Stepwise assembly of mixed-metal coordination cages containing both kinetically inert and kinetically labile metal ions: introduction of metal-centred redox and photophysical activity at specific sites

Stepwise preparation of the heterometallic octanuclear coordination cages [(Ma)4(Mb)4L12]16+ is reported, in which Ma = Ru or Os and Mb = Cd or Co (all in their +2 oxidation state). This requires initial preparation of the kinetically inert mononuclear complexes [(Ma)L3]2+ in which L is a ditopic ligand with two bidentate chelating pyrazolyl-pyridine units: in the complexes [(Ma)L3]2+ one terminus of each ligand is bound to the metal ion, such that the complex has three pendant bidentate sites at which cage assembly can propagate by coordination to additional labile ions Mb in a separate step. Thus, combination of four [(Ma)L3]2+ units and four [Mb]2+ ions results in assembly of the complete cages [(Ma)4(Mb)4L12]16+ in which a metal ion lies at each of the eight vertices, and a bridging ligand spans each of the twelve edges, of a cube. The different types of metal ion necessarily alternate around the periphery with each bridging ligand bound to one metal ion of each type. All four cages have been structurally characterised: in the Ru(II)/Cd(II) cage (reported in a recent communication) the Ru(II) and Cd(II) ions are crystallographically distinct; in the other three cages [Ru(II)/Co(II), Os(II)/Cd(II) and Os(II)/Co(II), reported here] the ions are disordered around the periphery such that every metal site refines as a 50 : 50 mixture of the two metal atom types. The incorporation of Os(II) units into the cages results in both redox activity [a reversible Os(II)/Os(III) couple for all four metal ions simultaneously, at a modest potential] and luminescence [the Os(II) units have luminescent 3MLCT excited states which will be good photo-electron donors] being incorporated into the cage superstructure

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added

Catalysis in a Cationic Coordination Cage Using a Cavity-Bound Guest and Surface-Bound Anions: Inhibition, Activation, and Autocatalysis

The Kemp elimination (reaction of benzisoxazole with base to give 2-cyanophenolate) is catalyzed in the cavity of a cubic M8L12coordination cage because of a combination of (i) benzisoxazole binding in the cage cavity driven by the hydrophobic effect, and (ii) accumulation of hydroxide ions around the 16+ cage surface driven by ion-pairing. Here we show how reaction of the cavity-bound guest is modified by the presence of other anions which can also accumulate around the cage surface and displace hydroxide, inhibiting catalysis of the cage-based reaction. Addition of chloride or fluoride inhibits the reaction with hydroxide to the extent that a new autocatalytic pathway becomes apparent, resulting in a sigmoidal reaction profile. In this pathway the product 2-cyanophenolate itself accumulates around the cationic cage surface, acting as the base for the next reaction cycle. The affinity of different anions for the cage surface is therefore 2-cyanophenolate (generating autocatalysis) > chloride > fluoride (which both inhibit the reaction with hydroxide but cannot deprotonate the benzisoxazole guest) > hydroxide (default reaction pathway). The presence of this autocatalytic pathway demonstrates that a reaction of a cavity-bound guest can be induced with different anions around the cage surface in a controllable way; this was confirmed by adding different phenolates to the reaction, which accelerate the Kemp elimination to different extents depending on their basicity. This represents a significant step toward the goal of using the cage as a catalyst for bimolecular reactions between a cavity-bound guest and anions accumulated around the surface

New Approach to GUTs

We introduce a new string-inspired approach to the subject of grand unification which allows the GUT scale to be small, \lesssim 200 TeV, so that it is within the reach of {\em conceivable} laboratory accelerated colliding beam devices. The key ingredient is a novel use of the heterotic string symmetry group physics ideas to render baryon number violating effects small enough to have escaped detection to date. This part of the approach involves new unknown parameters to be tested experimentally. A possible hint at the existence of these new parameters may already exist in the EW precision data comparisons with the SM expectations.Comment: 8 pages; improved text and references, note added; extended text, 1 figure added; extended text for publication in Eur. Phys. Journal

