerge as the most robust and competitive across a broad range of conditions, offering up to a 43% performance improvement over market standards. In contrast, semitransparent thermal and photovoltaic architectures yield only marginal benefits, limited to specific operating regimes and locations. These findings highlight that hybrid PV–CST systems evaluated offer modest gains over established technologies, emphasizing the need for rigorous and unified benchmarking frameworks to accurately identify and guide the development of truly competitive hybrid solar systems.

We address the question of numerically simulating the coupling of diffusion, advection and one-speed linear transport, with a specific focus on managing geometrical complexity. We base our work on recent advances from the computer graphics community, which has developed Monte Carlo algorithms simulating linear radiation transport in physically realistic scenes, with numerical costs that remain unaffected by geometrical refinement: adding more details to the scene description does not impact the computation time. The resulting benefits in terms of engineering flexibility are already fully integrated into the cinema industry and are gradually being adopted by the video game industry. Here we demonstrate that the same insensitivity to the geometric complexity can be achieved when considering not only one-speed linear transport, but also its coupling with diffusion and advection. In this case, pure linear-transport paths are replaced with advection-diffusion/linear-transport paths, which are composed of subpaths. Each subpath represents one of the three physical phenomena, and coupling is handled by switching from one subpath (i.e. phenomenon) to another. This approach is illustrated using a porous medium involving up to 10,000 pores, with the computation time being strictly independent of the number of pores, showing its ability to facilitate engineering calculations in complex geometries.

Computing the flux densities provided by solar concentrators or focusing heliostats can be done in two different ways: A grid ray-tracing (GRT) procedure that makes use of a large number of ray bundles, starting from the solar disk and finally impinging the focal plane of the concentrator. The method is reliable and accurate, but requires extensive computing times. Alternatively, the flux densities can be estimated by using convolution algorithms. This latter method requires much less computing time, but is known to be less accurate when the incidence angle of the sunrays on the reflector increases. The objective of this contribution is to define an algorithm based on convolution products and fast Fourier transforms having high accuracy. The results show that RMS error differences between both models are typically lower then 1%.

Concentrated solar power is a promising technique enabling renewable energy production with large scale solar power plants in the near future. Estimating quantitatively the reflectivity of a solar concentrator is a major issue, since it has a significant impact on the flux distribution formed at the solar receiver. Moreover, it is desirable that the mirrors can be measured during operation in order to evaluate environmental factors such as day/night thermal cycles or soiling and ageing effects at the reflective surfaces. For that purpose, a backward gazing method that was originally developed to measure mirror shape and misalignment error was developed. The method operates in quasi real-time without disturbing the heat production process. It was successfully tested at the Themis solar tower power plant in Targasonne, France. Its basic principle consists in acquiring four simultaneous images of a Sun-tracking heliostat, captured from different observation points located near the thermal receiver. The images are then processed with a minimization algorithm allowing the determination of the reflectance and slopes errors of the mirrors. In this communication, it is shown that the algorithm allows one to get quantitative reflectivity maps at the surface of the heliostat. The measurement is fully remote and is used to evaluate surface reflectivity that depends on optical coatings quality and soiling effects. Preliminary results obtained with a Themis heliostat are presented. They show that reflectivity measurements can be carried out within repeatability about ± 5% Peak-to-Valley (PTV) and 1% RMS. Ways to improving these numbers are discussed in the paper.