Optical Tunnelling from One-Dimensional Square-Well Potentials

The authors study a one-dimensional model for optical tunnellingwith a refractive index in the shape of a square well. The relevanceof the model and its limiting cases are discussed. The mainresult is the leading behaviour of the exponentially small imaginarypart of the eigenvalue which determines the radiation loss.The leading behaviour of the imaginary part is calculated usingBerry's formula which controls the asymptotic expansion of theAiry function Bi(z) to better-than-exponential accuracy.     

Determination of total ammonium-nitrogen and free ammonia in a fermentation medium by sequential injection analysis

Summary Automated methods for the determination of ammonium and ammonia are reviewed, and techniques based on gas diffusion using a semi-permeable membrane were selected for the determination of both total ammonium-nitrogen and free ammonia in fermentation samples. A simple and robust instrument based on sequential injection analysis (SIA) consisting of a piston pump and two selector valves was used. Two different methods of ammonia detection, the Berthelot method and detection using pH-indicators, have been evaluated and compared. The indicator method showed higher reproducibility and the range of determination could easily be adjusted to match the concentrations of the samples. The range of determination could be adjusted from 0.05 mmol/l to 350 mmol/l, depending on choice of acceptor solution. This method has been evaluated with fermentation medium samples and tested on-line in a yeast fermentation process.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

The amplitude and phase of a transmission holographic grating due to four-wave interaction in a photorefractive medium

Based on a previously developed two-level model of four-wave interaction in photorefractive crystals, expressions for the amplitude and phase of a transmission holographic grating have been obtained. The analysis of these expressions points to the dependence of both the amplitude and the phase of the grating on the intensity of the readout beam.     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007     

Nonlinear optical properties of regioregular main‐chain polyesters

We have prepared new polyesters containing quadratic, nonlinear optical (NLO) active chromophores covalently incorporated into the main chain. In these polymers, the sequence of the chromophore units along the main chain is rigorously head to tail. All the polyesters are processable, both in the melt and in solution. For one polyester, a full second‐order NLO characterization has been performed. An out‐of‐resonance d₃₃ coefficient of 21 pm/V at 1368 nm has been measured. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2719–2725, 2007     

Glass transitions and mixed phases in block SBS

Differential scanning calorimetry (DSC) does not allow for easy determination of the glass‐transition temperature (T_g) of the polystyrene (PS) block in styrene–butadiene–styrene (SBS) block copolymers. Modulated DSC (MDSC), which deconvolutes the standard DSC signal into reversing and nonreversing signals, was used to determine the (T_g) of both the polybutadiene (PB) and PS blocks in SBS. The T_g of the PB block was sharp, at ?92 °C, but that for the PS blocks was extremely broad, from ?60 to 125 °C with a maximum at 68 °C because of blending with PB. PS blocks were found only to exist in a mixed PS–PB phase. This concurred with the results from dynamic mechanical analysis. Annealing did not allow for a segregation of the PS blocks into a pure phase, but allowed for the segregation of the mixed phase into two mixed phases, one that was PB‐rich and the other that was PS‐rich. It is concluded that three phases coexist in SBS: PB, PB‐rich, and PS‐rich phases. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 276–279, 2005     

Hierarchical models of unified theories

A modernized conception of hierarchical structure of reality is proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–6, December, 1980.     

Symmetries of space-time,conservation laws and forbidden motion i: General discussion

The classical (first integral) methods of studying restrictions on the possible motion of gravitationally interacting bodies are reviewed. The simple and flexible inequality method is extended to a similar approach to the relationship between possible forbidden motion and (asymptotic) symmetries in the relativistic few-body problem. This extended method is used to reproduce the standard results of bounded motion for a test particle in a Schwarzschild geometry. The existence of bounded motion is shown for the general relativistic few-body problem and the difficulties in determining such bounded motion is analysed. The use of this approach to obtaining a relativistic alternative to the classical Roche lobe analysis in contact binaries is discussed.