Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature

We present some new results for the asymptotic behavior of the complex parabolic Ginzburg–Landau equation. In particular, we establish that, as the parameter ε tends to 0, vorticity evolves according to motion by mean curvature in Brakke's weak formulation. The only assumption we make is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Dynamics of multiple degree Ginzburg–Landau vortices

For the two-dimensional complex parabolic Ginzburg–Landau equation we prove that, asymptotically, vortices evolve according to a simple ordinary differential equation, which is a gradient flow of the Kirchhoff–Onsager functional. This convergence holds except for a finite number of times, corresponding to vortex collisions and splittings, which we describe carefully. The only assumption is a natural energy bound on the initial data. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Homotopy types for tamely approximable Sobolev maps between manifolds

We define a class ^p (M,N) of Sobolev maps from a manifoldM into a manifoldN, in such a way that each mapu ^p (M, N) has a well defined [p]-homotopy type, providedN satisfies a topological hypothesis. Using this, we prove the existence of minimizers in [p]-homotopy classes for some polyconvex variational problems.     

Exciplex Formation in Lipid-bound Escherichia coli Flavohemoglobin

Flavohemoglobins have the particular capability of binding unsaturated and cyclopropanated fatty acids as free acids or phospholipids. Fatty acid binding to the ferric heme results in a weak but direct bonding interaction. Ferrous and ferric protein, in presence or absence of a bound lipid molecule, have been characterized by transient absorption spectroscopy. Measurements have been also carried out both on the ferrous deoxygenated and on the CO bound protein to investigate possible long-range interaction between the lipid acyl chain moiety and the ferrous heme. After excitation of the deoxygenated derivatives the relaxation process reveals a slow dynamics (350 ps) in lipid-bound protein but is not observed in the lipid-free protein. The latter feature and the presence of an extra contribution in the absorption spectrum, indicates that the interaction of iron heme with the acyl chain moiety occurs only in the excited electronic state and not in the ground electronic state. Data analysis highlights the formation of a charge-transfer complex in which the iron ion of the lipid-bound protein in the expanded electronic excited state, possibly represented by a high spin Fe III intermediate, is able to bind to the sixth coordination ligand placed at a distance of at 3.5 Å from the iron. A very small nanosecond geminate rebinding is observed for CO adduct in lipid-free but not in the lipid-bound protein. The presence of the lipid thus appears to inhibit the mobility of CO in the heme pocket.     

Codimension one minimal cycles with coefficients inZ orZ p , and variational functionals on fibered spaces

Given a compact, oriented Riemannian manifold M, without boundary, and a codimension-one homology class in H_* (M, Z) (or, respectively, in H_* (M, Z_p) with p an odd prime), we consider the problem of finding a cycle of least area in the given class: this is known as the homological Plateau’s problem. We propose an elliptic regularization of this problem, by constructing suitable fiber bundles ξ (resp. ζ) on M, and one-parameter families of functionals defined on the regular sections of ξ, (resp. ζ), depending on a small parameter ε. As ε → 0, the minimizers of these functionals are shown to converge to some limiting section, whose discontinuity set is exactly the minimal cycle desired.     

NN final-state interaction in two-nucleon knockout from <Superscript>16</Superscript><Emphasis Type="Italic">O</Emphasis>

The influence of the mutual interaction between the two outgoing nucleons (NN-FSI) in electro- and photoinduced two-nucleon knockout from ¹⁶O has been investigated perturbatively. It turns out that the effect of NN-FSI depends on the kinematics and on the type of reaction considered. The effect is generally larger in pp- than in pn-knockout and in electroinduced than in photoinduced reactions. In superparallel kinematics NN-FSI leads in the (e,epp) channel to a strong increase of the cross-section, that is mainly due to a strong enhancement of the -current contribution. In pn-emission, however, this effect is partially cancelled by a destructive interference with the seagull current. For photoreactions NN-FSI is considerably reduced in superparallel kinematics and can be practically negligible in specific kinematics.Received: 1 July 2003, Published online: 10 February 2004PACS: 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) - 21.60.-n Nuclear structure models and methods - 25.30.Fj Inelastic electron scattering to continuum     

Electromagnetic proton-neutron knockout off <Superscript>16</Superscript>O : New achievements in theory

Results for the cross-sections of the exclusive ¹⁶O(e, e'pn)¹⁴N and ¹⁶O(γ, pn)¹⁴N knockout reactions are presented and discussed in different kinematics. In comparison with earlier work, a complete treatment of the center-of-mass (CM) effects in the nuclear one-body current is considered in connection with the problem of the lack of orthogonality between initial bound and final scattering states. The effects due to CM and orthogonalization are investigated in combination with different treatments of correlations in the two-nucleon overlap function and for different parametrizations of the two-body currents. The CM effects lead in super-parallel kinematics to a dramatic increase of the ¹⁶O(e, e'pn) cross-section to the 1₂ ⁺ excited state (3.95MeV) of ¹⁴N . In all the situations considered the results are very sensitive to the treatment of correlations. A crucial role is played by tensor correlations, but also the contribution of long-range correlations is important.     

Analysis of new augmented Lagrangian formulations for mixed finite element schemes

Summary. Two new augmented Lagrangian formulations for mixed finite element schemes are presented. The methods lead, in some cases, to an improvement in the order of the approximation. An error analysis is provided, together with some interesting examples of applications. Received July 27, 1994 / Revised version received November 17, 1995