Replicated Polymer Light Guide Interconnector with Depth Modified Surface Relief Grating Couplers

Planar light guide plate with one in-coupling and N out-coupling surface relief gratings is designed to perform as optical backplane broadcasting system for board-to-board connections. The performance of the element is analyzed theoretically with rigorous electromagnetic theory and results are confirmed experimentally. In addition, optical backplane elements have been replicated using conventional injection molding and UV-replication techniques.     

Linear viscoelastic model for elongational viscosity by control theory

Flows involving different types of chain branches have been modelled as functions of the uniaxial elongation using the recently generated constitutive model and molecular dynamics for linear viscoelasticity of polymers. Previously control theory was applied to model the relationship between the relaxation modulus, dynamic and shear viscosity, transient flow effects, power law and Cox–Merz rule related to the molecular weight distribution (MWD) by melt calibration. Temperature dependences and dimensions of statistical chain tubes were also modelled. The present study investigated the elongational viscosity. We introduced earlier the rheologically effective distribution (RED), which relates very accurately and linearly to the viscoelastic properties. The newly introduced effective strain-hardening distribution (RED_H) is related to long-chain branching. This RED_H is converted to real long-chain branching distribution by melt calibration and a simple relation formula. The presented procedure is very effective at characterizing long-chain branches, and also provides information on their structure and distribution. Accurate simulations of the elongational viscosities of low-density polyethylene, linear low-density polyethylene and polypropylene, and new types of MWDs are presented. Models are presented for strain-hardening that includes the monotonic increase and overshoot effects. Since the correct behaviour at large Hencky strains is still unclear, these theoretical models may aid further research and measurements.     

Proximity effects of oxygen atoms on the enthalpies of formation of simple diethers: a computational G3(MP2)//B3 study

The enthalpies of formation of a number of acyclic, straight‐chain ethers and diethers were determined by G3(MP2)//B3 calculations. The principal aim of the work was to study the magnitude of the O…O proximity effect on the enthalpy contents of diethers as a function of the distance (number of bonds) between the O atoms. 1,4‐Diethers and 1,5‐diethers were computed to be destabilized by ca. 4.5 (±0.5) and 3.2 (±0.4) kJ mol^?1, respectively, by the O…O proximity effect. The effect was calculated to be negligible in diethers with the O atoms in positions more remote than 1,5 from each other, whereas 1,3‐diethers (acetals) are stabilized by ca. 22 kJ mol^?1, likely on account of the anomeric effect. Calculations on simple monoethers show that the contributions to of CH₂ groups in the β and γ positions (relative to O) are reduced by ca. 0.8 and 0.3 kJ mol^?1, respectively, relative to those of CH₂ groups more remote from the O atom. The computational enthalpies of formation of the studied monoethers and diethers, both cyclic and acyclic, are generally in good agreement with experimental data, another important result of the present work. Copyright © 2008 John Wiley & Sons, Ltd.     

String Scattering from Decaying Branes

We develop the general formalism of string scattering from decaying D-branes in bosonic string theory. In worldsheet perturbation theory, amplitudes can be written as a sum of correlators in a grand canonical ensemble of unitary random matrix models, with time setting the fugacity. An approach employed in the past for computing amplitudes in this theory involves an unjustified analytic continuation from special integer momenta. We give an alternative formulation which is well-defined for general momenta. We study the emission of closed strings from a decaying D-brane with initial conditions perturbed by the addition of an open string vertex operator. Using an integral formula due to Selberg, the relevant amplitude is expressed in closed form in terms of zeta functions. Perturbing the initial state can suppress or enhance the emission of high energy closed strings for extended branes, but enhances it for D0-branes. The closed string two point function is expressed as a sum of Toeplitz determinants of certain hypergeometric functions. A large N limit theorem due to Szegö, and its extension due to Borodin and Okounkov, permits us to compute approximate results showing that previous naive analytic continuations amount to the large N approximation of the full result. We also give a free fermion formulation of scattering from decaying D-branes and describe the relation to a grand canonical ensemble for a 2d Coulomb gas.     

