Grapevines were cane pruned with 12–14 nodes per cane. Vines were drip irrigated from May to September . A single irrigation pipeline was positioned on the soil with three drippers for each vine . Soil water potential was kept below −300 kPa, and leaf water potentials were maintained at values < −0.6 MPa. Fertilizer addition, pest control, and other vineyard operations were conducted according to local practices. A randomized block design was used with three blocks and three treatments, and each treatment in the block consisted of six grapevines selected with a uniform number of clusters. Each treatment consisted of: control, ethephon at 1445 mg/L, ethephon at 2890 mg/L. The concentrations used in this trial were established on results obtained in preliminary studies . Ethephon was dispersed in water with 0.1% of a surfactant and applied directly to the clusters of vines selected for abscission treatments. Clusters from control vines were treated with water containing the surfactant only. The ethephon or control solutions were applied with a handheld sprayer until run-off when the fruits reached sufficient soluble solids for harvest . After the berries dried, raspberry cultivation pot each cluster was enclosed in a mesh bag to collect any berries that may abscise.Berries were sampled before treatment, 2 h after treatment and in successive days, as reported in Table 1.
Measurements of FDF, berry skin color, and firmness were as described previously. In brief, FDF was determined as the force required to detach the berry from the rachis as measured with a mechanical gauge. A hand-held, temperature compensating digital refractometer and an automatic titrator were used for the following determinations: soluble solids content , pH, titratable acidity . For all these measurements, 10 clusters from each vine were selected and three berries from each cluster were sampled to measure the FDF and three berries for the other measurements. Pre-harvest abscission was determined by counting any abscised berries that had collected in the mesh bags on observation days . Abscised berries were placed in plastic bags and stored in a portable ice box for transport to the laboratory where the integrity of the berry, including the presence/absence of a pedicel, and a wet or dry stem scar was observed with the aid of a binocular microscope at 30× . Berries that abscised pre-harvest and those that fell during harvest, handling or after light shaking constituted the total percentage of dropped berries. The abscised berry percentage was calculated as [/ × 100].Ethephon residues were determined according to the method proposed by Takenaka . For each treatment 30 berries were randomly collected from 10 clusters, stored in a portable FIGURE 1 | Mesh bags to prevent pre-harvest berry loss of Thompson Seedless and Crimson Seedless table grapes. ice box, and carried to the laboratory for analysis. Cartridges SPE NH2 500 mg of Phenomenex activated as suggested by manufacturer were used in the purification step. The purified samples were evaporated to dryness with a rotavapor at 40◦C, taken up with 1 ml of methanol and subjected to derivatization.
One hundred microliters of reconstituted samples were transferred to 1.5 mL eppendorf, diluted with 500 µL of acetone and derivatized by adding 10 µL of trimethylsilyldiazomethane . The reaction vials were maintained at 50◦C for 30 min, then 10 µL of 1 M acetic acid in methanol were added in order to stop the reaction. After centrifugation, 2 µL of the clear upper phase were injected in the GC-MS system.Ethephon application did not affect berry color of Thompson Seedless until 14 days after treatment . At that time, ethephon-treated fruit was darker in color , and had lower C ∗ and a greater h◦ , indicating the fruit were somewhat more yellow colored than non-treated fruit and generally had a more mature appearance. These findings are consistent with other reports that ethephon affects berry skin color by stimulating the accumulation of phenolic compounds . Ethephon treatments clearly reduced FDF because most of the berries on treated clusters were so loosely attached that they abscised before harvest or during handling . However, the few remaining berries on treated clusters were just as tightly held as the berries on non-treated clusters, so no treatment effects on FDF could be measured . A similar result was reported for Thompson Seedless treated with methyl jasmonate, another abscission agent . FDF may decline within a few days of treatment with abscission agents , so timely harvest may be needed when reductions in FDF are large. Abscission agents did not reduce fruit firmness, but FDF and berry firmness decreased from the time of ethephon application whether the clusters were treated or not . As suggested earlier, ethephon at either concentration tested stimulated an almost complete berry abscission from the rachis .
