Synthesis and Study of Olefin Metathesis Catalysts Supported by Redox-Switchable Diaminocarbene 3 Ferrocenophanes

A redox-switchable ligand, N,N'-dimethyldiaminocarbene[3]ferrocenophane (5), was synthesized and incorporated into a series of Ir- and Ru-based complexes. Electrochemical and spectroscopic analyses of (5) Ir(CO)(2)Cl (15) revealed that 5 displayed a Tolman electronic parameter value of 2050 cm(-1) in the neutral state and 2061 cm(-1) upon oxidation. Moreover, inspection of X-ray crystallography data recorded for (5) Ir(cis,cis-1,5-cyclooctadiene)Cl (13) revealed that 5 was sterically less bulky (%V-Bur = 28.4) than other known diaminocarbene[3]ferrocenophanes, which facilitated the synthesis of (5)(PPh3)Cl2Ru-(3-phenylindenylid-1-ene) (18). Complex 18 exhibited quasi-reversible electrochemical processes at 0.79 and 0.98 V relative to SCE, which were assigned to the Fe and Ru centers in the complex, respectively, based on UV-vis and electron pair resonance spectroscopic measurements. Adding 2,3-dichloro-5,6-dicyanoquinone over the course of a ring-opening metathesis polymerization of cis, cis-1,5-cyclooctadiene catalyzed by 18 ([monomer](0)/[18](0) = 2500) reduced the corresponding rate constant of the reaction by over an order of magnitude (pre-oxidation: k(obs) = 0.045 s(-1); post-oxidation: k(obs) = 0.0012 s(-1)). Subsequent reduction of the oxidized species using decamethylferrocene restored catalytic activity (post-reduction: k(obs) = up to 0.016 s(-1), depending on when the reductant was added). The difference in the polymerization rates was attributed to the relative donating ability of the redox-active ligand (i.e., strongly donating 5 versus weakly donating 5(+)) which ultimately governed the activity displayed by the corresponding catalyst.U. S. Army Research Office W911NF-09-1-0446Chemistr

Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold

We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah-Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole dynamics to be translated into results about the dynamics of 3-monopoles. Using a numerical ADHMN construction we compute the monopole energy density at various points on two interesting geodesics. The first is a geodesic over the two-dimensional rounded cone submanifold corresponding to right angle scattering and the second is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit

Massive Hyper-Kahler Sigma Models and BPS Domain Walls

With the non-Abelian Hyper-Kahler quotient by U(M) and SU(M) gauge groups, we give the massive Hyper-Kahler sigma models that are not toric in the N=1 superfield formalism. The U(M) quotient gives N!/[M! (N-M)!] (N is a number of flavors) discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua. We derive BPS domain wall solution in the case of N=2 and M=1 in the U(M) quotient model.Comment: 16 pages, 1 figure, contribution to the Proceedings of the International Conference on "Symmetry Methods in Physics (SYM-PHYS10)" held at Yerevan, Armenia, 13-19 Aug. 200

Memory difference control of unknown unstable fixed points: Drifting parameter conditions and delayed measurement

Difference control schemes for controlling unstable fixed points become important if the exact position of the fixed point is unavailable or moving due to drifting parameters. We propose a memory difference control method for stabilization of a priori unknown unstable fixed points by introducing a memory term. If the amplitude of the control applied in the previous time step is added to the present control signal, fixed points with arbitrary Lyapunov numbers can be controlled. This method is also extended to compensate arbitrary time steps of measurement delay. We show that our method stabilizes orbits of the Chua circuit where ordinary difference control fails.Comment: 5 pages, 8 figures. See also chao-dyn/9810029 (Phys. Rev. E 70, 056225) and nlin.CD/0204031 (Phys. Rev. E 70, 046205

Chaos in free electron laser oscillators

The chaotic nature of a storage-ring Free Electron Laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.Comment: Accepted in EPJ

Synthesis of Fluorine-18 Functionalized Nanoparticles for use as in vivo Molecular Imaging Agents

Nanoparticles containing fluorine-18 were prepared from block copolymers made by ring opening metathesis polymerization (ROMP). Using the fast initiating ruthenium metathesis catalyst (H_2IMes)(pyr)_2(Cl)_2Ru=CHPh, low polydispersity amphiphilic block copolymers were prepared from a cinnamoyl-containing hydrophobic norbornene monomer and a mesyl-terminated PEG-containing hydrophilic norbornene monomer. Self-assembly into micelles and subsequent cross-linking of the micelle cores by light-activated dimerization of the cinnamoyl groups yielded stable nanoparticles. Incorporation of fluorine-18 was achieved by nucleophilic displacement of the mesylates by the radioactive fluoride ion with 31% incorporation of radioactivity. The resulting positron-emitting nanoparticles are to be used as in vivo molecular imaging agents for use in tumor imaging

Restricted feedback control of one-dimensional maps

Dynamical control of biological systems is often restricted by the practical constraint of unidirectional parameter perturbations. We show that such a restriction introduces surprising complexity to the stability of one-dimensional map systems and can actually improve controllability. We present experimental cardiac control results that support these analyses. Finally, we develop new control algorithms that exploit the structure of the restricted-control stability zones to automatically adapt the control feedback parameter and thereby achieve improved robustness to noise and drifting system parameters.Comment: 29 pages, 9 embedded figure

M-theory on `toric' G_2 cones and its type II reduction

We analyze a class of conical G_2 metrics admitting two commuting isometries, together with a certain one-parameter family of G_2 deformations which preserves these symmetries. Upon using recent results of Calderbank and Pedersen, we write down the explicit G_2 metric for the most general member of this family and extract the IIA reduction of M-theory on such backgrounds, as well as its type IIB dual. By studying the asymptotics of type II fields around the relevant loci, we confirm the interpretation of such backgrounds in terms of localized IIA 6-branes and delocalized IIB 5-branes. In particular, we find explicit, general expressions for the string coupling and R-R/NS-NS forms in the vicinity of these objects. Our solutions contain and generalize the field configurations relevant for certain models considered in recent work of Acharya and Witten.Comment: 45 pages, references adde

Twisting gauged non-linear sigma-models

We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of the vortex equations and computes the Hamiltonian Gromov-Witten invariants. When the target is equivariantly Calabi-Yau, i.e. when its first G-equivariant Chern class vanishes, the supersymmetric theory can also be twisted into a gauged B-model. This model localizes to the Kaehler quotient X//G.Comment: 33 pages; v2: small additions, published versio