On the equation of state of classical one-component systems with long-range forces

Several definitions of the pressure are introduced for one-component systems and shown to be nonequivalent in the presence of a rigid neutralizing background. Relations between these pressures are derived for finite and infinite systems; these relations depend on the asymptotic behavior of the force at infinity, with the Coulomb force at the borderline between different properties. It is argued that only one of those definitions is physically acceptable and its properties are discussed in relation to the asymptotic behavior of the force. It is seen in particular that a knowledge of the state of the infinite system is not sufficient to determine its thermodynamic properties. The results are illustrated by some typical examples.For example, for two-dimensional systems with three-dimensional Coulomb interaction see refs. 2–4.     

Spectroscopic properties of RBiBO4 (R = Ca,Sr) glasses doped with TiO2

Transparent glasses, melt quenching derived, containing 10RO·20Bi₂O₃·(70 ? x)B₂O₃·xTiO₂ [R = Ca, Sr] with x = 0, 0.5, 1.0 wt% were characterized by X-ray powder diffraction. Physical and spectroscopic properties viz., density, absorption, emission, electron paramagnetic resonance (EPR) and FTIR were investigated. The absorption band around 823 nm in pure glass samples is attributed to the electronic transition of ³P₀ to ³P₂ of Bi⁺ radicals. A small absorption hump centered around 609 nm is found in all doped glasses due to ²T_2g to ²E_g transition of octahedral Ti³⁺ ions. The emission results revealed that all the samples exhibit a broad emission band covering entire visible-light range, with λ_ex = 360 nm, centered 470–520 nm corresponds to electronic transition of ³P₁ to ¹S₀ of Bi³⁺ ions, therefore the present materials can be potentially used as tunable or full-color display systems. And a strong emission around 706 nm with λ_ex = 514 nm due to transition of ²P_3/2 to ²P_1/2 of Bi²⁺ ions. In SrO mixed glasses Ti⁴⁺ ions effect the environment of Bi³⁺ ion symmetry units from C₂ to C_3i. A small EPR signal (at room temperature) is observed in titanium doped glasses due to Ti³⁺ ions. In both the series with increase of TiO₂ concentration BO₄ units are gradually converted into BO₃ units and new cross linkages are formed, like B–O–Ti, Bi–O–Ti at the expense of B–O–B bonds.     

Assessing the polarization of a quantum field from stokes fluctuations

We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.     

Analysis of domain-solutions in reaction-diffusion systems

We investigate a standard model for bistable reaction-diffusion-systems, which shares characteristic properties with the van-der-Pol oscillator for distributed generators and the FitzHugh-Nagumo system. In this system we study the effect of a long ranging inhibitor. As a main result we show the existence of two inhomogeneous stationary solutions—the smaller one is always a saddle which corresponds to a critical nucleus, while the larger one arises as astable solution. In carrying out the linear stability analysis for these solutions, we have to treat the Schrödinger-equation for a double-well potential. This is done approximately by a supersymmetric approach which yields the eigenvalues and eigenfunctions of the Schrödinger-equation. Furthermore we compare our analytical findings with numerical results-especially the occurrence of oscillating solutions is shown.     

Second-harmonic generation and wave-front correction of a terawatt laser system

By combining second-harmonic generation and wave-front correction of a hybrid Ti:sapphire-Nd:glass terawatt laser chain, we were able to generate a focused intensity above 10(19) W/cm(2), with an estimated 10(9):1 intensity contrast ratio. The frequency of the laser is doubled by use of a type I KDP crystal, and wave-front correction is achieved with a deformable mirror coupled to a wave-front sensor.     

Zwitterionic titanoxanes {Cp[η-C5H4B(C6F5)3]Ti}2O and {(η-PrC5H4)[η-1,3-PrC5H3B(C6F5)3]Ti}2O as catalysts for cationic ring-opening polymerization

Zwitterionic titanoxanes {Cp[η⁵-C₅H₄B(C₆F₅)₃]Ti}₂O (I) and {(η⁵-ⁱPrC₅H₄)[η⁵-1,3-ⁱPrC₅H₃B(C₆F₅)₃]Ti}₂O (II), which contain two positively charged Ti(IV) centres in the molecule, are able to catalyse the ring-opening polymerization of -caprolactone (-CL) in toluene solution and in bulk. The process proceeds with a noticeable rate even at room temperature and accelerates strongly on raising the temperature to 60 °C. The best results have been obtained on carrying out the reaction in bulk. Under these conditions, the use of I as a catalyst (-CL:I = 1000:1) gives at 60 °C close to quantitative yield of poly--CL with the molecular mass of 197 000. An increase in the -CL:I ratio to 6000:1 increases the molecular mass of poly--CL to 530 000. Tetrahydrofuran (THF) is also polymerized under the action of I albeit with a lesser rate. However, the molecular mass of the resulting poly-THF can reach rather big values under optimal conditions (up to 217 000 at 20 °C and the THF:I ratio of 770:1). A rise in the reaction temperature from 20 to 60 °C results here to a decrease in the efficiency of the process. Titanoxane II is close to I in its catalytic activity in the -CL polymerization but it is much less active in the polymerization of THF. Propylene oxide (PO), in contrast to -CL and THF, gives with I only liquid oligomers in wide temperature and PO:I molar ratio ranges (−30 to +20 °C, PO:I = 500–2000:1). γ-Butyrolactone and 1-methyl-2-pyrrolidone are not polymerized under the action of I at room temperature. The reactions found are the first examples of catalysis of the cationic ring-opening polymerization by zwitterionic metallocenes of the group IVB metals.     

L-proline catalyzed asymmetric transfer aldol reaction between diacetone alcohol and aldehydes

We demonstrate for the first time, L-proline as a chiral catalyst for transfer aldol reaction between aldehydes and diacetone alcohol.     

Generation of 3rd and 5th harmonics in a thin superconducting film by temperature oscillations and isothermal nonlinear current response

The generation of harmonics of the voltage response is considered when an AC current is applied through a superconducting film above T_c. It is shown that almost at all temperatures the mechanism of the temperature oscillations created by the AC current and the temperature dependence of the resistance dominates over the isothermal nonlinear electric conductivity. Only in a narrow critical region close to T_c the latter is essential for the generation of the harmonics. A detailed investigation of harmonics generation provides an accurate method for measuring the thermal boundary conductance between the film and the insulating substrate. The critical behaviour of the third harmonic will give a new method for the determination of the lifetime of metastable Cooper pairs above T_c. The comparison of the calculated fifth harmonics of the voltage with the experiment is proposed as an important test for the applicability of the employed theoretical models. Received 8 September 2001