Invariance results for definable extensions of groups

We show that in an o-minimal expansion of an ordered group finite definable extensions of a definable group which is defined in a reduct are already defined in the reduct. A similar result is proved for finite topological extensions of definable groups defined in o-minimal expansions of the ordered set of real numbers.     

Exploring the free energy surfaces of clusters using reconnaissance metadynamics

A new approach is proposed for exploring the low-energy structures of small to medium-sized aggregates of atoms and molecules. This approach uses the recently proposed reconnaissance metadynamics method [G. A. Tribello, M. Ceriotti, and M. Parrinello. Proc. Natl. Acad. Sci. U.S.A. 107(41), 17509 (2010)] in tandem with collective variables that describe the average structure of the coordination sphere around the atoms/molecules. We demonstrate this method on both Lennard-Jones and water clusters and show how it is able to quickly find the global minimum in the potential energy surface, while exploring the finite temperature free energy surface.     

Linear and nonlinear optical properties of cationic bipyridyl iridium(III) complexes: tunable and photoswitchable?

A series of cationic Ir(III) substituted bipyridyl ()(N(∧)N (N(∧)N-bpy) complexes incorporating electron-donor and -acceptor substituents, [Ir(C(∧)N-ppy-R')(2)(N(∧)N-bpy-CH═CH-C(6)H(4)-R)][X] (X(-) = PF(6)(-) or C(12)H(25)SO(3)(-)), 2 (a, R = NEt(2) and R' = Me; b, R = O-Oct and R' = Me; c, R = NO(2) and R' = C(6)H(13); C(∧)N-ppy = cyclometalated 2-phenylpyridine, [Ir(C(∧)N-ppy-Me)(2)(N(∧)N-bpy-CH═CH-thienyl-Me)][PF(6)], 2d, and the dithienylethene (DTE)-containing complex 2e have been synthesized and characterized, and their absorption, luminescence, and quadratic nonlinear optical (NLO) properties are reported. Density functional theory (DFT) and time-dependent-DFT (TD-DFT) calculations on the complexes facilitate a detailed assignment of the excited states involved in the absorption and emission processes. All five complexes are luminescent in a rigid glass at 77 K, displaying vibronically structured spectra with long lifetimes (14-90 μs), attributed to triplet states localized on the styryl-appended bipyridines. The second-order NLO properties of 2a-d and related complexes 1a-d with 1,10-phenanthrolines have been investigated by both electric field induced second harmonic generation (EFISH) and harmonic light scattering (HLS) techniques. They are characterized by high negative EFISH μβ values which decrease when the ion pair strength between the cation and the counterion (PF(6)(-), C(12)H(25)SO(3)(-)) increases. The EFISH response is mainly controlled by metal-to-ligand charge-transfer/ligand-to-ligand charge-transfer (MLCT/L'LCT) processes. A combination of HLS and EFISH techniques is used to evaluate both the dipolar and octupolar contributions to the total quadratic hyperpolarizability, demonstrating that the major contribution is controlled by the octupolar part. The incorporation of a photochromic DTE unit into the N(∧)N-bpy ligand (complex 2e) allows the luminescence to be switched ON or OFF. The photocyclisation of the DTE unit can be triggered by using either UV (365 nm) or visible light (430 nm), leading to an efficient quenching of the ligand-based 77 K luminescence, which can be restored upon irradiation of the closed form at 715 nm. In contrast, no significant modification of the EFISH μβ value is observed upon photocyclization, suggesting that the quadratic NLO response is dominated by the MLCT/L'LCT processes, rather than by the intraligand excited states localized on the substituted bipyridine ligand.     

Excited states in electron-transfer reaction products: ultrafast relaxation dynamics of an isolated acceptor radical anion

The spectroscopy and ultrafast relaxation dynamics of excited states of the radical anion of a representative charge-transfer acceptor molecule, 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane, have been studied in the gas phase using time-resolved photoelectron spectroscopy. The photoelectron spectra reveal that at least two anion excited states are bound. Time-resolved studies show that both excited states are very short-lived and internally convert to the anion ground state, with the lower energy state relaxing within 200 fs and a near-threshold valence-excited state relaxing on a 60 fs time scale. These excited states, and in particular the valence-excited state, present efficient pathways for electron-transfer reactions in the highly exergonic inverted region which commonly displays rates exceeding predictions from electron-transfer theory.     

