Long-wavelength limit of gyrokinetics in a turbulent tokamak and its intrinsic ambipolarity

Recently, the electrostatic gyrokinetic Hamiltonian and change of coordinates have been computed to order $\epsilon^2$ in general magnetic geometry. Here $\epsilon$ is the gyrokinetic expansion parameter, the gyroradius over the macroscopic scale length. Starting from these results, the long-wavelength limit of the gyrokinetic Fokker-Planck and quasineutrality equations is taken for tokamak geometry. Employing the set of equations derived in the present article, it is possible to calculate the long-wavelength components of the distribution functions and of the poloidal electric field to order $\epsilon^2$. These higher-order pieces contain both neoclassical and turbulent contributions, and constitute one of the necessary ingredients (the other is given by the short-wavelength components up to second order) that will eventually enter a complete model for the radial transport of toroidal angular momentum in a tokamak in the low flow ordering. Finally, we provide an explicit and detailed proof that the system consisting of second-order gyrokinetic Fokker-Planck and quasineutrality equations leaves the long-wavelength radial electric field undetermined; that is, the turbulent tokamak is intrinsically ambipolar.Comment: 70 pages. Typos in equations (63), (90), (91), (92) and (129) correcte

Lelong numbers on projective varieties

Given a positive closed (1,1)-current $T$ defined on the regular locus of a projective variety $X$ with bounded mass near the singular part of $X$ and $Y$ an irreducible algebraic subset of $X$, we present uniform estimates for the locus inside $Y$ where the Lelong numbers of $T$ are larger than the generic Lelong number of $T$ along $Y$

Angle detector

An angle detector for determining a transducer's angular disposition to a capacitive pickup element is described. The transducer comprises a pendulum mounted inductive element moving past the capacitive pickup element. The capacitive pickup element divides the inductive element into two parts L sub 1 and L sub 2 which form the arms of one side of an a-c bridge. Two networks R sub 1 and R sub 2 having a plurality of binary weighted resistors and an equal number of digitally controlled switches for removing resistors from the networks form the arms of the other side of the a-c bridge. A binary counter, controlled by a phase detector, balances the bridge by adjusting the resistance of R sub 1 and R sub 2. The binary output of the counter is representative of the angle

Sources of intrinsic rotation in the low flow ordering

A low flow, $\delta f$ gyrokinetic formulation to obtain the intrinsic rotation profiles is presented. The momentum conservation equation in the low flow ordering contains new terms, neglected in previous first principles formulations, that may explain the intrinsic rotation observed in tokamaks in the absence of external sources of momentum. The intrinsic rotation profile depends on the density and temperature profiles and on the up-down asymmetry.Comment: 20 page

Brassinosteroiders roll i stimulering av tillväxt och stress tolerans hos växter efter priming med nyttiga bakterier

Brassinosteroids (BR) are plant hormones widely distributed throughout the plant kingdom in low concentrations and with structural homology to animal and insect steroids. BR are involved in numerous physiological processes, and they also fulfill an antagonistic role in anti-herbivory structure formation in tomato (Campos et al., 2009). In order to characterize the role of BR upon priming with B. amyloliquefasciens 5113, gene expression analysis of BR genes was assessed in Arabidopsis thaliana. BAK1, BRI1 and DWF1 expression down-regulates, while DET2 upregulates upon bacterial priming. CPD gene expression was not affected by priming. qPCR analysis of VSP2 and PR1 were performed on BR mutants upon priming with B. amyloliquefasciens 5113. Basal levels of PR1 were higher in det2, bak1 and dwf1 compared to primed samples. Primed bri1 displayed two-fold higher expression of PR1 compared to untreated bri1. VSP2 level goes up on det2, bak1 and bri1 upon priming. No changes of VSP2 expression were observed in dwf1 upon priming. Methyl jasmonate treatment up-regulates VSP2 level twofold in det2 and nine-fold in bak1. The role of BR genes in response to insect attack was examined. BR genes appear not to be responsive to herbivory by S. littoralis. However, S. littoralis larvae fed more on BR mutants compared to those that fed on Col-0 WT. In order to understand the role of BR in JA signaling pTRV-JAR1 and pTRV-LOX2 constructs were developed and virus induced gene silencing were performed on Col-0 and BR mutants bak1 and det2. Gene silencing was confirmed by qPCR analysis of the target genes in Col-0 and det2, but not in bak1. Further insect feeding experiments are required to elucidate if BR play a role in defense responses to herbivory when JA signaling pathway is compromised

Continuity of the spectra for families of magnetic operators on Z^d

For families of magnetic self-adjoint operators on ${\mathbb Z}^d$ whose symbols and magnetic fields depend continuously on a parameter $\epsilon$, it is shown that the main spectral properties of these operators also vary continuously with respect to $\epsilon$. The proof is based on an algebraic setting involving twisted crossed product C*-algebras.Comment: 13 page