Textured surfaces nucleation morphology, geometry random fields integral geometry segmentation image processing video mist.Īpplicants should send a letter of application and CV preferentially by email to: A special care will be taken to the registration of the drops and surfaces observations. Geometrical models (including topological, morphological and stereological aspects) will be compared to experiments. Then, the temporal evolution will be taken into account (evolution, location, and coalescence).
Correlations between the nucleation sites (position, number, density…) and the topographical properties will be studied. First, important parameters (number of drops, density and size, spatial distribution) will be studied. The successful candidate will geometrically characterize and model the nucleation of drops on textured surfaces. The project intends to study the nucleation and the growth of such drops with regard to the topographical surface properties. Micro and nano water drops apparition highly depend on physical and chemical properties of the surfaces, like their topography. Mist on transparent surfaces (windshields, headlights, displays) is an important issue for manufacturers in the automotive, aerospace as well as for sports equipment. Researchers work in the fields of mathematical and computational image processing (mathematical morphology, segmentation), geometry (integral geometry, stochastic geometry, stereology) and probability theory (random fields), as well as in the fields of physics, mechanics and tribology. At last, the mathematical notion of granulometry (size distribution) is studied by using an axiomatic method.The applicants should have a strong interest to work in an interdisciplinary team from two CNRS labs (French national center for scientific research). Interesting classes of functionals T are obtained if A is indefinitely divisible or semi‐markovian. The functionals T defined by T(K) = P(A ∩ K ≠ Ø) for K compact are characterized as alternating capacities of infinite order. If A is considered as a closed set, we obtain a random closed‐sets theory, closely connected with integral geometry.
Thus, a probabilistic formalism is associated with this experimental technique and facilitates its interpretation. SUMMARY In order to study objects forming a sub‐set A of euclidean space, mathematical morphology uses structuring figures B and notes the frequency of events such as ‘B hits A’, ‘B is included into A’ etc. Random sets theory and its applications to stereology Random sets theory and its applications to stereology
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