Ring Expansion Of Alkylidenecarbenes Derived From Lactams, Lactones, And Thiolactones Into Strained Heterocyclic Alkynes: A Theoretical Study

Strained cycloalkynes are of considerable interest to theoreticians and experimentalists, and possess much synthetic value as well. Herein, a series of cyclic alkylidenecarbenes—formally obtained by replacing the carbonyl oxygen of four-, five-, and six-membered lactams, lactones, and thiolactones with a divalent carbon—were modeled at the CCSD(T)/cc-pVTZ//B3LYP/6-311+G** and CCSD(T)/cc-pVTZ//CCSD/6-311+G** levels of theory. The singlet carbenes were found to be more stable than the triplets. The strained heterocyclic alkynes formed by ring expansion of these singlet carbenes were also modeled. Interestingly, the C≡C bonds in the five-membered heterocycles, obtained from the rearrangement of β-lactam- and β-lactone-derived alkylidenecarbenes, displayed lengths intermediate between formal double and triple bonds. Furthermore, 2-(1-azacyclobutylidene)carbene was found to be nearly isoenergetic with its ring-expanded isomer, and 1-oxacyclopent-2-yne was notably higher in energy than its precursor carbene. In all other cases, the cycloalkynes were lower in energy than the corresponding carbenes. The transition states for ring-expansion were always lower for the 1,2-carbon shifts than for 1,2-nitrogen or oxygen shifts, but higher than for the 1,2-sulfur shifts. These predictions should be verifiable using carbenes bearing appropriate isotopic labels. Computed vibrational spectra for the carbenes, and their ring-expanded isomers, are presented and could be of value to matrix isolation experiments

Bessel processes, the Brownian snake and super-Brownian motion

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in memory of Marc Yo

Astrophotonic micro-spectrographs in the era of ELTs

The next generation of Extremely Large Telescopes (ELT), with diameters up to 39 meters, will start opera- tion in the next decade and promises new challenges in the development of instruments. The growing field of astrophotonics (the use of photonic technologies in astronomy) can partly solve this problem by allowing mass production of fully integrated and robust instruments combining various optical functions, with the potential to reduce the size, complexity and cost of instruments. In this paper, we focus on developments in integrated micro-spectrographs and their potential for ELTs. We take an inventory of the identified technologies currently in development, and compare the performance of the different concepts. We show that in the current context of single-mode instruments, integrated spectrographs making use of, e.g., a photonic lantern can be a solution to reach the desired performance. However, in the longer term, there is a clear need to develop multimode devices to improve overall the throughput and sensitivity, while decreasing the instrument complexity.Comment: 9 pages. 2 figures. Proceeding of SPIE 9147 "Ground-based and Airborne Instrumentation for Astronomy V

Detection of confinement and jumps in single molecule membrane trajectories

We propose a novel variant of the algorithm by Simson et al. [R. Simson, E.D. Sheets, K. Jacobson, Biophys. J. 69, 989 (1995)]. Their algorithm was developed to detect transient confinement zones in experimental single particle tracking trajectories of diffusing membrane proteins or lipids. We show that our algorithm is able to detect confinement in a wider class of confining potential shapes than Simson et al.'s one. Furthermore it enables to detect not only temporary confinement but also jumps between confinement zones. Jumps are predicted by membrane skeleton fence and picket models. In the case of experimental trajectories of $\mu$-opioid receptors, which belong to the family of G-protein-coupled receptors involved in a signal transduction pathway, this algorithm confirms that confinement cannot be explained solely by rigid fences.Comment: 4 pages, 3 figure

Shock statistics in higher-dimensional Burgers turbulence

We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated.Comment: 4 pages, 8 figure

The CANADA-FRANCE REDSHIFT SURVEY XIII: The luminosity density and star-formation history of the Universe to z ~ 1

The comoving luminosity density of the Universe is estimated from the CFRS faint galaxy sample in three wavebands (2800A, 4400A and 1 micron) over the redshift range 0 < z < 1. In all three wavebands, the comoving luminosity density increases markedly with redshift. For a (q_0 = 0.5, Omega = 1.0) cosmological model, the comoving luminosity density increases as $(1+z)^{2.1 \pm 0.5}$ at 1 micron, as $(1+z)^{2.7 \pm 0.5}$ at 4400A and as $(1+z)^{3.9 \pm 0.75}$ at 2800A, these exponents being reduced by 0.43 and 1.12 for (0.05,0.1) and (-0.85,0.1) cosmological models respectively. The variation of the luminosity density with epoch can be reasonably well modelled by an actively evolving stellar population with a Salpeter initial mass function (IMF) extending to 125 M_sun, a star-formation rate declining with a power 2.5, and a turn-on of star-formation at early epochs. A Scalo (1986) IMF extending to the same mass limit produces too many long-lived low mass stars. This rapid evolution of the star-formation rate and comoving luminosity density of the Universe is in good agreement with the conclusions of Pei and Fall (1995) from their analysis of the evolving metallicity of the Universe. One consequence of this evolution is that the physical luminosity density at short wavelengths has probably declined by two orders of magnitude since z ~ 1.Comment: uuencoded compressed tar file containing 8 page Tex file, 2 postscript figures and 2 tables. Ap J Letters, in press. Also available at http://www.astro.utoronto.ca/~lilly/CFRS/papers.htm

Observation of correlations up to the micrometer scale in sliding charge-density waves

High-resolution coherent x-ray diffraction experiment has been performed on the charge density wave (CDW) system K$_{0.3}$MoO$_3$. The $2k_F$ satellite reflection associated with the CDW has been measured with respect to external dc currents. In the sliding regime, the $2k_F$ satellite reflection displays secondary satellites along the chain axis which corresponds to correlations up to the micrometer scale. This super long range order is 1500 times larger than the CDW period itself. This new type of electronic correlation seems inherent to the collective dynamics of electrons in charge density wave systems. Several scenarios are discussed.Comment: 4 pages, 3 figures Typos added, references remove