Ring Airy-Like Beams along Predesigned Parabolic Trajectories

By phase-modulating ring Airy Gaussian beams, ring Airy-like beams propagating along predesigned parabolic trajectories are presented which combine the properties of accelerating beams and abruptly autofocusing beams analytically and numerically for the first time. The enhancement of the quadratic term ratio α shortens the autofocus distance and increases the slope of the beams after autofocusing. Interestingly, the main lobe tends to break into pieces as α increases and the possible reasons have been discussed. Furthermore, the distribution factor β and the radius of the primary r₀ can prominently affect the autofocus distance and the intensity at the focal point but do not change the slope of the beams after the autofocusing. In addition, the self-healing properties are validated to be retainable while RAiG beams via predesigned parabolic trajectories with various α.     

Influence of spin–orbit interaction,Zeeman effect and light polarisation on the electronic and optical properties of pseudo-elliptic quantum rings under magnetic field

ABSTRACT

We theoretically investigated the influences of the magnetic field and light polarisation on the electronic and optical properties of a GaAs/GaAlAs pseudo-elliptic quantum ring, modelled by an outer ellipsis and an inner circle, in the presence of the Rashba and Dresselhaus spin–orbit interactions and Zeeman effect. We show that Aharonov-Bohm oscillations of the energy spectrum are not affected by the presence of the Zeeman effect alone but, in the presence of Rashba and Dresselhaus spin–orbit couplings, the periodicity of certain levels becomes hardly definite. The Zeeman effect generally enhances/diminishes the separation levels produced by Rashba/Dresselhaus interactions (SOI) and when both types of SOI are considered, the effect depends on their relative strength. The magnetic field can trigger spin-flip for each type of spin–orbit interaction and Zeeman effect or their combination through anticrossings in the energy spectra. Our results reveal that the absorption spectra are very sensitive to the magnetic field and light polarisation. For all polarisations considered, the magnetic field increment leads to the redshift or blueshift of some particular peaks (an effect of this ring geometry) and a better separation of the peaks. The x-polarised light determines spectra with many small, but separated peaks while the circular polarised light leads to spectra with large peaks of high amplitude.     

Synthesis,Characterisation and Crystal Structures of Two Bi‐oxadiazole Derivatives Featuring the Trifluoromethyl Group

The synthesis, characterisation, and crystal structure determination of the closely related compounds 3,3′‐bi‐(5‐trifluoromethyl‐1,2,4‐oxadiazole) and 5,5′‐bi‐(2‐ trifluoromethyl‐1,3,4‐oxadiazole) are reported. These two compounds are known for their bioactivity; however, in this study they serve as model compounds to evaluate the suitability of the heterocyclic oxadiazole ring system for energetic materials when the fluorine atoms in the exocyclic CF₃ groups are substituted successively by nitro groups. Quantum chemical calculations for the bi‐1,3,4‐ oxadiazole derivatives with difluoronitromethyl, fluorodinitromethyl, and trinitromethyl groups have been carried out and predict promising energetic performances for both explosive and propulsive applications.     

Low glass transition temperature polymer electrolyte prepared from ionic liquid grafted polyethylene oxide

In this contribution, we report a new type of poly (ionic liquids) prepared by imidazolium ionic liquids directly grafting onto polyethylene oxide backbone. Different molecular weights of poly (ionic liquids) are obtained with a low glass transition temperature up to ?14 °C. The materials as polymer electrolyte achieve a high conductivity around 10^?5 S cm^?1 at 30 °C and close to 10^?3 S cm^?1 at 90 °C. High viscosity up to 4000 Pa s at room temperature would minimize the electrolytes leaking in electrochemical devices. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2104–2110     

Self‐healing of poly(propylene oxide)‐polybenzoxazine thermosets by photoinduced coumarine dimerization

In this work, a self‐healing strategy for poly(propylene oxide)s bearing coumarine‐benzoxazine units (PPO‐CouBenz)s based on light induced coumarine dimerization reactions is described. Four different types of poly(propylene oxide) amines with molecular weights ranging from 440 to 5000 Da were reacted with formaldehyde and 4‐methyl‐7‐hydroxycoumarin to yield desired (PPO‐CouBenz)s. The crosslinked polymer films were prepared by solvent casting of various compositions of PPO‐CouBenzs in chloroform followed by thermal ring opening reaction of benzoxazine groups at 210–240 °C. Thermal curing and thermal stability of the initial PPOs and final products were investigated. Using allyl benzoxazine in the formulation, it was demonstrated that the toughness of the films was improved. Photoinduced healing of coumarin‐based cured PPO‐CouBenz polymer films was investigated. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2911–2918     

Injective and automorphism-invariant non-singular modules

Every automorphism-invariant non-singular right A-module is injective if and only if the factor ring of the ring A with respect to its right Goldie radical is a right strongly semiprime ring.     

Columnar Liquid‐Crystalline Dinaphthoperylenetetracarboxdiimides

Although the double Friedel–Crafts acylation of arenes with ethyl chloroglyoxylate is hindered by the strongly deactivating effect of the first‐entering glyoxylic substituent, the double reaction is successful with the reactive arene perylene under long reaction times and with concomitant ester hydrolysis. The reaction is regiospecific, giving the 3,9‐regioisomer exclusively. This perylenylenediglyoxylic acid is condensed first with o‐bromophenylacetic acid and then with α‐branched alkylamines to yield the title compounds. Whilst the corresponding tetraalkyl esters only show monotropic mesophases, these diimides show enantiotropic columnar mesophases that can be maintained at room temperature if racemically branched alkyl chains of moderate size are used. A palladium‐induced C?C bond migration during the build‐up of the arene system leads to an isomeric side product of reduced symmetry that can be isolated by aggregation‐controlled chromatographic separation. The HOMO and LUMO energies of the title compounds are considerably higher than those of established perylenetetracarboxdiimides.