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Presents several short stories excerpted from "L'Homme-soeur," by P. Lapeyre, translated from the French by Robert Bononno.

• Sensitivity transport models are presented in order to estimate the shape derivatives of objective functions in the context of radiative transfers. • Regarding the sensitivity transport, the sources of geometrical sensitivities emerge as boundary conditions. • Different types of sensitivity sources are identified and illustrated in four configurations involving semi-transparent medium, reflective surfaces and curved surfaces. • The Monte Carlo method is used to solve the sensitivity model and we use two configurations to illustrate how we extend it to complex geometries ; we also show that it does not present any convergence issue. We address the question of evaluating shape derivatives of objective functions for radiative-transfer engineering involving semi-transparent media. After recalling the standard Monte-Carlo approach to sensitivity estimation and its current limitations, a new method is presented for the specific case of geometrical sensitivities. This method is then tested on configurations with multiple-scattering and absorbing (non-emitting) semi-transparent medium. A new geometrical sensitivity algorithm is presented with full details in order to extend, on several examples, its implementation in complex geometries. [ABSTRACT FROM AUTHOR]

• Monte Carlo algorithm is used to evaluate simultaneously the observable and its Jacobian. • Null-collision algorithm (NCA) are very successful when dealing with linear-physics in heterogeneous media. • We showed that NCA are sources of convergence difficulties to sensitivity-evaluations of optical parameter. • We propose an alternative solution. When a Monte Carlo algorithm is used to evaluate a physical observable A , it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives ∂ ς A of A with respect to each problem-parameter ς. The principle is the following: Monte Carlo considers A as the expectation of a random variable, this expectation is an integral, this integral can be derivated as function of the problem-parameter to give a new integral, and this new integral can in turn be evaluated using Monte Carlo. The two Monte Carlo computations (of A and ∂ ς A) are simultaneous when they make use of the same random samples, i.e. when the two integrals have the exact same structure. It was proven theoretically that this was always possible, but nothing ensures that the two estimators have the same convergence properties: even when a large enough sample-size is used so that A is evaluated very accurately, the evaluation of ∂ ς A using the same sample can remain inaccurate. We discuss here such a pathological example: null-collision algorithms are very successful when dealing with radiative transfer in heterogeneous media, but they are sources of convergence difficulties as soon as sensitivity-evaluations are considered. We analyse theoretically these convergence difficulties and propose an alternative solution. [ABSTRACT FROM AUTHOR]