Orbital stability of periodic waves for the nonlinear Schroedinger equation

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.Comment: 34 pages, 7 figure

On the density-potential mapping in time-dependent density functional theory

The key questions of uniqueness and existence in time-dependent density functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead however to non-analyticities. We reformulate these questions in terms of a non-linear Schr\"odinger equation with a potential that depends non-locally on the wavefunction.Comment: 8 pages, 2 figure

Gene induction during differentiation of human monocytes into dendritic cells: an integrated study at the RNA and protein levels

Changes in gene expression occurring during differentiation of human monocytes into dendritic cells were studied at the RNA and protein levels. These studies showed the induction of several gene classes corresponding to various biological functions. These functions encompass antigen processing and presentation, cytoskeleton, cell signalling and signal transduction, but also an increase in mitochondrial function and in the protein synthesis machinery, including some, but not all, chaperones. These changes put in perspective the events occurring during this differentiation process. On a more technical point, it appears that the studies carried out at the RNA and protein levels are highly complementary.Comment: website publisher: http://www.springerlink.com/content/ha0d2c351qhjhjdm

Two-dimensional individual clustering model

10 pagesInternational audienceThis paper is devoted to study a model of individual clustering with two specific reproduction rates in two space dimensions. Given q > 2 and an initial condition in W 1,q (Ω), the local existence and uniqueness of solution have been shown in [6]. In this paper we give a detailed proof of existence of global solution

Higher order Schrodinger and Hartree-Fock equations

The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.Comment: 19 pages, to appear in J. Math. Phy

Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system

We describe the asymptotic behavior as time goes to infinity of solutions of the 2 dimensional corotational wave map system and of solutions to the 4 dimensional, radially symmetric Yang-Mills equation, in the critical energy space, with data of energy smaller than or equal to a harmonic map of minimal energy. An alternative holds: either the data is the harmonic map and the soltuion is constant in time, or the solution scatters in infinite time

Well-posedness for a model of individual clustering

25 pagesInternational audienceWe study the well-posedness of a model of individual clustering. Given p > N ≥ 1 and an initial condition in W 1,p (Ω), the local existence and uniqueness of a strong solution is proved. We next consider two specific reproduction rates and show global existence if N = 1, as well as, the convergence to steady states for one of these rates

Interannual variations in degree-2 Earth's gravity coefficients C-2,C-0, C-2,C-2, and S-2,S-2 reveal large-scale mass transfers of climatic origin

ISI Document Delivery No.: 208EO Times Cited: 0 Cited Reference Count: 24 Cited References: Boening C, 2012, GEOPHYS RES LETT, V39, DOI 10.1029/2012GL053055 CAZENAVE A, 2012, MAR GEOD S1, V35, P82 Chao BF, 2003, GEOCHEM GEOPHY GEOSY, V4, DOI 10.1029/2003GC000589 Chen JL, 2005, J GEODESY, V78, P535, DOI 10.1007/s00190-004-0417-y Cheng M., 2013, J GEOPHYS RES SOLID, V118, P1, DOI 10. 1002/jgrb. 50058 Cheng MK, 2004, J GEOPHYS RES-SOL EA, V109, DOI 10.1029/2004JB003028 Cox CM, 2002, SCIENCE, V297, P831, DOI 10.1126/science.1072188 Desai SD, 2002, J GEOPHYS RES-OCEANS, V107, DOI 10.1029/2001JC001224 Dickey JO, 2002, SCIENCE, V298, P1975, DOI 10.1126/science.1077777 Doll P, 2003, J HYDROL, V270, P105, DOI 10.1016/S0022-1694(02)00283-4 Forste C, 2008, J GEODESY, V82, P331, DOI 10.1007/s00190-007-0183-8 Gu GJ, 2011, J CLIMATE, V24, P2258, DOI 10.1175/2010JCLI3727.1 Ishii M, 2009, J OCEANOGR, V65, P287, DOI 10.1007/s10872-009-0027-7 Levitus S, 2012, GEOPHYS RES LETT, V39, DOI 10.1029/2012GL051106 Llovel W, 2011, GLOBAL PLANET CHANGE, V75, P76, DOI 10.1016/j.gloplacha.2010.10.008 Lyard F, 2006, OCEAN DYNAM, V56, P394, DOI 10.1007/s10236-006-0086-x Marcus SL, 2009, GEOPHYS RES LETT, V36, DOI 10.1029/2009GL041130 Milly PCD, 2002, J HYDROMETEOROL, V3, P283, DOI 10.1175/1525-7541(2002)0032.0.CO;2 Nerem RS, 2011, GEOPHYS RES LETT, V38, DOI 10.1029/2011GL047879 Pavlis NK, 2012, J GEOPHYS RES-SOL EA, V117, DOI 10.1029/2011JB008916 Pearlman MR, 2002, ADV SPACE RES, V30, P135, DOI 10.1016/S0273-1177(02)00277-6 Roy K, 2011, GEOPHYS RES LETT, V38, DOI 10.1029/2011GL047282 Syed TH, 2009, J HYDROMETEOROL, V10, P22, DOI 10.1175/2008JHM993.1 Zhang Y, 1997, J CLIMATE, V10, P1004, DOI 10.1175/1520-0442(1997)0102.0.CO;2 Meyssignac, B. Lemoine, J. M. Cheng, M. Cazenave, A. Gegout, P. Maisongrande, P. Centre National d'Etudes Spatiales (CNES); NASA [NNX12AK13G] This work was supported by the Centre National d'Etudes Spatiales (CNES). The CSR time series was produced by NASA's MEaSUREs program under JPL contract. M. K. Cheng is supported by NASA grant NNX12AK13G. The altimeter products used here were produced by Ssalto/Duacs and distributed by AVISO with support from CNES. 0 AMER GEOPHYSICAL UNION WASHINGTON GEOPHYS RES LETTSeveral recent studies have shown evidences for large water transfers in the climate system at interannual to decadal time scales, in particular during El Nino-Southern Oscillation events. In this study, we investigate further these water transfers and their signature in the gravity field. We analyze variations of the low-degree spherical harmonics C-2,C-0 (Earth's oblateness), C-2,C-2, and S-2,S-2 (eccentricity at the Earth's equator) from satellite laser ranging data during the 19 year period 1993-2012. We also estimate the water mass transfers in the climate system using satellite altimetry corrected for the steric effect, atmospheric reanalysis, and land hydrology models. We find a large signal in the water mass redistribution during the 1997/1998 El Nino which is consistent with an increase of the ocean mass in the tropical Pacific, a decrease of water storage in the Amazon Basin, and an increase of water storage in the Congo Basin