Asymptotic behaviour for interacting diffusion processes with space-time random birth

We study the asymptotic behaviour of a system of interacting particles with space-time random birth. We have propagation of chaos and obtain the convergence of the empirical measures, when the size of the system tends to infinity. Then we show the convergence of the fluctuations, considered as cadlag processes with values in a weighted Sobolev space, to an Ornstein-Uhlenbeck process, the solution of a generalized Langevin equation. The tightness is proved by using a Hilbertian approach. The uniqueness of the limit is obtained by considering it as the solution of an evolution equation in a greater Banach space. The main difficulties are due to the unboundedness of the operators appearing in the semimartingale decomposition

Effects of HMW-& LMW-glutenins and grain hardness on size of gluten polymers

International audiencePrevious studies on wheat near-isogenic lines have shown that kernel hardness affects molecular mass of storage protein polymers (Lesage et al. 2011). Size of glutenins‘ polymers is known to be involved in rheological properties of dough (strength, elasticity and extensibility). In order to assess effects of both grain hardness and glutenin alleles on storage proteins polymers, genetic diversity of various traits including grain hardness (GH), protein content (PC), glutenin alleles, polymer characteristics: mass (Mw), polydispersity index (Mw/Mn), polymer radius (Rw), and percentages of five protein fractions was investigated in a set of French cultivars grown in six locations in France and two successive years. Polymer characteristics were evaluated by Asymmetrical Flow Field-Flow Fractionation (AFFFF) and percentage of five protein fractions (F1 to F5) was obtained by Size Exclusion-HPLC (SE-HPLC). Growing locations significantly influenced both PC and Mw, and these two traits were never correlated in each location. Grain hardness had a strong influence on Mw, Mw/Mn and Rw. Variation in GH resulted in an average increase of polymer masses of 21.4% in Soft varieties compared to Hard ones for the two years. Conversely, grain hardness did not influence PC and SE-HPLC fractions. LMW-glutenins were shown to have a major effect on percentage of protein fractions. Glu-B3 was highly influent on percentages of all protein fractions. Surprinsingly, in addition to grain hardness effects, significant interactions were revealed between GH and glutenin alleles encoded at Glu-A1, -B1, -D1, -A3, -B3, -D3 loci. Indeed, glutenin alleles had contrasted effects on polymer characteristics (Mw, Mw/Mn, Rw) according to grain hardness classes. For example, polymer masses were significantly higher in Soft varieties carrying Glu-A1-2* allele compared to hard ones. In the same way, GH and glutenin alleles interactions strongly influenced percentage of protein fractions. For instance, Glu-A1-1 subunit was favorable to % F2 fraction in Hard varieties and unfavorable in soft varieties.Allelic variations of puroindolines, genetic basis of softness, were also analyzed in the set of cultivars and their effects on polymers size were tested

Structure and fluctuations of a single floating lipid bilayer

A single lipid molecular bilayer of 17 or 18 carbon chain phosphocholines, floating in water near a flat wall, is prepared in the bilayer gel phase and then heated to the fluid phase. Its structure (electron density profile) and height fluctuations are determined by using x-ray reflectivity and nonspecular scattering. By fitting the off-specular signal to that calculated for a two-dimensional membrane using a Helfrich Hamiltonian, we determine the three main physical quantities that govern the bilayer height fluctuations: The wall attraction potential is unexpectedly low; the surface tension, roughly independent on chain length and temperature, is moderate (≈5 × 10(–4) J·m(–2)) but large enough to dominate the intermediate range of the fluctuation spectrum; and the bending modulus abruptly decreases by an order-of-magnitude from 10(–18) J to 10(–19) J at the bilayer gel-to-fluid transition