Neumann–Rosochatius system for (m,n) string in $$AdS_3 \times S^3$$ with mixed flux

Abstract$$SL(2,{\mathbb {Z}})$$ S L ( 2 , Z ) invariant action for probe (m, n) string in $$AdS_3\times S^3\times T^4$$ A d S 3 × S 3 × T 4 with mixed three-form fluxes can be described by an integrable deformation of an one-dimensional Neumann–Rosochatius (NR) system. We present the deformed features of the integrable model and study general class of rotating and pulsating solutions by solving the integrable equations of motion. For the rotating string, the explicit solutions can be expressed in terms of elliptic functions. We make use of the integrals of motion to find out the scaling relation among conserved charges for the particular case of constant radii solutions. Then we study the closed (m, n) string pulsating in $$R_t\times S^3$$ R t × S 3 . We find the string profile and calculate the total energy of such pulsating string in terms of oscillation number $$({\mathcal {N}})$$ ( N ) and angular momentum $$({\mathcal {J}})$$ ( J ) .

On the quantization of folded strings in non-critical dimensions

Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

Evaluation of the Risk of Spreading Fire Blight in Apple Orchards with a Mechanical String Blossom Thinner

The risk of spreading fire blight in apples after mechanical thinning with a rotating string blossom thinner was evaluated in field and potted-tree experiments. In the field experiment, using the mechanical thinner on noninoculated trees immediately after operating the equipment on inoculated trees significantly (P < 0.01) increased fire blight incidence resulting in 90 ± 20.01 (mean ± SE) infected shoots compared with 23.5 ± 8.97 diseased shoots in similar trees that were not thinned mechanically. A similar result was obtained in greenhouse experiments whereby healthy apple plants positioned adjacent to diseased plants before the group was subjected to the mechanical thinner developed more than twice the number of infected shoots as that on similar plants that were not thinned. These results indicate that under conditions conducive to infection, the mechanical blossom thinner significantly increases the risk of spreading Erwinia amylovora. The use of the thinner should therefore be limited to orchards with no history of disease in the last 3 years and on days when predicted weather is not suitable for tree infection by E. amylovora; otherwise, a severe fire blight epidemic could develop in the orchard.