Observation of weak impact of a stochastic magnetic field on fast-ion confinement

Fast ions are observed to be very well confined in the Madison Symmetric Torus reversed field pinch despite the presence of stochastic magnetic field. The fast-ion energy loss is consistent with the classical slowing down rate, and their confinement time is longer than expected by stochastic estimates. Fast-ion confinement is measured from the decay of d-d neutrons following a short pulse of a 20 keV atomic deuterium beam. Ion confinement agrees with computation of particle trajectories in the stochastic magnetic field, and is understood through consideration of ion guiding center islands.     

Mode-locked fiber laser frequency-controlled with an intracavity electro-optic modulator

We demonstrate a mode-locked, erbium-doped fiber laser with its repetition frequency synchronized to a second fiber laser via an intracavity electro-optic modulator (EOM). With servo control from the EOM (bandwidth approximately 230 kHz) and a slower speed intracavity piezoelectric transducer (resonance at approximately 20 kHz), we demonstrate stabilization of the repetition frequency with an in-loop rms timing jitter of 10 fs, integrated over a bandwidth from 1 Hz to 100 kHz. This represents what is to our knowledge the first time an EOM has been introduced inside a mode-locked laser cavity for fast servo action and the lowest timing jitter reported for a mode-locked fiber laser.     

Chromium(0)-promoted multicomponent cycloaddition of tethered diynes with cyclic trienes: application to the total synthesis of 9-epi-pentalenic acid

An efficient protecting group controlled regioselective chromium(0)-mediated three-component higher order cycloaddition of tethered diynes with cyclic trienes that generates five rings and six stereogenic centers in one step is described. Following a sequence of reactions featuring a chemoselective Baeyer-Villiger rearrangement and a regioselective cyclopropane hydrogenolysis, the total synthesis of 9-epi-pentalenic acid was achieved.     

Highly symmetric networks derived from cubane-related octametallic complexes of a new oxyanion of carbon, C4O7(4-), each molecule attached to eight neighbors by 24 equivalent hydrogen bonds

Aqueous reaction mixtures containing dihydroxyfumaric acid, M2+ (M = Zn, Co, Fe, and Mg) and acetate ion at room temperature give crystals, suitable for single-crystal X-ray diffraction studies, of composition [(MII)8(C4O7)4(H2O)12].24H2O, in which the C4O74- component is the alkoxide-tricarboxylate tetra-anionic species -OC(CO2-)3, a new oxyanion of carbon. All four compounds crystallize in the body-centered space group I3m with cell dimensions a approximately 15.0 A. Discrete electrically neutral [(MII)8(C4O7)4(H2O)12] molecules are present, with a cubane-like core consisting of four trigonal prismatic metal centers and four mu3-alkoxo bridges from separate -OC(CO2-)3 ligands. The octametallic molecule is highly symmetrical, with four fac tri-aqua octahedral metal centers tetrahedrally appended to the central cubane-based [(MII)8(C4O7)4 ]8- unit. The molecules assemble in the crystal in a body-centered cubic fashion, each being attached to its eight neighbors by 24 equivalent hydrogen bonds-an extreme example of self-complementarity.     

The inelastic neutron scattering spectrum of H3B:NH3 and the reproduction of its solid-state features by periodic DFT

The inelastic neutron scattering (INS) and periodic density functional theory (DFT) vibrational spectra of H3B:NH3 are reported to 1600 cm-1. The H3B:NH3 structural and INS features, specifically the reduced solid-state B:N dative bond length and the altered B:N stretching frequency, are reproduced by the periodic DFT calculations, placing the B:N stretching mode at 800 cm-1, in excellent agreement with experiment relative to previous nonperiodic theoretical treatments of this molecule.     

Chaotic cluster itinerancy and hierarchical cluster trees in electrochemical experiments

Experiments on an array of 64 globally coupled chaotic electrochemical oscillators were carried out. The array is heterogeneous due to small variations in the properties of the electrodes and there is also a small amount of noise. Over some ranges of the coupling parameter, dynamical clustering was observed. The precision-dependent cluster configuration is analyzed using hierarchical cluster trees. The cluster configurations varied with time: spontaneous changes of number of clusters and their configurations were detected. Simple transitions occurred with the switch of a single element or groups of elements. During more complicated transitions subclusters were exchanged among clusters but original cluster configurations were revisited. At weaker coupling the system itinerated among lower-dimensional quasistationary chaotic two-cluster states and higher-dimensional states with many clusters. In this region the transitions showed characteristics of on-off intermittency.     

Why CH3CH3+* formation competes with H* loss from CCCO C3H6O+* isomers

How formation of CH3CH3+* competes with H* loss from C3H6O+* isomers with the CCCO framework has been a puzzle of gas phase ion chemistry because the first reaction has a substantially higher threshold and a supposedly tighter transition state. These together should make CH3CH3+* formation much the slower of the two reactions at all internal energies. However, the rates of the two reactions become comparable at about 20 kJ x mol(-1) above the threshold for CH3CH3+* formation. It was recently shown that losses of atomic fragments increase in rate much more slowly with increasing internal energy than do the rates of competing dissociations to two polyatomic fragments. This occurs because fewer frequencies are substantially lowered in transition states for the former type of reaction than for the latter. The resulting lower transition state sums of states cause the rates of dissociations producing atoms as fragments to increase much more slowly than competing processes with increasing energy. Here we show that this is why CH3CH3+* formation competes with H* loss from CH3CH2CHO+*. These results further establish that the dependence on energy of the rate of a simple unimolecular dissociation is usually directly related to the number of rotational degrees of freedom in the products, a newly recognized factor in determining the dependence of unimolecular reaction rates on internal energy.     

A new bound for the smallest

Let denote the number of primes and let denote the usual integral logarithm of . We prove that there are at least integer values of in the vicinity of with . This improves earlier bounds of Skewes, Lehman, and te Riele. We also plot more than 10000 values of in four different regions, including the regions discovered by Lehman, te Riele, and the authors of this paper, and a more distant region in the vicinity of , where appears to exceed by more than . The plots strongly suggest, although upper bounds derived to date for are not sufficient for a proof, that exceeds for at least integers in the vicinity of . If it is possible to improve our bound for by finding a sign change before , our first plot clearly delineates the potential candidates. Finally, we compute the logarithmic density of and find that as departs from the region in the vicinity of , the density is , and that it varies from this by no more than over the next integers. This should be compared to Rubinstein and Sarnak.