Qualitative and quantitative ultrashort echo time (UTE) imaging of cortical bone

We describe the use of two-dimensional ultrashort echo time (2D UTE) sequences with minimum TEs of 8 μs to image and quantify cortical bone on a clinical 3T scanner. An adiabatic inversion pulse was used for long T(2) water and fat signal suppression. Adiabatic inversion prepared UTE acquisitions with varying TEs were used for T(2) measurement. Saturation recovery UTE acquisitions were used for T(1) measurement. Bone water concentration was measured with the aid of an external reference phantom. UTE techniques were evaluated on cadaveric specimens and healthy volunteers. A signal-to-noise ratio of around 30, contrast-to-noise ratio of around 27/20 between bone and muscle/fat were achieved in tibia in vivo with a nominal voxel size of 0.23 × 0.23 × 6.0 mm(3) in a scan time of 5 min. A mean T(1) of 223 ± 11 ms and mean T(2) of 390 ± 19 μs were found. Mean bone water concentrations of 23.3 ± 1.6% with UTE and 21.7 ± 1.3% with adiabatic inversion prepared UTE sequences were found in tibia in five normal volunteers. The results show that in vivo qualitative and quantitative evaluation of cortical bone is feasible with 2D UTE sequences.     

Phenoxyl radicals: H-bonded and coordinated to Cu(II) and Zn(II)

Two pro-ligands ((R)LH) comprised of an o,p-di-tert-butyl-substituted phenol covalently bonded to a benzimidazole ((Bz)LH) or a 4,5-di-p-methoxyphenyl substituted imidazole ((PhOMe)LH), have been structurally characterised. Each possesses an intramolecular O-H[dot dot dot]N hydrogen bond between the phenolic O-H group and an imidazole nitrogen atom and (1)H NMR studies show that this bond is retained in solution. Each (R)LH undergoes an electrochemically reversible, one-electron, oxidation to form the [(R)LH] (+) radical cation that is considered to be stabilised by an intramolecular O...H-N hydrogen bond. The (R)LH pro-ligands react with M(BF(4))(2).H(2)O (M = Cu or Zn) in the presence of Et(3)N to form the corresponding [M((R)L)(2)] compound. [Cu((Bz)L)(2)] (), [Cu((PhOMe)L)(2)] (), [Zn((Bz)L)(2)] and [Zn((PhOMe)L)(2)] have been isolated and the structures of .4MeCN, .2MeOH, .2MeCN and .2MeCN determined by X-ray crystallography. In each compound the metal possesses an N(2)O(2)-coordination sphere: in .4MeCN and .2MeOH the {CuN(2)O(2)} centre has a distorted square planar geometry; in .2MeCN and .2MeCN the {ZnN(2)O(2)} centre has a distorted tetrahedral geometry. The X-band EPR spectra of both and , in CH(2)Cl(2)-DMF (9 : 1) solution at 77 K, are consistent with the presence of a Cu(ii) complex having the structure identified by X-ray crystallography. Electrochemical studies have shown that each undergo two, one-electron, oxidations; the potentials of these processes and the UV/vis and EPR properties of the products indicate that each oxidation is ligand-based. The first oxidation produces [M(II)((R)L)((R)L )](+), comprising a M(ii) centre bound to a phenoxide ((R)L) and a phenoxyl radical ((R)L ) ligand; these cations have been generated electrochemically and, for R = PhOMe, chemically by oxidation with Ag[BF(4)]. The second oxidation produces [M(II)((R)L )(2)](2+). The information obtained from these investigations shows that a suitable pro-ligand design allows a relatively inert phenoxyl radical to be generated, stabilised by either a hydrogen bond, as in [(R)LH] (+) (R = Bz or PhOMe), or by coordination to a metal, as in [M(II)((R)L)((R)L )](+) (M = Cu or Zn; R = Bz or PhOMe). Coordination to a metal is more effective than hydrogen bonding in stabilising a phenoxyl radical and Cu(ii) is slightly more effective than Zn(II) in this respect.     

CeO2 catalysed conversion of CO, NO2 and NO from first principles energetics

First principles calculations using density functional theory with corrections for on-site Coulomb interactions (DFT + U) are presented in which we compute the energy for the conversion of CO to CO(2), NO(2) to NO and NO to N(2) over ceria surfaces. The surface sensitivity is discussed on the basis of the vacancy formation energies.     

