Normalizations with exponentially small remainders for nonautonomous analytic periodic vector fields

In this paper we deal with analytic nonautonomous vector fields with a periodic time-dependancy, that we study near an equilibrium point. In a first part, we assume that the linearized system is split in two invariant subspaces E0 and E1. Under light diophantine conditions on the eigenvalues of the linear part, we prove that there is a polynomial change of coordinates in E1 allowing to eliminate up to a finite polynomial order all terms depending only on the coordinate u0 of E0 in the E1 component of the vector field. We moreover show that, optimizing the choice of the degree of the polynomial change of coordinates, we get an exponentially small remainder. In the second part, we prove a normal form theorem with exponentially small remainder. Similar theorems have been proved before in the autonomous case : this paper generalizes those results to the nonautonomous periodic case

3-D HOS simulations of extreme waves in open seas

In the present paper we propose a method for studying extreme-wave appearance based on the Higher-Order Spectral (HOS) technique proposed by West et al. (1987) and Dommermuth and Yue (1987). The enhanced HOS model we use is presented and validated on test cases. Investigations of freak-wave events appearing within long-time evolutions of 2-D and 3-D wavefields in open seas are then realized, and the results are discussed. Such events are obtained in our periodic-domain HOS model by using different kinds of configurations: either i) we impose an initial 3-D directional spectrum with the phases adjusted so as to form a focused <i>forced</i> event after a while, or ii) we let 2-D and 3-D wavefields defined by a directional wave spectrum evolve up to the <i>natural</i> appearance of freak waves. Finally, we investigate the influence of directionality on extreme wave events with an original study of the 3-D shape of the detected freak waves

A Non-Algebraic Patchwork

Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle more flexible than Viro's original algebraic one. It was natural to wonder if the former method allows one to construct non-algebraic objects. In this paper we construct the first examples of patchworked real pseudoholomorphic curves in $\Sigma_n$ whose position with respect to the pencil of lines cannot be realised by any homologous real algebraic curve.Comment: 6 pages, 1 figur

RESEAL II: a large-scale in situ demonstration for repository sealing in an argillaceous host rock: phase II

Final ReportPreprin

Mutations on the FG surface loop of human papillomavirus type 16 major capsid protein affect recognition by both type-specific neutralizing antibodies and cross-reactive antibodies.

The aim of this study was to further characterize the conformational neutralizing epitopes present on the surface-exposed FG loop of human papillomavirus (HPV) type 16 L1 major capsid protein. We have generated previously two chimeric L1 proteins by insertion of a foreign peptide encoding an epitope of the hepatitis B core (HBc) antigen within the FG loop. In addition, three other chimeric L1 proteins were obtained by replacing three different FG loop sequences by the HBc motif and three others by point mutations. All these chimeric L1 proteins retained the ability to self-assemble into virus-like particles (VLPs), with the exception of the mutant with substitution of the L1 sequence 274-279 by the HBc motif. The eight chimeric VLPs were then analyzed for differential reactivity with a set of six HPV-16 and HPV-31 monoclonal antibodies that bound to conformational and linear epitopes. The binding patterns of these monoclonal antibodies confirmed that the FG loop contained or contributed to neutralizing conformational epitopes. The results obtained suggested that the H31.F7 antibody, an anti-HPV-31 cross-reacting and neutralizing antibody, recognized a conformational epitope situated before the 266-271 sequence. In addition, H16.E70 neutralizing antibody reactivity was reduced with L1 VLPs with an Asn to Ala point mutation at position 270, suggesting that Asn is a part of the epitope recognized by this antibody. This study contributes to the understanding of the antigenic structure of HPV-16 and -31 L1 proteins by confirming that the FG loop contributes to neutralizing epitopes and suggesting the existence of both type-specific and cross-reactive conformational epitopes within the FG loop

Advancing Tests of Relativistic Gravity via Laser Ranging to Phobos

Phobos Laser Ranging (PLR) is a concept for a space mission designed to advance tests of relativistic gravity in the solar system. PLR's primary objective is to measure the curvature of space around the Sun, represented by the Eddington parameter $\gamma$, with an accuracy of two parts in $10^7$, thereby improving today's best result by two orders of magnitude. Other mission goals include measurements of the time-rate-of-change of the gravitational constant, $G$ and of the gravitational inverse square law at 1.5 AU distances--with up to two orders-of-magnitude improvement for each. The science parameters will be estimated using laser ranging measurements of the distance between an Earth station and an active laser transponder on Phobos capable of reaching mm-level range resolution. A transponder on Phobos sending 0.25 mJ, 10 ps pulses at 1 kHz, and receiving asynchronous 1 kHz pulses from earth via a 12 cm aperture will permit links that even at maximum range will exceed a photon per second. A total measurement precision of 50 ps demands a few hundred photons to average to 1 mm (3.3 ps) range precision. Existing satellite laser ranging (SLR) facilities--with appropriate augmentation--may be able to participate in PLR. Since Phobos' orbital period is about 8 hours, each observatory is guaranteed visibility of the Phobos instrument every Earth day. Given the current technology readiness level, PLR could be started in 2011 for launch in 2016 for 3 years of science operations. We discuss the PLR's science objectives, instrument, and mission design. We also present the details of science simulations performed to support the mission's primary objectives.Comment: 25 pages, 10 figures, 9 table

N-1 modal interactions of a three-degree-of-freedom system with cubic elastic nonlinearities

In this paper the (Formula presented.) nonlinear modal interactions that occur in a nonlinear three-degree-of-freedom lumped mass system, where (Formula presented.), are considered. The nonlinearity comes from springs with weakly nonlinear cubic terms. Here, the case where all the natural frequencies of the underlying linear system are close (i.e. (Formula presented.)) is considered. However, due to the symmetries of the system under consideration, only (Formula presented.) modes interact. Depending on the sign and magnitude of the nonlinear stiffness parameters, the subsequent responses can be classified using backbone curves that represent the resonances of the underlying undamped, unforced system. These backbone curves, which we estimate analytically, are then related to the forced response of the system around resonance in the frequency domain. The forced responses are computed using the continuation software AUTO-07p. A comparison of the results gives insights into the multi-modal interactions and shows how the frequency response of the system is related to those branches of the backbone curves that represent such interactions