Maximum coefficient of light extinction in a nonabsorbing dispersive medium

The maximum value of the light extinction coefficient μ, which can be observed in a dispersive medium with a relative refractive index n of the scattering particles, is studied within the framework of a quasi-crystalline approximation for nonabsorbing dispersive media consisting of monodisperse spherical scatterers. A change in the diffraction parameter x of the scattering particles and their volume concentration c _v is accompanied by nonmonotonic variations of the extinction coefficient, and the function μ(x, c _v ) exhibits several maxima. The dimensions and concentrations of particles are determined, for which the extinction coefficient reaches the absolute maximum μ^max. The μ^max value exhibits a monotonic growth with increasing relative refractive index n of the scattering particles. The conditions of validity of the Ioffe-Regel criterion of radiation localization have been studied. It is established that the localization in nonabsorbing dispersive media can be observed only for n ? 2.7. The intervals of x and c _v in which the criterion of radiation localization is satisfied in dispersive media consisting of particles with n = 3.0 and 3.5 are determined.     

Robust optimization of uncertain multistage inventory systems with inexact data in decision rules

In production-inventory problems customer demand is often subject to uncertainty. Therefore, it is challenging to design production plans that satisfy both demand and a set of constraints on e.g. production capacity and required inventory levels. Adjustable robust optimization (ARO) is a technique to solve these dynamic (multistage) production-inventory problems. In ARO, the decision in each stage is a function of the data on the realizations of the uncertain demand gathered from the previous periods. These data, however, are often inaccurate; there is much evidence in the information management literature that data quality in inventory systems is often poor. Reliance on data “as is” may then lead to poor performance of “data-driven” methods such as ARO. In this paper, we remedy this weakness of ARO by introducing a model that treats past data itself as an uncertain model parameter. We show that computational tractability of the robust counterparts associated with this extension of ARO is still maintained. The benefits of the new model are demonstrated by a numerical test case of a well-studied production-inventory problem. Our approach is also applicable to other ARO models outside the realm of production-inventory planning.     

Influence of surfactant structure on reverse micelle size and charge for nonpolar electrophoretic inks

Electrophoretic inks, which are suspensions of colorant particles that are controllably concentrated and dispersed by applied electric fields, are the leading commercial technology for high-quality reflective displays. Extending the state of the art for high-fidelity color in these displays requires improved understanding and control of the colloidal systems. In these inks, reverse micelles in nonpolar media play key roles in media and particle charging. Here we investigate the effect of surfactant structure on reverse micelle size and charging properties by synthesizing different surfactants with variations in polyamine polar head groups. Small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS) were used to determine the micelle core plus shell size and micelle hydrodynamic radius, respectively. The results from SAXS agreed with DLS and showed that increasing polyamines in the surfactant head increased the micelle size. The hydrodynamic radius was also calculated on the basis of transient current measurements and agreed well with the DLS results. The transient current technique further determined that increasing polyamines increased the charge stabilization capability of the micelles and that an analogous commercial surfactant OLOA 11000 made for a lower concentration of charge-generating ions in solution. Formulating magenta inks with the various surfactants showed that the absence of amine in the surfactant head was detrimental to particle stabilization and device performance.     

Accurate distance determination of nucleic acids via Förster resonance energy transfer: implications of dye linker length and rigidity

