Daniel Petit

Zinc tolerance and hyperaccumulation are genetically independent characters.

The hyperaccumulation of metals by a rare class of plants is a fascinating and little understood phenomenon. No genetic analysis has been possible since no intraspecific variation is known for this character. Here, we report on crosses between the zinc–hyperaccumulating and –tolerant species Arabidopsis halleri and the non–hyperaccumulating, non–tolerant species Arabidopsis petraea. The F2 segregates for both characters and it appears that the two characters are genetically independent. The data for tolerance are consistent with a single major gene for this character (although the number of genes for hyperaccumulation cannot be determined) but is probably not very large.

Multiple origin of metallicolous populations of the pseudometallophyte Arabidopsis halleri (Brassicaceae) in central Europe: the cpDNA testimony

The population structure of the pseudo‐metallophyte herb, Arabidopsis halleri, was studied using Polymerase Chain Reaction‐Restriction Fragment Length Polymorphism (PCR–RFLP) on chloroplast DNA (cpDNA). The history of metallicolous (M) populations showing increased zinc tolerance was investigated. Eight primer‐enzyme combinations out of 72 tested were applied to a total of 625 individuals from 28 widespread populations, 14 of them being M. Eleven distinct chlorotypes were found: five were common to nonmetallicolous (NM) and M populations, whereas six were only observed in one edaphic type (five in NM and one in M). No difference in chlorotype diversity between edaphic types was detected. Computed on the basis of chlorotype frequencies, the level of population differentiation was high but remained the same when taking into account levels of molecular divergence between chlorotypes. Isolation by distance was largely responsible for population differentiation. Geographically isolated groups of M populations were more genetically related to their closest NM populations than to each other. Our results suggest that M populations have been founded separately from distinct NM populations without suffering founding events and that the evolution towards increased tolerance observed in the distinct M population groups occurred independently.

Model reduction for the resolution of multidimensional inverse heat conduction problems

Abstract For large linear heat conduction systems, it is proposed here to solve an inverse heat conduction problem (IHCP) that consists in the identification of several time-varying thermal solicitations from simulations of measured temperatures. For this inversion, instead of using a detailed model of large size, this one is first transformed into a reduced model. The latter is built with identified dominant eigenmodes of the system leading to a reduced state representation that links the inputs (unknown solicitations) to the outputs (simulated temperatures). The procedure is sequential and uses future time steps. At first, a numerical 2D IHCP is provided: two time-varying heat flux densities are estimated from various positions of two sensors. A specific study on static and dynamic sensitivities is made. An example of a 3D IHCP is also given. The method is particularly interesting in this last case where, at each time step, the resolution of a system of order 9 (the reduced model) takes the place of a system of order 1331 (the detailed model).

Model reduction in linear heat conduction: use of interface fluxes for the numerical coupling

Abstract In the framework of numerical modelling in transient heat conduction, it is shown in this paper, how to introduce different kinds of coupling on a part of the domain boundary without changing the original matrices of the model. The technique uses specific fluxes applied to the boundary which is treated: at each time step the coupling variables—temperatures and fluxes—are computed at first, and then, the influence of the fluxes are distributed on the rest of the domain and no iteration procedure is used. This permits the treatment of unexpected problems such as: variations of heat transfer coefficients, model connection and radiative boundary conditions. The method is particularly well adapted to a reduced model which acts as a substitute for a detailed model with diminution of computation time. Although the reduced model is obtained with some kind of boundary conditions and usually functions within the latter, with these coupling fluxes, the reduced model can also be used in other conditions.

An experimental identification of line heat sources in a diffusive system using the boundary element method

Abstract This paper deals with an inverse problem which consists of the experimental identification of line heat source strength in an homogeneous solid using temperature measurements. An inverse formulation using the boundary element method, is used to identify the strength of line heat sources. In the case of multiple sources identification the location is assumed to be known but, in the case of a single source, an iterative algorithm for the location identification is proposed. The experiment consists of the identification of the power dissipated by Joule effect in one or two thin wires placed in a long square section cement bar. The measurements necessary to solve the inverse problem are provided by thermocouples for the internal temperatures and by infrared thermography for the superficial temperatures. A time regularization procedure associated to future time steps is used to correctly solve the ill-posed problem.