Direct measurement of the quality factor in a two-dimensional photonic-crystal microcavity

A new microcavity design is proposed and structures are realized with a two-dimensional photonic-crystal slab. The cavity consists of seven defect holes that encompass a hexagon and is designed to reduce vertical light leakage. From a direct transmission measurement, a Q value of 816+/-30 is achieved at lambda =1.55 mum . This high- Q cavity will permit the realistic realization of spontaneous-emission modification and on-off optical switches.     

The structure and decay dynamics of exciplexes derived from dibenzoyl-methanatoboron difluoride and alkylbenzenes in cyclohexane

Dibenzomethanatoboron difluoride (DBMBF2) interacted with alkylbenzenes from its singlet excited state to form exciplexes ranging from weak polarity up to contact radical ion pairs (CRIP); this exciplex series shows the characteristics in the Marcus "normal" region. In cyclohexane these exciplexes gave intense fluorescence spectra and high quantum yields (phi(infinity)ex). The dipole moment of these exciplexes calculated from the solvatochromic shift of the fluorescence maximums (vmax) was used to estimate the coefficient ("a" and "c") of the CT and LE terms in the exciplex wavefunction. On the basis of the measured lifetimes and phi(infinity)ex of these exciplexes, the radiative (k(ex)f) and nonradiative (k(ex)NR) rate constants were calculated. The former k(ex)f were also computed from a semi-empirical approach based on the assumption that the exciplex wavefunction could be adequately described by CT and LE states, and that *DBMBF2 primarily contributes to the probability of exciplex emission. Two results agree with each other with small systematic deviations for those less polar exciplexes. The plots of k(ex)r and k(ex)NR (or their logarithmic value) against the LE contribution (c2) and transition energy gaps (hvmax) afford better correlation than those against -deltaG(-et). This indicates the role played by the LE contribution in generating the stabilization energy (U(s)) in these exciplexes through the A-D+)<==> *AD) resonance interaction; U(s), in turn, modifies -deltaG(-et) to afford the decay driving force hvmax. Also, those plots from k(ex)f values (being determined directly from experiments) show better correlation than those from k(ex)NR. In contrast to the CRIP type exciplexes in the Marcus "inverted" region, these k(ex)f and k(ex)NR increase in the common trend with increasing transition energy gaps. The k(ex)NR plots show less steep slopes and attains more quickly a minimum toward the CRIP region; the latter is identified as the turning point from the "normal" to "inverted" region. Both the attenuation and reversal of the k(ex)NR value with increasing polarity are believed to be generated by the emerging contribution of the intersystem crossing process as an additional nonradiative process, which is induced by the increased spin-orbit coupling in highly polar exciplexes.     

Center manifolds for smooth invariant manifolds

We study dynamics of flows generated by smooth vector fields in in the vicinity of an invariant and closed smooth manifold . By applying the Hadamard graph transform technique, we show that there exists an invariant manifold (called a center manifold of ) based on the information of the linearization along , which contains every locally bounded solution and is persistent under small perturbations.

     

Theory of electronic structure and nuclear quadrupole interactions in the BF3–NH3 complex and methyl derivatives

Magnetic Hyperfine and Nuclear Quadrupole Interactions (HFI and NQI) are now important tools for characterization of systems of interest in materials research and industry. Boron-Trifluoride is an inorganic compound that is very important in this respect as a catalyst in chemical physics research and industry, forming complexes in the process with compounds like ammonia, water and methyl alcohol. The present paper deals with the BF₃–NH₃ complex and methyl derivatives BF₃NH_x(CH₃)_3?x for which we have studied the electronic structures, binding energies, and ¹⁹F* (I?=?5/2) nuclear quadrupole interactions using the first-principles Hartree–Fock–Roothaan procedure combined with electron correlation effects. Our results for the ¹⁹F* nuclear quadrupole coupling constant (e ² qQ/h) in units of MHz compare well with experiment. Trends in the binding energies and NQI parameters between the complexes are discussed.     

Naming Game with Multiple Hearers

A new model called Naming Game with Multiple Hearers (NGMH) is proposed in this paper. A naming game over a population of individuals aims to reach consensus on the name of an object through pair-wise local interactions among all the individuals. The proposed NGMH model describes the learning process of a new word, in a population with one speaker and multiple hearers, at each interaction towards convergence. The characteristics of NGMH are examined on three types of network topologies, namely ER random-graph network, WS small-world network, and BA scale-free network. Comparative analysis on the convergence time is performed, revealing that the topology with a larger average (node) degree can reach consensus faster than the others over the same population. It is found that, for a homogeneous network, the average degree is the limiting value of the number of hearers, which reduces the individual ability of learning new words, consequently decreasing the convergence time; for a scale-free network, this limiting value is the deviation of the average degree. It is also found that a network with a larger clustering coefficient takes longer time to converge; especially a small-word network with smallest rewiring possibility takes longest time to reach convergence. As more new nodes are being added to scale-free networks with different degree distributions, their convergence time appears to be robust against the network-size variation. Most new findings reported in this paper are different from that of the single-speaker/single-hearer naming games documented in the literature.     

Some Elementary Consequences of Perelman’s Canonical Neighborhood Theorem

In this purely expository note, we deduce a few known direct consequences of Perelman’s canonical neighborhood theorem for 3-dimensional Ricci flow and compactness theorem for 3-dimensional κ-solutions. These corollaries regard elementary properties of 3-dimensional singularity models and κ-solutions.     

Pressure-induced electron spin transition in the paramagnetic phase of the GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> Heisenberg magnet

The HS → LS spin crossover effect (high-spin → low-spin transition) induced by high pressure in the range 45–53 GPa is observed in trivalent Fe³⁺ ions in the paramagnetic phase of a Gd⁵⁷Fe₃(BO₃)₄ gadolinium iron borate crystal. This effect is studied in high-pressure diamond-anvil cells by two experimental methods using synchrotron radiation: nuclear resonant forward scattering (NFS) and Fe K _β high-resolution x-ray emission spectroscopy (XES). The manifestation of the crossover in the paramagnetic phase, which has no order parameter to distinguish between the HS and LS states, correlates with the optical-gap jump and with the insulator-semiconductor transition in the crystal. Based on a theoretical many-electron model, an explanation of this effect at high pressures is proposed.     

Type 2 intramolecular N-acylazo Diels-Alder reaction: regio- and stereoselective synthesis of bridgehead bicyclic 1,2-diazines

The type 2 intramolecular N-acylazo Diels-Alder reaction provides a regio- and stereoselective synthesis of bicyclic 1,2-diazine systems. A new method for the generation of N-acylazo dienophiles with tetra-n-butylammonium periodate is reported. X-ray crystallographic analysis allowed the quantification of structural distortions of the nonplanar bridgehead olefin and lactam functionalities in 1,2-diazine cycloadducts 11 and 15. Caprolactams and enantholactams were formed by stereoselective bridgehead alkene reduction, a process that transfers stereochemistry from the bridgehead lactam nitrogen to the bridgehead carbon. The sequence of transformations offers a convenient route for the diastereoselective synthesis of medium-ring nitrogen heterocycles and 1,4-diamines.