In Fo?rster resonance energy transfer (FRET) experiments, the donor (D) and acceptor (A) fluorophores are usually attached to the macromolecule of interest via long flexible linkers of up to 15 ? in length. This causes significant uncertainties in quantitative distance measurements and prevents experiments with short distances between the attachment points of the dyes due to possible dye-dye interactions. We present two approaches to overcome the above problems as demonstrated by FRET measurements for a series of dsDNA and dsRNA internally labeled with Alexa488 and Cy5 as D and A dye, respectively. First, we characterize the influence of linker length and flexibility on FRET for different dye linker types (long, intermediate, short) by analyzing fluorescence lifetime and anisotropy decays. For long linkers, we describe a straightforward procedure that allows for very high accuracy of FRET-based structure determination through proper consideration of the position distribution of the dye and of linker dynamics. The position distribution can be quickly calculated with geometric accessible volume (AV) simulations, provided that the local structure of RNA or DNA in the proximity of the dye is known and that the dye diffuses freely in the sterically allowed space. The AV approach provides results similar to molecular dynamics simulations (MD) and is fully consistent with experimental FRET data. In a benchmark study for ds A-RNA, an rmsd value of 1.3 ? is achieved. Considering the case of undefined dye environments or very short DA distances, we introduce short linkers with a propargyl or alkenyl unit for internal labeling of nucleic acids to minimize position uncertainties. Studies by ensemble time correlated single photon counting and single-molecule detection show that the nature of the linker strongly affects the radius of the dye's accessible volume (6-16 ?). For short propargyl linkers, heterogeneous dye environments are observed on the millisecond time scale. A detailed analysis of possible orientation effects (κ(2) problem) indicates that, for short linkers and unknown local environments, additional κ(2)-related uncertainties are clearly outweighed by better defined dye positions.     

The Rearrangement of 2,2‐Diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane to 3,4,4‐Triphenylcyclopent‐1‐ene: a DFT Analysis

A computational study on the rearrangement of 2,2‐diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane ( 1 ) is presented, using density functional theory (DFT), (U)B3LYP with the 6‐31G* basis set (DFT1) and (U)M05‐2X with the 6‐311+G** basis set (DFT2). In agreement with a biradical character of the transition structure (TS) or intermediate, the potential‐energy hypersurface is lowered by the influence of three conjugated Ph groups. Surprisingly, two conformations of the geminal diphenyl group (different twist angles) induce two different minimum‐energy pathways for the rearrangement. Independent of the functional used, the first hypersurface harbors true biradical intermediates, whereas the second energy surface is a flat, slightly ascending slope from the starting material to the TS. The functional (U)M05‐2X with the basis set 6‐311+G** provides realistic energies which seem to be close to experiment. The activation energy for racemization of enantiomers of 1 is lower than that of rearrangement by 2.5 kcal mol^?1, in agreement with experiment.     

A Simple and Effective Chemical Phosphorylation Procedure for Biomolecules

A general chemical phosphorylation method based on P(III) chemistry has been developed. The system is demonstrated for the phosphorylation of oligonucleotides, directly after their synthesis on a solid support, and for the O-phosphorylation of serine, threonine, and tyrosine as well as for a serine-containing peptide.     

A spline interpolation method for solving boundary value problems of potential theory from discretely given data

An interpolation procedure using harmonic splines is described and analyzed for solving (exterior) boundary value problems of Laplace's equation in three dimensions (from discretely given data). The theoretical and computational aspects of the method are discussed. Some numerical examples are given.     

Dyadic Diaphony of Digital Nets Over ?2

The dyadic diaphony, introduced by Hellekalek and Leeb, is a quantitative measure for the irregularity of distribution of point sets in the unit-cube. In this paper we study the dyadic diaphony of digital nets over ℤ₂. We prove an upper bound for the dyadic diaphony of nets and show that the convergence order is best possible. This follows from a relation between the dyadic diaphony and the L₂{\cal L}_2 discrepancy. In order to investigate the case where the number of points is small compared to the dimension we introduce the limiting dyadic diaphony, which is defined as the limiting case where the dimension tends to infinity. We obtain a tight upper and lower bound and we compare this result with the limiting dyadic diaphony of a random sample.     

Energy Transfer from a Lumazine (= Pteridine-2,4(1H,3H)-dione) Chromophore to Bathophcnanthroline-ruthenium(II) Complexes during Hybridization Processes of DNA

We incorporated 6,7-dimethyllumazine chromophores and a [Ru^II(bathophenanthroline)] complex into different oligodeoxynucleotides, the former via the corresponding phosphoramidites of the 2′-deoxynucleosides and the latter specifically by the phosphonate approach at the 5′-end of synthetic oligonucleotides, directly in the course of their synthesis on solid support. Efficiency measurements of this energy-transfer system with the lumazine as energy donor and the Ru complex as energy acceptor allowed us to distinguish between the hybridized and the non-hybridized state of oligonucleotides. Thus, the approach should be of value in DNA probe technology for the detection of single-stranded DNA targets.