Quantum Hall Quantized Cyclotron Entrance Channels

Quantum Hall plateaus are entered via quantized cyclotron (QC) cloud-chamber orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both canonical and magnetic angular momentum components, which add together to form the invariant kinematic angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the u _n,l eigenstates u _n,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.     

The simulation of 31P NMR line shapes of lipid bilayers using an analytically soluble model

Van Faassen's method for obtaining an explicit solution to a first order stochastic differential equation is applied to the simulation of 31P NMR line shapes of unoriented phospholipid bilayers in the Lalpha phase and of oriented bilayers in both the Lalpha and Lbeta' phases. The effects of the two slowest motions on the density matrix are described by the stochastic Liouville equation (SLE) which is solved analytically using the method of van Faassen. These two slowest motions are assumed to be a rotational re-orientation about the long molecular axis and a uniform wobble of this axis within a conical volume with re-orientation rates characterised by correlation times tau(parallel) and tau(perpendicular) respectively. In the present work the Hamiltonian contains the intramolecular dipole-dipole interaction between the phosphorous nucleus and the four closest methylene protons of the choline headgroup, as well as the anisotropic chemical shielding interaction. Hence the contribution to relaxation from cross correlation between the dipole-dipole and anisotropic chemical shielding interactions is included. The reorientation of the headgroup is assumed to be a rotation sufficiently fast to lead to complete axially symmetric averaging of the Hamiltonian about the rotational axis (the P-O11 bond axis). Evaluation of the line shape in the present work involves only numerical integration and is therefore less computationally demanding than the large matrix inversions involved in the approaches of Campbell, Freed et al. The present theory also uses fewer parameters than that of Dufourc et al. but nevertheless results in good agreement with these authors' measurements on DMPC bilayers, using a fixed value of 10 for the ratio tau(perpendicular)/tau(parallel) in the case of the Lalpha phase. However, in contrast to Dufourc et al., we find that these correlation times are equal for the Lbeta' phase. Finally, we have simulated the decoupled powder line shapes obtained from the Lbeta' phase of DPPC by Campbell and Meirovitch. Again, we get good agreement providing tau(perpendicular)=tau(parallel).     

Lewis acid mediated cyclisations of silylated methylenecyclopropyl hydrazones

Silylated methylenecyclopropyl hydrazones on treatment with BF3 x Et2O cyclise to give heterocyclic products involving a novel sequence of hydride and silyl shifts via a series of increasingly stable cationic intermediates.     

Antitumour polycyclic acridines. Palladium(0) mediated syntheses of quino[4,3,2-kl]acridines bearing peripheral substituents as potential telomere maintenance inhibitors

Pd(0) mediated couplings between substituted 2-(pivaloylamino)benzeneboronic acids and 3,6-disubstituted-10-methylacridones 13 bearing a bromo or trifluoromethylsulfonyloxy substituent in the 1-position yield intermediate 1-arylacridones 16 which can be can be cyclised to new 8-methylquino[4,3,2-kl]acridines 17 with phosphorus oxychloride or 6 M HCI in EtOH. Heck reactions between triflate-substituted substrates 17 and acrylic acid derivatives afforded quinoacridines with unsaturated side-chains in the 6-position. Alkylboranes, prepared by interaction of 9-borabicyclo[3,3,1]nonane (9-BBN) and allyl acetate or N-allyltrifluoroacetamide, participated in Suzuki-Miyaura reactions with chloro-substituted 8-methylquinoacridines to form derivatives bearing functionalised propyl groups in the 6- and 10-positions. Representative 8-methylquinoacridines were methylated with methyl iodide to yield telomerase-inhibitory 8,13-dimethylquinoacridinium iodides 24.     

Syntheses of dendritic branches based on L-lysine: is the stereochemistry preserved throughout the synthesis?

This paper reports the syntheses of individual dendritic branches based on L-lysine and functionalised with either Boc or Bz surface groups. Convergent and divergent synthetic approaches were employed and the preservation of stereochemistry during the syntheses was monitored using polarmetry, NMR and HPLC. In addition, racemic dendritic branches based on D,L-lysine were synthesised for comparative purposes. It was observed that the preservation of stereochemistry in the dendritic peptide was dependent on the method of synthesis, with divergent methodology being preferred. The results are discussed in terms of the known stereochemical outcomes of traditional peptide coupling processes, and are generalised to the synthesis of other dendritic peptides. Such observations about the chirality of dendritic peptides are of relevance to chemists developing dendritic systems for applications where single enantiomer dendrimers would clearly be preferred, such as enantioselective catalysis or pharmaceutical chemistry.     

Application of cogwheel phase cycling to sideband manipulation experiments in solid-state NMR

Cogwheel phase-cycling schemes are applied to sideband suppression and sideband separation experiments in solid-state NMR. It is shown that cogwheel phase cycles lead to the elimination of most pulse imperfection effects, while using far fewer experimental signal acquisitions than conventional phase-cycling methods.     

A UNIFIED QUANTUM HALL CLOSE-PACKED COMPOSITE BOSON (CPCB) MODEL

Single-wavelength Landau cyclotron orbitals (SWOs) have been used as quantum Hall basis states to reproduce integer quantum Hall plateaus in a two-dimensional (2D) close-packing representation. But at the high magnetic fields B that correspond to fractional Hall plateaus, these SWOs are too small to give close packing. It is conventionally assumed that the fractional quantum Hall states are formed from collective electron excitations (CEEs). However, by invoking the use of multiple-wavelength Landau orbitals (MWOs), we can close-pack the fractional Hall plateaus in the same manner as the integer plateaus. Quantum Hall plateaus are characterized by the filling fractions n _e/n =k/m, where k=1, 2,... (all integers) and m=1, 3,... (all odd integers), and where n _e and n are the 2D electron e and magnetic flux =h/e densities, respectively. A composite particle (CP) is a bound state of an electron and m flux quanta . If m is even or odd, the CP is a composite fermion (CF) or composite boson (CB). In the CEE models, both CF and CB formalisms have been used. In the alternative MWO approach introduced here, the close-packed MWOs on a =k/m plateau each contain m de Broglie wavelengths . Each MWO traps m external flux quanta, produces m diamagnetic induced flux quanta, and carries the filling fraction , which accounts for the extreme accuracy (one part in 10⁸) of the Hall plateau conductance, _H= e ²/h. Since m is odd, these MWOs are CB states, and they form a boson condensate of close-packed composite boson (CPCB) states. The m=1 (m<1) CPCBs tile the integer (fractional) Hall plateaus. The filling fraction index k corresponds to k layers of CPCB orbitals. Plateau formation itself is due to the linear B dependence of the density of CPCB states. The CPCBs are decoupled from the semiconductor substrate, and hence may have large m* effective mass values. THE MWOs near the =1/2 non-plateau region are m=2 CF states.     

Asymptotic infiltration into a soil which contains cracks or holes but whose surface is otherwise impermeable

An asymptotic, one-dimensional Green-Ampt model is derived for infiltration into a soil whose surface is impermeable except for regularly spaced vertical cracks, and infiltration into a cylindrical soil column whose top surface is also impermeable except for a central hole. The model is valid at times when the wetting front has become horizontal and corresponds to one-dimensional infiltration initiated from a plane lying above or below the soil surface, depending on the crack spacing/depth ratio (or column radius/hole depth ratio). When applicable, asymptotic Green-Ampt solutions are shown to agree well, in selected cases, with corresponding finite difference solutions of the saturated-unsaturated flow equations.