Finding approximate patterns in strings

Let p (the pattern) be a string and t ≥ 0 an integer. The problem of locating in any string a substring whose edit distance from p is at most a given constant t is considered. An algorithm is presented to construct a deterministic finite-state automaton that solves the problem.     

Preparation and structure determination of 1-benzyl-, 1-methyl- and 1H-5-[(2-nitro-2-phenyl)ethenyl]imidazoles

1-R-5-[(2-Nitro-2-phenyl)ethenyl]imidazoles (R = Bn, Me, H) 6a,b,c were synthesized by the Knoevenagel reaction of the corresponding aldehydes 4a,b,c with phenylnitromethane 5 . The E-isomers 6a,b,c were precipitated from the reaction mixture as crystalline compounds in 89, 81 and 60% yields, respectively. Traces of the Z-isomers 6a′b′,c′ were found in the reaction mixtures but could be obtained in a ratio of 4:3 from the E-form with UV irradiation. The E-forms were more stable and the Z-isomers changed again to the E-isomers in several weeks.     

Well-Defined Fuzzy Sentential Logic

A many-valued sentential logic with truth values in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV-algebra. In the well-defined fuzzy sentential logic holds the Compactness Theorem, while the Deduction Theorem and the Finiteness Theorem in general do not hold. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning.     

Multiple-conjugation expansion in distortion elimination by phase conjugation

The multiple-conjugation expansion results from a method of phase-conjugate scattering analysis that is convenient in connection with strong aberrators and weak phase conjugators. Based on this expansion, a new proof is obtained of a recently established theorem according to which a complete cancellation of distortion is possible in the absence of gains or losses. The proof makes use of the reciprocity property and of the generalized optical theorem of potential scattering.     

Copper and Copper Oxide Nanoparticle Formation by Chemical Vapor Nucleation From Copper (II) Acetylacetonate

Crystalline nanometer-size copper and copper (I) oxide particle formation was studied by thermal decomposition of copper acetylacetonate Cu(acac)₂ vapor using a vertical flow reactor at ambient nitrogen pressure. The experiments were performed in the precursor vapor pressure range of P _prec = 0.06 to 44 Pa at furnace temperatures of 431.5°C, 596.0°C, and 705.0°C. Agglomerates of primary particles were formed at P _prec0.1 Pa at all temperatures. At 431.5°C the number mean size of the primary particles increased from D _p = 3.7 nm (with geometric standard deviation _g = 1.42) to D _p = 7.2 nm (_g = 1.33) with the increasing precursor vapor particle pressure from 1.8 to 16 Pa. At 705.0°C the primary particle size decreased from D _p = 24.0 nm (_g=1.57) to D _p = 7.6 nm (_g = 1.54), respectively.At furnace temperatures of 431.5°C and 596.0°C only crystalline copper particles were produced. At 705.0°C the crystalline product of the decomposition depended on the precursor vapor pressure: copper particles were formed at P _prec>10 Pa, copper (I) oxide at P _precleq 1 Pa, and a mixture of the metal and its oxide at intermediate vapor pressures. A kinetic restriction on copper particle growth was shown, which leads to the main role of Cu₂ molecule participation in the particle formation. The formation of copper (I) oxide particles occurs due to the surface reaction of the decomposition products (mainly carbon dioxide). For the explanation of the experimental results, a model is proposed to build a semiempirical phase diagram of the precursor decomposition products.     

Random variables as pathwise integrals with respect to fractional Brownian motion

We give both necessary and sufficient conditions for a random variable to be represented as a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand. We also show that any random variable is a value of such integral in an improper sense and that such integral can have any prescribed distribution. We discuss some applications of these results, in particular, to fractional Black–Scholes model of financial market.