Homeopathic Preparations to Control the Rosy Apple Aphid (Dysaphis plantaginea Pass.)

A laboratory model system with the rosy apple aphid (Dysaphis plantaginea Pass.) on apple seedlings was developed to study the effects of homeopathic preparations on this apple pest. The assessment included the substance Lycopodium clavatum and a nosode of the rosy apple aphid. Each preparation was applied on the substrate surface as aqueous solution of granules (6c, 15c, or 30c). Controls were aqueous solutions of placebo granules or pure water. In eight independent, randomized, and blinded experiments under standardized conditions in growth chambers, the development of aphids on treated and untreated apple seedlings was observed over 17 days, each. Six experiments were determined to assess the effects of a strict therapeutic treatment; two experiments were designed to determine the effects of a combined preventative and therapeutic treatment. After application of the preparations, the number of juvenile offspring and the damage on apple seedlings were assessed after 7 and 17 days, respectively. In addition, after 17 days, the seedling weight was measured. In the final evaluation of the six strictly therapeutic trials after 17 days, the number of juvenile offspring was reduced after application of L. clavatum 15c (-17%, p = 0.002) and nosode 6c (-14%, p = 0.02) compared to the pure water control. No significant effects were observed for leaf damage or fresh weight for any application. In the two experiments with combined preventative and therapeutic treatment, no significant effects were observed in any measured parameter. Homeopathic remedies may be effective in plant-pest systems. The magnitude of observed effects seems to be larger than in models with healthy plants, which renders plant-pest systems promising candidates for homeopathic basic research. For successful application in agriculture, however, the effect is not yet sufficient. This calls for further optimization concerning homeopathic remedy selection, potency level, dosage, and application routes.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Optimization of Schwinger pair production in colliding laser pulses

Recent studies of Schwinger pair production have demonstrated that the asymptotic particle spectrum is extremely sensitive to the applied field profile. We extend the idea of the dynamically assisted Schwinger effect from single pulse profiles to more realistic field configurations to be generated in an all-optical experiment searching for pair creation. We use the quantum kinetic approach to study the particle production and employ a multi-start method, combined with optimal control theory, to determine a set of parameters for which the particle yield in the forward direction in momentum space is maximized. We argue that this strategy can be used to enhance the signal of pair production on a given detector in an experimental setup.