Towards Grower-friendly Apple Crop Thinning by Tree Shading

Light management with shading nets, which reduce sunlight by 74%, might be an alternative to chemicals commonly used for thinning on apple trees. To study the effect of shading on crop load and fruit quality, trials were conducted in field experiments with the cultivars Golden Delicious and Elstar in 2006. Trees were either covered 25 days after full bloom (DAFB) with a net during three days, or until the peak of fruit fall, observed after seven days shading. Ideal time length for optimal crop yield was seven days shading for Elstar and three days shading for Golden Delicious. Alternate bearing could be decreased as flower initiation counts the following year showed. In both experiments, inner quality of fruit such as sugar and firmness showed good values at optimal shading duration compared with chemical + hand thinning. In 2007, a second field trial was conducted with cultivars Golden Delicious and Topaz to study the time period for shading in further detail. Shading was done for three days at 19, 26 and 33 DAFB using two net types (three- and two-meter-net width, covering the trees entirely or only down to 50 cm above ground). For Golden Delicious, shading after 19 and 26 days reduced fruits per 100 flower cluster to the same extent as with chemical + hand thinning. There was no difference between the two net types. For Topaz, shading after 19 days showed the best results. Regarding inner quality of both cultivars, only sugar content for Golden Delicious could be significantly improved after 19 and 26 days shading. Further analyses are still under way (e.g. for acidity). This study is part of an effort for increasing European consumption with fruit from sustainable production systems, the ISAFRUIT-EU-project

Faddeev equations with three-nucleon force in momentum space

Modified Faddeev equations that allow the inclusion of irreducible three-body forces in addition to two-body interactions are formulated and the technical apparatus for their solution in momentum space is described. Results for the triton binding energy are obtained with realistic two-nucleon interactions and the Tucson-Melbourne two-pion exchange three-nucleon force and compared with previous calculations. Excellent agreement with the results of other groups is found confirming that the accuracy of present-day techniques for handling three-nucleon forces is very high indeed

Relativistic calculation of the triton binding energy and its implications

First results for the triton binding energy obtained from the relativistic spectator or Gross equation are reported. The Dirac structure of the nucleons is taken into account. Numerical results are presented for a family of realistic OBE models with off-shell scalar couplings. It is shown that these off-shell couplings improve both the fits to the two-body data and the predictions for the binding energy.Comment: 5 pages, RevTeX 3.0, 1 figure (uses epsfig.sty

Triton calculations with π\pi and ρ\rho exchange three-nucleon forces

The Faddeev equations are solved in momentum space for the trinucleon bound state with the new Tucson-Melbourne $\pi$ and $\rho$ exchange three-nucleon potentials. The three-nucleon potentials are combined with a variety of realistic two-nucleon potentials. The dependence of the triton binding energy on the $\pi NN$ cut-off parameter in the three-nucleon potentials is studied and found to be reduced compared to the case with pure $\pi$ exchange. The $\rho$ exchange parts of the three-nucleon potential yield an overall repulsive effect. When the recommended parameters are employed, the calculated triton binding energy turns out to be very close to its experimental value. Expectation values of various components of the three-nucleon potential are given to illustrate their significance for binding.Comment: 17 pages Revtex 3.0, 4 figures. Accepted for publication in Phys. Rev.

Covariant equations for the three-body bound state

The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including the Wigner rotations and rho-spin decomposition of the off-shell particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative rho-spin states of the off-shell particle.Comment: 57 pages, RevTeX, 6 figures, uses epsf.st

The six-nucleon Yakubovsky equations for 6He

The six-nucleon problem for the bound state is formulated in the Yakubovsky scheme. Hints for a numerical implementation are provided.Comment: 25 pages, 0 figure

Gauging the three-nucleon spectator equation

We derive relativistic three-dimensional integral equations describing the interaction of the three-nucleon system with an external electromagnetic field. Our equations are unitary, gauge invariant, and they conserve charge. This has been achieved by applying the recently introduced gauging of equations method to the three-nucleon spectator equations where spectator nucleons are always on mass shell. As a result, the external photon is attached to all possible places in the strong interaction model, so that current and charge conservation are implemented in the theoretically correct fashion. Explicit expressions are given for the three-nucleon bound state electromagnetic current, as well as the transition currents for the scattering processes \gamma He3 -> NNN, Nd -> \gamma Nd, and \gamma He3 -> Nd. As a result, a unified covariant three-dimensional description of the NNN-\gamma NNN system is achieved.Comment: 23 pages, REVTeX, epsf, 4 Postscript figure

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

Three-Nucleon Force and the Δ\Delta-Mechanism for Pion Production and Pion Absorption

The description of the three-nucleon system in terms of nucleon and $\Delta$ degrees of freedom is extended to allow for explicit pion production (absorption) from single dynamic $\Delta$ de-excitation (excitation) processes. This mechanism yields an energy dependent effective three-body hamiltonean. The Faddeev equations for the trinucleon bound state are solved with a force model that has already been tested in the two-nucleon system above pion-production threshold. The binding energy and other bound state properties are calculated. The contribution to the effective three-nucleon force arising from the pionic degrees of freedom is evaluated. The validity of previous coupled-channel calculations with explicit but stable $\Delta$ isobar components in the wavefunction is studied.Comment: 23 pages in Revtex 3.0, 9 figures (not included, available as postscript files upon request), CEBAF-TH-93-0