The effects of the two concentrations were similar, with only a few berries still attached to the rachis by harvest time , and the abscised berries generally had dry stem scars . Dry stem scars could be desirable for fresh-cut fruit since the scars help prevent juice leakage and minimize the exposure of interior berry tissues to the atmosphere and to pathogens that might reduce shelf-life or berry quality. However, pre-harvest berry abscission could lead to significant yield losses , though yield loss might be minimized byearlier harvest or the use of catch systems, i.e., nets under the canopy. Ethephon did not affect SSC, pH, or TA . Few studies have examined the effect of abscission agents on grape berry composition, but our results generally agree with Uzquiza et al. who reported few and minor treatment effects on winegrapes. Even though a registered use of ethephon on grape is the promotion of fruit maturity, effects on grape composition are often variable, and ethephon applications to promote fruit maturity are made at veraison, a much earlier stage of fruit development . Abscission agents are applied to mature fruit, so there is less opportunity to affect fruit composition. Moreover, abscission agents quickly initiate the development of an abscission layer between the pedicel and berry . The rapid action of abscission agents necessitates a short time period between application and harvest, further limiting the potential for differences in composition to develop.Ethephon reduced the lightness and purity of the skin color as previously observed for Thompson Seedless, and similarly to that observed by others . The FDF was significantly reduced , whereas SSC and acidity were not affected as in a previous work . A short post-harvest interval limits the possible compositional effects , as discussed above. However, in a previous trial on Crimson Seedless, an increase of tartaric acid, procyanidin P2, terpenoid derivatives, and peonidin-3-glucoside as well as a decrease of catechin and epicatechin was observed after treatments with ethephon a few days before harvest .Treatment with either concentration of ethephon stimulated significant pre-harvest abscission , both >40% and almost 55% at the dose of 2890 mg/L . A similar effect on Crimson Seedless has been recently reported . The treatments tested were less effective at inducing abscission of Crimson Seedless than they were at inducing abscission of Thompson Seedless. Differences among varieties in responsiveness to abscission agents has been previously reported in grape , low round pots and it has also been observed that some table grape varieties are more susceptible than others to “shatter,” or “dry drop,” a post-harvest disorder characterized by the development of an abscission layer between the pedicel and berry . The physiological basis for varietal differences in responsiveness to abscission agents is uncertain, but the application of very high rates of ethephon can induce abscission in varieties that are otherwise non-responsive , suggesting that the less responsive varieties may be less sensitive to ethylene. As observed with Thompson Seedless, SSC, pH, and TA of Crimson Seedless were not affected by abscission agents .The lack of compositional effects are probably due to similar reasons identified and discussed earlier for Thompson Seedless.No present model of solids can predict all microscopic electrical properties of a solid. Two approaches are used in the quantum mechanical study of the electrical properties of solids: free electron models, and bound electron models. Models such as the nearly free electron model, suppose that electrons are free of atoms, and then impose restrictions on how electrons may move. Models such as the tight binding model suppose that electrons are bound to atoms, and then provide ways in which electrons may move.
Meanwhile, bound electron models are necessary for explaining the subtle microscopic properties of solids. A cornerstone the microscopic theory of solids is the Quantum Hall Effect. Within real solids, there is disorder: wave functions and crystal lattices are not uniform or periodic throughout space. With disorder, electrons tend to localize, and materials become insulators. However, within two dimensional materials such as graphene, for certain magnetic fields, even in the presence of disorder, a delocalization of electrons is observed. This conduction is the Quantum Hall Effect, which experimentally exhibits conduction values of exact integer numbers of electrons, or, surprisingly, fractional numbers of electrons known as quasiparticles. Each phase of conduction, or topological phase, is described by a quantum number called the Chern Number, which is an integer that uniquely specifies that topological phase. It is particularly interesting that the transitions between topological phases, known as Plateau Phase Transitions, may described using exactly the same model as for phase transitions between states of matter. This model is the Landau Theory of Phase Transitions, in which a phase transition is quantified through a set of numbers known as critical exponents. Within quantum mechanics, the two basic states of particles are standing waves and traveling waves. Particles in the absence of a global potential take the form of traveling waves and are delocalized. Particles in a global potential take the form of standing waves and are localized. In the global potential created by a magnetic field, electrons behave as standing waves that are circles perpendicular to the magnetic field, also known as cyclotron orbits. In the local, periodic potential created by uniformly spaced atoms, electrons behave as traveling waves of wavelengths such that they will miss the atoms. The Hofstadter Model combines a global magnetic field with a linear combination of atomic orbitals. It is a tight binding model that first assumes that electrons are bound to atoms, and then provides ways to conduct electrons to nearby atoms. Within the Hofstadter Model, the degree of locality is quantified by a distance known as the “localization length.” This length is strongly dependent on the magnetic field and electron concentration, and at Plateau Transitions, this length becomes infinite. In this paper, we proceed by way of an introduction with background given on the theories of electronic conduction, the Classical Hall Effect, Landau Levels, and the Quantum Hall Effect. These sections give a semi-classical and experimental motivation for the notions of localization and topological phase. Next, we introduce the tight-binding model for electronic motion in one dimension, solve it analytically and numerically using the modules, similar results are then obtained for the two-dimensional tight-binding model. The Hofstadter Model is covered, presented as a result of a sum over translation operators, and is then solved numerically using the modules at a variety of fluxes to find the Hofstadter Butterfly. Chern numbers are introduced with the experimental motivation of the Quantum Hall Effect. A method to calculate Chern numbers through the Berry Curvature is presented, as is an efficient algorithm by Fukui, Hatsugai, and Suzuki. This algorithm forms the basis of the Chern number module. This is then applied to a simple model of a Topological Insulator as well as the Hofstadter Model. After that, the concept of localization is introduced and presented in the form of the Anderson Model. This model is then numerically analyzed using modules for transfer matrices and results are described. Finally, the Chalker-Coddington Model is analyzed using the modules and the results are consistent with the literature.Free electron models are a class of models of electron conduction that work well on metals or near-metals. Free electron models assume that there is either no, or very little interaction between an electron and the lattice If there is no interaction with the lattice, then the electron behavior is that of a Fermi gas, where momentum is pF which is given by the Fermi energy _x000F_ F = p 2 F /2m. This is a smooth quadratic function in momentum, and it cannot explain the behavior of insulators which have discontinuities in their energy dispersion.