Vibrational spectroscopy and normal-mode analysis of Fe(II) octaethylporphyrin

The normal-mode spectrum for the four-coordinated heme compound Fe(II) octaethylporphyrin, Fe(OEP), has been determined by refining force constants to the experimental Fe vibrational density of states measured with nuclear resonance vibrational spectroscopy (NRVS). Convergence of the calculated spectrum to the data was achieved by first imposing D4 symmetry on the model structure as well as the force constants, progressively including different internal coordinates of motion, then allowing the true Ci (or S2) point group symmetry of the C(i)1 Fe(OEP) crystal structure. The NRVS-refined normal modes are in good agreement with Raman and IR spectra at high frequencies. Prior density functional theory predictions for a model porphyrin are similar to the core modes computed with the best-fit force field, but significant differences between D4 and Ci modes underline the sensitivity of porphyrin Fe normal modes to structural details. Some differences between the Ci best fit and the NRVS data can be attributed to intermolecular contacts not included in the normal-mode analysis.     

Stretching of polymer chains by fluctuating flow fields

We investigate polymer stretching by fluctuating flow fields via numerical solutions of the Brownian dynamics of multibead polymer chains taking into account nonlinear elasticity, hydrodynamic interactions and good solvent, excluded volume interaction effects. By varying the scaling exponent of the energy spectrum whilst keeping the same Reynolds and Deborah numbers, as well as microscale length and turnover times, we show that steeper spectra are associated with stronger stretching. We compute the probability density functions of chain length, and explain their main features by examining explicit molecular histories. We quantify the interaction between strain rate tensor structure and chain geometry as a means of understanding better the different stretching mechanisms in mild, moderate and strong polymer stretching regimes.     

Morse theory for the space of Higgs <Emphasis Type="Italic">G</Emphasis>–bundles

Fix a C ^∞ principal G–bundle E⁰_G{E^0_G} on a compact connected Riemann surface X, where G is a connected complex reductive linear algebraic group. We consider the gradient flow of the Yang–Mills–Higgs functional on the cotangent bundle of the space of all smooth connections on E⁰_G{E^0_G}. We prove that this flow preserves the subset of Higgs G–bundles, and, furthermore, the flow emanating from any point of this subset has a limit. Given a Higgs G–bundle, we identify the limit point of the integral curve passing through it. These generalize the results of the second named author on Higgs vector bundles.     

On the Stability of Travelling Waves Arising in Nematic Liquid Crystals

Abstract

The stability of travelling waves which occur when a nematic liquid crystal is subjected to crossed electric and magnetic fields has been studied previously where conditions on a control parameter q for stability to occur have been given. This article is concerned with the behaviour of the stable perturbations as time increases. For each of the three travelling wave solutions we can determine the long-term monotonic or oscillatory behaviour of the perturbations using knowledge of the spectrum of the operator governing the perturbation equation.     

Numerical solutions of the orbital equations for diatomic molecules

A basis of Hermite splines is used in conjunction with the collocation method to solve the orbital equations for diatomic molecules. Accurate solutions of the Hartree-Fock equations are obtained using iterative methods over most regions of space, while solving the equations by Gaussian elimination near the nuclear centres. In order to improve the speed and accuracy of our iterative scheme, a new self-adjoint form of the Hartree-Fock equation is derived. Using this new equation, our iterative subroutines solve the Hartree-Fock equations to one part in 10⁶. The Gaussian elimination routines are accurate to better than one part in 10⁸.     

Asymptotic enumeration of sparse 2‐connected graphs

We determine an asymptotic formula for the number of labelled 2‐connected (simple) graphs on n vertices and m edges, provided that m ‐ n →∞ and m = O(nlog n) as n →∞. This is the entire range of m not covered by previous results. The proof involves determining properties of the core and kernel of random graphs with minimum degree at least 2. The case of 2‐edge‐connectedness is treated similarly. We also obtain formulae for the number of 2‐connected graphs with given degree sequence for most (“typical”) sequences. Our main result solves a problem of Wright from 1983. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013