Identification of the trans isomers of abscisic acid and of abscisyl-β-D-glucopyranoside in latent buds of the grapevine and their evolution during the post-dormancy phase

The trans isomers(t-ABA and t-ABA-GE) of abscisic acid (ABA) and of abscisyl-β-D-glucopyranoside (ABA-GE) have been identified in the latent buds of Vitis vinifera L.. cv. Merlot, during the post-dormancy phase. During this phase, the amounts of the four forms of ABA in the buds became minimal. The quantities of ABA-GE and of t-ABA-GE, normally present in much greater quantities than free ABA, decreased strongly. This diminution appeared to be directly linked to the increase of water content of the buds. Although potential bud burst can be related to these phenomena, the role of the trans isomers remains obscure

Relations entre l'ultrastructure des plastes et les phases du cycle végétatif des bourgeons latents de la vigne (Vitis vinifera L. var. Ugni blanc)

Relationships between the ultrastructure of plastids and the phases of the vegetative cycle of latent buds of the vine (Vitis vinifera L. var. Ugni blanc)Salient features in the development of plastids and starch of the central bud into dormant buds of the vine occur during the stages of dormancy called ,,entrée en dormance" and ,,levée de dormance". Prolamellar bodies differentiate into plastids during the first stage and starch is hydrolysed during the later one. Starch changes in the plastids of central buds occur in agreement with the changes of glucid amounts in shoots

Global well-posedness of the KP-I initial-value problem in the energy space

We prove that the KP-I initial value problem is globally well-posed in the natural energy space of the equation

Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity, II

We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in space dimension $N \geq 2$. We show that minimization of the energy at fixed momentum can be used whenever the associated nonlinear potential is nonnegative and it gives a set of orbitally stable traveling waves, while minimization of the action at constant kinetic energy can be used in all cases. We also explore the relationship between the families of traveling waves obtained by different methods and we prove a sharp nonexistence result for traveling waves with small energy.Comment: Final version, accepted for publication in the {\it Archive for Rational Mechanics and Analysis.} The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-017-1131-

Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation

The phase shift of line solitons for the KP-II equation

The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi, Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the $L^\infty$-bound for the local phase shift of modulating line solitons for polynomially localized perturbations

An effective mass theorem for the bidimensional electron gas in a strong magnetic field

We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr\"odinger equations in the plane $(x,y)$, coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator

Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at http://www.mis.mpg.de/preprints/index.html