Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas

The superfluid fraction of an atomic cloud is defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. A fully quantum mechanical calculation of this moment is based on the dispersion of L_z instead of quasi-classical averages. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples. Received 30 June 2000     

Theory of atomic diffraction from evanescent waves

We review recent theoretical models and experiments dealing with the diffraction of neutral atoms by a reflection grating, formed by a standing evanescent wave. We analyze diffraction mechanisms proposed for normal and grazing incidence, point out their scopes and confront the theory with experiment. Received: 12 June 1999 / Published online: 8 September 1999     

Interactions between Functional Groups. Part III. The Structure of N,N-Dimethyl-8-nitro-1-naphthaleneamine in Seven Crystalline Environments

The N,N-dimethyl-8-nitro-1-naphthaleneamine molecule has been observed in seven environments in three crystal modifications. A range of conformations, related by conrotatory motions about the two exocyclic C? N bonds, is observed. In all seven conformations, the lone pair of the amino N-atom is directed approximately towards the nitro N-atom, which is slightly pyramidalized towards the amino group. The NO₂ group appears to be a poorer through-space electron acceptor than the carboxylic ester group, in contrast to their through-bond electron-accepting properties.     

Synthesis,Structure and Chemistry of a Twisted Olefinic Bis-didentate Proligand: 5,5′-Bi-5H-cyclopenta[2,1-b : 3,4-b′]dipyridinylidene

The elusive chiral twisted alkene, 5,5′-bi-5H-cyclopenta[2,1-b : 3,4-b′]dipyridinylidene, known also as 9,9′-bi-4,5-diazafluorenylidene (BDAF), has been prepared in racemic form from 9-bromo-4,5-diazafluorene and from 9,9′-bi-4,5-diazafluorenyl and fully characterised. X-Ray measurements show that there is a twist of 37.8° about the double bond between the 4,5-diazafluorenylidene units. A 1 : 1 charge-transfer compound with 7,7,8,8-tetracyanoquinodimethane (TCNQ) contains an unusual packing arrangement which is centred around the formation of spiral stacks. Each BDAF molecule contributes one 4,5-diazofluorenylidene unit to the backbone of the stack, while the second half is involved in hydrogen-bonding interactions and additional stacking with TCNQ. Examples of complexes containing the axially symmetric tetradentate ligand binding to one and to two metal ions, [M(bdaf)Cl₂] and [(MCl₂)₂(bdaf)] (M=Co, Ni, Zn), are reported.     

ACCURATE NUMERICAL SIMULATION OF ADVECTION USING LARGE TIME STEPS

This paper describes a technique for achieving accurate numerical simulations of advective transport at large Courant numbers using large time steps. The scheme is called ULTIMATE DISCUS and it implements Leonard's universal flux limiter and QUICKEST algorithms within a semi- Lagrangian treatment of advection. This enables the scheme to achieve monotonic solutions, mass conservation and, most importantly, high accuracy without any limit on the time step (or Courant number). The results of numerical experiments of advection over a fixed distance show that the accuracy of the method increases with increasing spatial resolution and generally increases (but in a non-trivial manner) with increasing Courant number. Accuracy is exact at all integer values of Courant number; for Courant numbers increasing between zero and one, accuracy improves rapidly and monotonically; for other integer–integer ranges of Courant number there is a minimum of accuracy close to the mid-range value. This behaviour is explained in terms of the known accuracy of the QUICKSET algorithm as a function of Courant number and the reducing number of interpolative steps required in the simulations as the Courant number increases. The use of the flux limiter is shown to remove non-physical oscillations from the solution, but at the price of a few per cent reduction in global accuracy caused by increased suppression of peak values. © 1997 by John Wiley & Sons, Ltd.     

1,6‐Interactions between di­methyl­amino and aldehyde groups in two bi­phenyl derivatives

The title compounds, 2‐(di­methyl­amino)­bi­phenyl‐2′‐carbox­aldehyde, C₁₅H₁₅NO, and 2‐(di­methyl­amino)­bi­phenyl‐2′,6′‐dicarbox­aldehyde, C₁₆H₁₅­NO₂, show similar 1,6‐interactions [N?C=O 2.929 (3) to 3.029 (3) Å] between the di­methyl­amino and aldehyde groups located in the ortho positions of the two rings, which lie at 58.1 (1)–62.4 (1)° to each other.     

Electrical characterisation of AlGaN/GaN heterostructure wafers for high-power HFETs

Undoped 28 nm AlGaN on 1 μm GaN was grown by MOVPE for high power microwave HFETs. Non-destructive methods for rapid characterisation of the layers are described. Double contact mercury probe capacitance voltage measurements gave valuable information on AlGaN layer leakage, thickness and quality, but only gave an estimate of the carrier concentration and pinch-off voltage due to the absence of an ohmic contact to the 2DEG layer. A non-contact resistivity mapping system gave accurate average sheet resistance, but underestimated the cross-wafer variation.     

Cubic arcs in cubic nets

The idea of an arc in a finite plane or block design, and in particular of a maximal arc, is extended to nets. This concept is explored, and in particular 3-arcs in cubic nets are characterized.