Bend and splay elastic constants of a discotic nematic

We report the dielectric constants and the splay and bend elastic constants of hexan-dodecanoyloxy truxene in the nematic phase, which occurs between two columnar phases. The dielectric anisotropy is positive. The elastic constants are ∼10−7 dyne, which is of the same order as for nematics of rod-like molecules. Further, k33 > k11, probably as a consequence of the columnar short range order in the medium

19-Ferrocenyl-18-oxa-8,16-diaza­penta­cyclo­[8.6.3.01,10.02,7.012,16]nona­deca-2(7),3,5-triene-9,17-dione

In the title compound, [Fe(C5H5)(C21H19N2O3)], both pyrrol­idine rings of the pyrrolizine substructure show an envelope conformation. In the ferrocenyl moiety, the unsubstituted cyclo­penta­dienyl ring is disordered over two orientations with site occupancies of 0.64 (2) and 0.36 (2). In the pyrrolizine ring, one C atom is disordered over two positions, with site occupancies of 0.71 (1) and 0.29 (1). Intra­molecular C—H⋯O inter­actions occur. The crystal packing is established through weak inter­molecular C—H⋯O and N—H⋯O inter­actions

4′-Ferrocenyl-1′-methylacenapthylene-1-spiro-2′-pyrrolidine-3′-spiro-2′′-indane-2,1′′,3′′(1H)-trione

In the title compound, [Fe(C5H5)(C29H20NO3)], the acenaphthyl­ene ring system makes a dihedral angle of 83.77 (3)° with the indane-1,3-dione ring system. The central pyrrolidine ring exhibits a twist conformation. In the crystal, mol­ecules are linked by a weak inter­molecular C—H⋯O inter­action into a chain along the b axis. Two weak intra­molecular C—H⋯O inter­actions are also present

Methyl 9-p-tolyl-8a,9,9a,10,11,12,13,14a-octa­hydro-8H-benzo[f]chromeno[3,4-b]indolizine-8a-carboxyl­ate

In the title compound, C28H29NO3, the fused pyrrolidine and piperidine rings of the octa­hydro­indolizine unit exhibit envelope and chair conformations, respectively. The dihedral angle between the naphthalene ring system and the benzene ring is 40.37 (5)°. The crystal packing is stabilized by weak inter­molecular C—H⋯O inter­actions

Methyl 9-(4-bromo­phen­yl)-8a,9,9a,10,11,12,13,14a-octa­hydro-8H-benzo[f]chromeno[3,4-b]indolizine-8a-car­box­ylate

In the title compound, C27H26BrNO3, the mean plane of the naphthalene ring system makes a dihedral angle of 22.0 (1)° with the bromo-substituted benzene ring. The pyrrolidine and piperidine rings exhibit envelope and chair conformations, respectively. An inter­molecular C—H⋯Br inter­action is observed

Weighing neutrinos using high redshift galaxy luminosity functions

Laboratory experiments measuring neutrino oscillations, indicate small mass differences between different mass eigenstates of neutrinos. The absolute mass scale is however not determined, with at present the strongest upper limits coming from astronomical observations rather than terrestrial experiments. The presence of massive neutrinos suppresses the growth of perturbations below a characteristic mass scale, thereby leading to a decreased abundance of collapsed dark matter halos. Here we show that this effect can significantly alter the predicted luminosity function (LF) of high redshift galaxies. In particular we demonstrate that a stringent constraint on the neutrino mass can be obtained using the well measured galaxy LF and our semi-analytic structure formation models. Combining the constraints from the Wilkinson Microwave Anisotropy Probe 7 year (WMAP7) data with the LF data at z = 4, we get a limit on the sum of the masses of 3 degenerate neutrinos \Sigma m_\nu < 0.52 eV at the 95 % CL. The additional constraints using the prior on Hubble constant strengthens this limit to \Sigma m_\nu < 0.29 eV at the 95 % CL. This neutrino mass limit is a factor of order 4 improvement compared to the constraint based on the WMAP7 data alone, and as stringent as known limits based on other astronomical observations. As different astronomical measurements may suffer from different set of biases, the method presented here provides a complementary probe of \Sigma m_\nu . We suggest that repeating this exercise on well measured luminosity functions over different redshift ranges can provide independent and tighter constraints on \Sigma m_\nu .Comment: 14 pages, 7 figures, submitted to PR

Simulating Particle Dispersions in Nematic Liquid-Crystal Solvents

A new method is presented for mesoscopic simulations of particle dispersions in nematic liquid crystal solvents. It allows efficient first-principle simulations of the dispersions involving many particles with many-body interactions mediated by the solvents. A simple demonstration is shown for the aggregation process of a two dimentional dispersion.Comment: 5 pages, 5 figure

Structure and vibrational properties of carbon tubules

The structure of multilayered carbon tubules has been investigated by electron microscopy and X-ray diffraction. The structure of tubules is characterized by disorder in the stacking of cylindrical graphene sheets. Raman scattering measurements have been carried out in tubules and compared with graphite. The observed features in the Raman spectra in tubules can be understood in terms of the influence of disorder. The additional Raman modes predicted for single layer carbon tubules have not been observed

Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models

Motivated by a real-life problem of sharing social network data that contain sensitive personal information, we propose a novel approach to release and analyze synthetic graphs in order to protect privacy of individual relationships captured by the social network while maintaining the validity of statistical results. A case study using a version of the Enron e-mail corpus dataset demonstrates the application and usefulness of the proposed techniques in solving the challenging problem of maintaining privacy \emph{and} supporting open access to network data to ensure reproducibility of existing studies and discovering new scientific insights that can be obtained by analyzing such data. We use a simple yet effective randomized response mechanism to generate synthetic networks under $\epsilon$-edge differential privacy, and then use likelihood based inference for missing data and Markov chain Monte Carlo techniques to fit exponential-family random graph models to the generated synthetic networks.Comment: Updated, 39 page

6-Phenyl-5a,6,6a,7,12,13a-hexa­hydro-5H-benzo[6,7]indolizino[3,2-a]pyrrolizine

In the title compound, C23H22N2, the central pyrrolidine ring adopts an envelope conformation. The benzene ring of the hexa­hydro­pyrroloisoquinoline ring system makes dihedral angles of 83.43 (6) and 61.99 (10)°, respectively, with the phenyl and pyrrole rings. In the crystal structure, weak C—H⋯π inter­actions are observed