Adaptive optics for airborne platforms—Part 1: modeling

Adaptive optics systems mitigate the atmospheric turbulence-induced distortion of a propagating light wavefront. The use of adaptive optics entails the design of a feedback controller, which requires the development of a model of the plant to be controlled. In adaptive optics, the plant consists of the atmosphere through which light is traveling. Moreover, a distinct feature of the adaptive optics control application is the presence of random signals in the plant. In optics, Zernike orthonormal polynomials are commonly used as a basis set for the expansion of wavefront phase distortions. Due to the atmospheric turbulence-induced random nature of the underlying physical process, the spatial-temporal correlation functions of the Zernike polynomial phase distortion expansion coefficients must be evaluated if a proper stochastic model of the plant is to be developed and adaptive optics is to be employed. In Part 1 of this paper, these correlation functions are developed using a layered atmospheric model and calculations for the first few low-order Zernike modes are performed. Using these correlation functions, an underlying stochastic linear dynamical system, which is adequate for control design, is synthesized. This system models the plant and, in turn, provides the basis for the employment of advanced model-based control and estimation concepts in an adaptive optics system for an airborne platform application.     

The outer-distance of nodes in random trees

The outer-distance of a nodeu in a rooted treeT _n is the height of the subtree determined byu and all nodesv such thatu is on the path joiningv and the root ofT. We show that the expected outer-distance of nodes of treesT _n in certain families is asymptotic toB logn where the constantB depends on .     

The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

Electromagnetic realization of orders-of-magnitude tunneling enhancement in a double well system

We report on tunneling enhancement in a periodically perturbed double well system. The double well system was realized by a structure of two optical waveguides. The transfer of light power from one waveguide to the another as induced by the periodic variations of the waveguide geometry was investigated. Our experimental measurements show that, in the presence of periodic perturbation, this transfer of light power can be enhanced by more than 500 times. We use an analogy between electromagnetic wave optics and the quantum wave phenomena to provide an experimental support to the theoretical model of tunneling enhancement of a quantum particle, facilitated by its interaction with auxiliary quantum states.     

Sortin1-hypersensitive mutants link vacuolar-trafficking defects and flavonoid metabolism in Arabidopsis vegetative tissues

Sortin1 is a chemical genetic-hit molecule that causes specific mislocalization of plant and yeast-soluble and membrane vacuolar markers. To better understand its mode of action, we designed a Sortin1-hypersensitive screen and identified several Sortin1-hypersensitive and flavonoid-defective mutants. Mechanistically, Sortin1 mimics the effect of the glutathione inhibitor buthionine sulfoximine and alters the vacuolar accumulation of flavonoids, likely blocking their transport through vacuole-localized ABC transporters. Structure-activity relationship studies conducted in Arabidopsis revealed the structural requirements for Sortin1 bioactivity and demonstrated that overlapping Sortin1 substructures can be used to discriminate between vacuolar-flavonoid accumulations and vacuolar-biogenesis defects. We conclude that Sortin1 is a valuable probe for dissecting novel links among flavonoid transport, vacuolar integrity, and the trafficking of vacuolar targeted cargoes in Arabidopsis.     

Gas chromatographic assay with pharmacokinetic applications for monitoring T-2 and HT-2 toxins in plasma

A gas-liquid chromatographic (GLC) method for monitoring T-2 and HT-2 toxins in plasma was developed. The procedure involved extraction of the toxins with ethyl acetate, chromatography on a C18 reversed-phase column and derivatization with heptafluorobutyric anhydride (HFBA). The T-2 and HT-2 HFBA derivatives were chromatographed on OV-17 at various temperatures and measured with an electron-capture detector. Iso-T-2 toxin and iso-HT-2 toxin were used as internal standards. Recoveries averaged 95.1 +/- 8.6% for T-2 toxin and 102.1 +/- 5.2% for HT-2 toxin at levels ranging from 40 to 120 ng/ml. The limits of detection were 30 and 5 ng/ml of T-2 and HT-2 toxin, respectively. The range of the assay covers plasma concentrations at which toxicity becomes manifest. The pharmacokinetic application of this GLC method is illustrated by simultaneous monitoring of T-2 and HT-2 toxins levels in plasma obtained after intravenous administration of T-2 toxin to a dog.     

Functionalization of polystyrene. III. Synthesis of polymeric thiol reagents

The synthesis of polymer-bound thiol reagents, supported on macroporous 4% divinylbenzene co-polymer (Amberlite XE-305), via three synthetic approaches is described: (i) Alkylation or acylation of XE-305 with 3-nitro-4-halogen-substituted benzyl chloride or benzoyl halide yielding 3-nitro-4-halobenzene-bound species, followed by substitution of the activated polymeric halogen atom with sulfur (see Scheme 1). (ii) Formation of a thiol ether by a direct substitution of an active polymeric halogen by reaction with benzylthiol, followed by chlorination, thiolation, and reduction (see Scheme 2). (iii) Attachment of a prepared tailor-made disulfide to aminomethyl function of a polymeric support, followed by reduction (see Scheme 3). The polymers were tested for their free-thiol content by 5, 5′-dithiobis(2-nitrobenzoic acid) (Ellman's reagent¹²) in DMF. Their thiolytic activity was investigated in the removal of 2-nitrophenylsulphenyl (Nps) group from Nps-protected amino acid (Scheme 4). Site-site interaction between the polymer-bound thiol with its activated halide precursor to yield polymeric sulfide during displacement reaction, and the interconversion of the polymeric thiols into polymeric disulfides at equilibrium or during reaction with Nps-amino acids, observed, and is attributed to the flexibility of the polymeric matrices.