An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

Effects of PEG-Induced Water Deficit in Solanum nigrum on Zn and Ni Uptake and Translocation in Split Root Systems

Drought strongly influences root activities in crop plants and weeds. This paper is focused on the performance of the heavy metal accumulator Solanum nigrum, a plant which might be helpful for phytoremediation. The water potential in a split root system was decreased by the addition of polyethylene glycol (PEG 6000). Rubidium, strontium and radionuclides of heavy metals were used as markers to investigate the uptake into roots, the release to the shoot via the xylem, and finally the basipetal transport via the phloem to unlabeled roots. The uptake into the roots (total contents in the plant) was for most makers more severely decreased than the transport to the shoot or the export from the shoot to the unlabeled roots via the phloem. Regardless of the water potential in the labeling solution, 63Ni and 65Zn were selectively redistributed within the plant. From autoradiographs, it became evident that 65Zn accumulated in root tips, in the apical shoot meristem and in axillary buds, while 63Ni accumulated in young expanded leaves and roots but not in the meristems. Since both radionuclides are mobile in the phloem and are, therefore, well redistributed within the plant, the unequal transfer to shoot and root apical meristems is most likely caused by differences in the cell-to-cell transport in differentiation zones without functional phloem (immature sieve tubes).

Giant Electric Field Enhancement in Split Ring Resonators Featuring Nanometer-Sized Gaps

Today's pulsed THz sources enable us to excite, probe, and coherently control the vibrational or rotational dynamics of organic and inorganic materials on ultrafast time scales. Driven by standard laser sources THz electric field strengths of up to several MVm−1 have been reported and in order to reach even higher electric field strengths the use of dedicated electric field enhancement structures has been proposed. Here, we demonstrate resonant electric field enhancement structures, which concentrate the incident electric field in sub-diffraction size volumes and show an electric field enhancement as high as ~14,000 at 50 GHz. These values have been confirmed through a combination of near-field imaging experiments and electromagnetic simulations.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.