Managing groundwater supplies subject to drought: perspectives on current status and future priorities from England (UK)

Effective management of groundwater resources during drought is essential. How is groundwater currently managed during droughts, and in the face of environmental change, what should be the future priorities? Four themes are explored, from the perspective of groundwater management in England (UK): (1) integration of drought definitions; (2) enhanced fundamental monitoring; (3) integrated modelling of groundwater in the water cycle; and (4) better information sharing. Whilst these themes are considered in the context of England, globally, they are relevant wherever groundwater is affected by drought

GG-Strands

A $G$-strand is a map $g(t,{s}):\,\mathbb{R}\times\mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. The SO(3)-strand is the $G$-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, $SO(3)_K$-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar\'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the $SO(3)_K$-strand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)-strand. Analogous results are obtained for the $Sp(2)$-strand. The $Sp(2)$-strand is the $G$-strand version of the $Sp(2)$ Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wave-like solutions in both cases. ${\rm Diff}(\mathbb{R})$-strand equations on the diffeomorphism group $G={\rm Diff}(\mathbb{R})$ are also introduced and shown to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc

All-optical switching and strong coupling using tunable whispering-gallery-mode microresonators

We review our recent work on tunable, ultrahigh quality factor whispering-gallery-mode bottle microresonators and highlight their applications in nonlinear optics and in quantum optics experiments. Our resonators combine ultra-high quality factors of up to Q = 3.6 \times 10^8, a small mode volume, and near-lossless fiber coupling, with a simple and customizable mode structure enabling full tunability. We study, theoretically and experimentally, nonlinear all-optical switching via the Kerr effect when the resonator is operated in an add-drop configuration. This allows us to optically route a single-wavelength cw optical signal between two fiber ports with high efficiency. Finally, we report on progress towards strong coupling of single rubidium atoms to an ultra-high Q mode of an actively stabilized bottle microresonator.Comment: 20 pages, 24 figures. Accepted for publication in Applied Physics B. Changes according to referee suggestions: minor corrections to some figures and captions, clarification of some points in the text, added references, added new paragraph with results on atom-resonator interactio

Strangeness Enhancement in p+Ap+A and S+AS+A Interactions at SPS Energies

The systematics of strangeness enhancement is calculated using the HIJING and VENUS models and compared to recent data on $\,pp\,$, $\,pA\,$ and $\,AA\,$ collisions at CERN/SPS energies ($200A\,\, GeV\,$). The HIJING model is used to perform a {\em linear} extrapolation from $pp$ to $AA$. VENUS is used to estimate the effects of final state cascading and possible non-conventional production mechanisms. This comparison shows that the large enhancement of strangeness observed in $S+Au$ collisions, interpreted previously as possible evidence for quark-gluon plasma formation, has its origins in non-equilibrium dynamics of few nucleon systems. % Strangeness enhancement %is therefore traced back to the change in the production dynamics %from $pp$ to minimum bias $pS$ and central $SS$ collisions. A factor of two enhancement of $\Lambda^{0}$ at mid-rapidity is indicated by recent $pS$ data, where on the average {\em one} projectile nucleon interacts with only {\em two} target nucleons. There appears to be another factor of two enhancement in the light ion reaction $SS$ relative to $pS$, when on the average only two projectile nucleons interact with two target ones.Comment: 29 pages, 8 figures in uuencoded postscript fil

Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics

We study the gauge covariance of the massive fermion propagator in three as well as four dimensional Quantum Electrodynamics (QED). Starting from its value at the lowest order in perturbation theory, we evaluate a non-perturbative expression for it by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the perturbative expansion of our findings with the known one loop results and observe perfect agreement upto a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.Comment: 9 pages, no figures, uses revte