Double addition of H2 to transition metal-borane complexes: a 'hydride shuttle' process between boron and transition metal centres

The addition of H(2) across a transition metal-borane bond is reported for the first time providing a mechanism for recharging borane functional groups to borohydride.     

Calix[4]arene nitroxide tetraradical and octaradical

1,3-Alternate calix[4]arene with para-phenylene spacers connecting nitroxide monoradicals and high-spin (S = 1) diradicals provides tetraradical and octaradical scaffolds that possess conformations with slow electron spin relaxation rates (1/T(1)). Such scaffolds may facilitate tuning of relaxation rates that are more favorable for MRI or DNP applications.     

Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

We introduce a novel algorithm (JEA) to simulate exactly from a class of one-dimensional jump-diffusion processes with state-dependent intensity. The simulation of the continuous component builds on the recent Exact Algorithm (Beskos et al., Bernoulli 12(6):1077–1098, 2006a). The simulation of the jump component instead employs a thinning algorithm with stochastic acceptance probabilities in the spirit of Glasserman and Merener (Proc R Soc Lond Ser A Math Phys Eng Sci 460(2041):111–127, 2004). In turn JEA allows unbiased Monte Carlo simulation of a wide class of functionals of the process’ trajectory, including discrete averages, max/min, crossing events, hitting times. Our numerical experiments show that the method outperforms Monte Carlo methods based on the Euler discretization.     

MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts.     

Relative cohomology theory for profinite groups

In this paper we define and develop the theory of the cohomology of a profinite group relative to a collection of closed subgroups. Having made the relevant definitions we establish a robust theory of cup products and use this theory to define profinite Poincaré duality pairs. We use the theory of groups acting on profinite trees to give Mayer–Vietoris sequences, and apply this to give results concerning decompositions of 3-manifold groups. Finally we discuss the relationship between discrete duality pairs and profinite duality pairs, culminating in the result that profinite completion of the fundamental group of a compact aspherical 3-manifold is a profinite Poincaré duality group relative to the profinite completions of the fundamental groups of its boundary components.     

The properties of some derivative autocorrelation functions computed with the atom-atom potential

High-resolution quasi-elastic neutron-scattering measurements have been made on two nematogens: DMBCA with a nematic range 108 to 119°C, and 5CB and a tail-deuteriated sample (D5CB), having a nematic range 22·6 to 35·1°C.

Results on 5CB in the crystal phase at ～18°C showed no significant quasielastic broadening, which means that any random motions of the alkyl chain are slower than about 5 × 10⁹ rad s^-1. Measurements were made at a single temperature in the nematic phases on specimens aligned in a magnetic field of 0·25T; for DMBCA with scattering vector Q⊥n (n is the nematic director) and for 5CB and D5CB with Q⊥n and Q∥n and also on the isotropic liquid phase of D5CB at 45°C. Analysis of the coherent scattering from nematic D5CB at Q = 1·2 Å^-1 and 25°C gave an order parameter <P ₂>=0·55, close to the simple mean field value for this temperature. The coherent scattering from DMBCA is too weak to allow this experiment to be performed.

The most remarkable qualitative feature of the results is the close similarity of the scattering law S(Q, ω) for D5CB (and 5CB) with Q⊥n and Q∥n. Analysis of the results in all cases was made using values for the translational diffusion constants measured previously. Corrections for multiple scattering are shown to be important and a single simple model has been devised which fits the line shapes of all the results for D5CB in nematic (Q⊥n and Q∥n) and isotropic liquid phases and DMBCA. The model involves uniaxial rotational diffusion about the long molecular axis m coupled to a displacement along the rotation axis giving a net rotation in a plane whose normal makes an angle ∝ relative to the direction m. Values for the rotational diffusion constant D _rd ns^-1 are as follows: D5CB, 25°C, 6 (∝ ～ 50°); 45°C, 10. DMBCA, 112°C, 16, (all ±10–15 per cent).

The results for D5CB and 5CB are so similar that no additional detailed model fitting was attempted for the fully hydrogenous sample and it is concluded that while the motion of the alkyl tails is freer, the time scale of the motions is not more than about a factor of 2 faster than that of the molecular cores.