Static characteristics of Josephson interferometers

This investigation deals with the range in operating currents for which a Josephson interferometer, sometimes also referred to as Superconducting QUantum Interference Device (SQUID), may remain in the zero-voltage Josephson condition. An interferometer consists of one or more inductive loops each of which contains two Josephson junctions or other weak links. Two types of current are considered. Gate currentI _gpasses the junctions in parallel. Control currentI _cgenerates magnetic flux via inductive coupling in the loops. Zero-voltage operation is possible within certain areas of theI _g,I _cplane. These areas are manifestations of flux-quantum states and their boundary lines are referred to as static characteristics. In view of the nonlinearity of the constituting equations, not all their formal solutions are physically realizable. A stability analysis yields criteria which permit the identification of realizable operating conditions. The static characteristics comprise operating conditions where the limit of stability is reached. To obtain the static characteristics, linearized equations may be utilized if theLI _o product, a measure for the size of an interferometer, is large compared to the flux quantumΦ ₀, whereL is the inductance per loop, andI _o the maximum Josephson current per junction. As a general method of solving system of transcendental equations, continuation is discussed. The utilization of continuation for obtaining interferometer characteristics is explained. It is shown that some changes in the gate-current feed arrangement are equivalent to shearing the characteristics in theI _g,I _cplane. Analytical results are given on extrema, inflexion points, and singularities in the shape of cusps which conceptually relate to the existence and connectivity of flux-quantum states. Experimental static characteristics are presented on two-and four-junction interferometers. They are in agreement with characteristics computed on the basis of simple lumped circuit models. Relevant circuit parameters are obtained from the experimental characteristics.     

The self-consistent response of the electron density of a crystal copper film to an external electrostatic field

The response of the electrons of an fcc copper (001) film to an external electrostatic field is calculated. In order to determine the distribution of the screening charge, the equations of the electron density-functional theory are solved self-consistently by an original method. The position of the “image plane,” which is involved in a correct asymptotic expression for the exchange-correlation potential in the vacuum region, is first determined when performing a quantum-mechanical calculation for an anisotropic crystal film. The nonlinear electron response is characterized by the evolution of the “center of gravity” of the induced charge, which is also investigated. The calculations take into account the crystal structure of the film, and the results differ essentially from the predictions of the “jelly” model.     

Photorefractive properties of Cr-doped Sr0.61Ba0.39Nb2O6 related to crystal purity and doping concentration

The purity and the concentrations of the constituents Sr, Ba, Nb and Cr were determined in single crystals of chromium-doped Sr_0.61Ba_0.39Nb₂O₆ (SBN) by instrumental neutron activation analysis (INAA) and X-ray fluorescence analysis (XRF). Experiments with different Cr concentrations C_Cr reveal constant Sr and Ba concentrations as well as a decreasing Nb concentration with an increasing C_Cr. Therefore, Cr is incorporated at Nb lattice sites. The distribution coefficient of Cr is 1.2 between 100 and about 7000 ppm Cr and 1 above. From measurements of the holographic two-beam coupling gain Γ for different C_Cr, we deduced response times for the buildup of holographic gratings. The saturation value of Γ depends in a nonlinear manner on C_Cr and reaches its maximum at about 6000 ppm Cr. The inverse photorefractive response time of the grating erasure depends linearly on the erasure intensity for all doping concentrations. Thus a one-center model can be assumed for the charge transport in SBN:Cr. Received: 8 December 2000 / Revised version: 23 January 2001 / Published online: 21 March 2001     

Isomerizing Olefin Metathesis

Isomerizing olefin metathesis is currently undergoing a transformation from laboratory curiosity to powerful synthetic concept at the heart of orthogonal tandem catalysis. In this process, an isomerization catalyst continuously moves double bonds along carbon chains, while a metathesis catalyst scrambles the residues at the C−C double bonds. This cooperative action of two catalysts can be used to access single, defined products from a complex mixture of compounds. Alternatively, it enables the transformation of uniform starting materials into complex product blends with defined, tunable properties. This concept article highlights recent developments and potential applications of this fascinating reaction concept.     

The synthesis of cyclic polymers by olefin metathesis: Achievements and challenges

Cyclic polymers have drawn considerable interest for their peculiar physical properties in comparison to linear polymers, despite their equivalent compositions. Synthetically, cyclic polymers can be accessed through either macrocyclic ring‐closure or by ring‐expansion polymerization, but the main challenge with either method is the production of highly pure cyclic polymer samples. This highlight describes advances in the area of cyclic polymer synthesis, with a particular focus on ring‐expansion metathesis polymerization. Methods for characterizing cyclic polymers and assessing their purity are also discussed in order to emphasize the need for additional robust and reliable methods for synthesizing and studying topologically complex macromolecules. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 228–242     

Self‐assembled polyurea macromer nanodispersion and resulting hybrid polyurea‐acrylic emulsions and films

A polyurea macromer (PUM) was synthesized and dispersed in basic conditions to form self‐assembled nanoparticles (<20 nm dispersions, up to 30 wt % aq. soln.). These nanoparticles enabled surfactant‐free emulsion polymerization to form hybrid polyurea‐acrylic particles despite the absence of a measureable water‐soluble fraction. The T_g of the starting PUM material was a strong function of the PUM's extent of neutralization and hydration (varying between 100 °C and >175 °C) due to changes in hydrogen and ionic bonding. Two separate hybrid polyurea‐acrylic emulsion systems were prepared: one by direct polymerization of (meth)acrylic monomers in the presence of the nanodispersion and a second by a physical blend of PUM nanodispersion with an acrylic latex control. The direct polymerization method resulted in a hybrid emulsion particle size that developed by a mechanism resembling conventional emulsion polymerization and was unlike that described for seeded polyurethane dispersion systems. Film hardness was shown to increase with increasing coating thickness for the hybrid film prepared by direct polymerization. The resulting mechanical properties could be explained by applying mechanical models for a composite foam structure. These results were unprecedented for normal elastomer films. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1373–1388     

A Phosphinine-Derived 1-Phospha-7-Bora-Norbornadiene: Frustrated Lewis Pair Type Activation of Triple Bonds

Salt metathesis of 1-methyl-2,4,6-triphenylphosphacyclohexadienyl lithium and chlorobis(pentafluorophenyl)borane affords a 1-phospha-7-bora-norbornadiene derivative 2 . The C≡N triple bonds of nitriles insert into the P−B bond of 2 with concomitant C−B bond cleavage, whereas the C≡C bonds of phenylacetylenes react with 2 to form λ⁴-phosphabarrelenes. Even though 2 must formally be regarded as a classical Lewis adduct, the C≡N and C≡C activation processes observed (and the mild conditions under which they occur) are reminiscent of the reactivity of frustrated Lewis pairs. Indeed, NMR and computational studies give insight into the mechanism of the reactions and reveal the labile nature of the phosphorus–boron bond in 2 , which is also suggested by detailed NMR spectroscopic studies on this compound. Nitrile insertion is thus preceded by ring opening of the bicycle of 2 through P−B bond splitting with a low energy barrier. By contrast, the reaction with alkynes involves formation of a reactive zwitterionic methylphosphininium borate intermediate, which readily undergoes alkyne 1,4-addition.     

Non-commutative generalization of integrable quadratic ODE systems

Letters in Mathematical Physics - We find all homogeneous quadratic systems of ODEs with two dependent variables that have polynomial first integrals and satisfy the Kowalevski–Lyapunov test....