Ehrhart Series and Lattice Triangulations

We express the generating function for lattice points in a rational polyhedral cone with a simplicial subdivision in terms of multivariate analogues of the h-polynomials of the subdivision and “local contributions” of the links of its nonunimodular faces. We also compute new examples of nonunimodal h ^*-vectors of reflexive polytopes. Supported by the Clay Mathematics Institute.     

The effects of ionization potential depression on the spectra emitted by hot dense aluminium plasmas

Recent experiments at the Linac Coherent Light Source (LCLS) X-ray Free-Electron-Laser (FEL) have demonstrated that the standard model used for simulating ionization potential depression (IPD) in a plasma (the Stewart–Pyatt (SP) model, J.C. Stewart and K.D. Pyatt Jr., Astrophysical Journal 144 (1966) 1203) considerably underestimates the degree of IPD in a solid density aluminium plasma at temperatures up to 200 eV. In contrast, good agreement with the experimental data was found by use of a modified Ecker–Kröll (mEK) model (G. Ecker and W. Kröll, Physics of Fluids 6 (1963) 62–69). We present here detailed simulations, using the FLYCHK code, of the predicted spectra from hot dense, hydrogenic and helium-like aluminium plasmas ranging in densities from 0.1 to 4 times solid density, and at temperatures up to 1000 eV. Importantly, we find that the greater IPDs predicted by the mEK model result in the loss of the n = 3 states for the hydrogenic ions for all densities above ≈0.8 times solid density, and for the helium-like ions above ≈0.65 solid density. Therefore, we posit that if the mEK model holds at these higher temperatures, the temperature of solid density highly-charged aluminium plasmas cannot be determined by using spectral features associated with the n = 3 principal quantum number, and propose a re-evaluation of previous experimental data where high densities have been inferred from the spectra, and the SP model has been used.     

Structure and electronic properties of native and defected gallium nitride nanotubes

Structure and electronic properties of GaN nanotubes (GaNNTs) are investigated by using ab initio density functional theory. By full optimization, the optimized structures (bond-lengths and angles between them) of zigzag GaNNTs (n,0) and armchair GaNNTs (n,n) (4<n<11) are calculated. The difference between nitrogen ring diameter and gallium ring diameter (buckling distance) and semiconducting energy gap in term of diameter for zigzag and armchair GaNNTs have also been calculated. We found that buckling distance decreases by increasing nanotube diameter. Furthermore, we have investigated the effects of nitrogen and gallium vacancies on structure and electronic properties of zigzag GaNNT (5,0) using spin dependent density functional theory. By calculating the formation energy, we found that N vacancy in GaNNT (5,0) is more favorable than Ga vacancy. The nitrogen vacancy in zigzag GaNNT induces a 1.0μB magnetization and makes a polarized structure. We have shown that in polarized GaNNT a flat band near the Fermi energy splits to occupied spin up and unoccupied spin down levels.     

Magnetic ordering in the frustrated system FeSc2S4

The sample of FeSc₂S₄ was prepared by solid reaction method. The crystallographic structure and the magnetic properties of the fabricated compound were investigated by X-ray, and superconducting quantum interference device (SQUID) magnetometer and Mössbauer spectroscopy. The polycrystalline FeSc₂S₄ confirmed the normal cubic spinel structure (space group Fd3m). The lattice constants a₀ and anion parameter u are 10.519 Å and 0.255, respectively. The Mössbauer spectroscopy has been studied for the FeSc₂S₄ at various temperatures, ranging from 4.2 K to room temperature. The spectra consist of two doublets at 4.2 K while a single line at room temperature. It is noticeable that the Mössbauer spectra of two doublet patterns with large electric quadrupole splitting (ΔE_Q) remain over the Néel temperature. Those are interpreted as a result of large electric quadrupole interaction compared to magnetic dipole interaction. The magnetic susceptibility measurements were performed with a SQUID magnetometer for temperatures 2<T<320 K, in external fields up to 5 kOe. Magnetic behavior shows antiferromagnetic behavior and the magnetic superexchange interactions between the Fe ions are weakly antiferromagnetic. The paramagnetic susceptibilities follow Curie–Weiss (CW) law with CW temperature Θ_CW=−100 K, and frustration parameter f=−Θ_CW/T_N is of the order of 1000. We conclude that two sublattices are coupled antiferromagnetically, leading to strong frustration effects.     

Condensation of free volume in structures of nematic and hexatic liquid crystals

Eight novel liquid crystalline materials were prepared containing highly branched terminal chains, either 2,4,4-trimethylpentyl or 3,5,5-trimethylhexyl. All materials exhibit nematic mesophases, with additional smectic (Sm) C, hexatic B and SmI phases for certain homologues. Analysis by small- and wide-angle X-ray scattering reveals continual build-up of the correlation length within the nematic phases, where we also observe splitting of the small angle peak into four lobes, indicating pretransitional Sm fluctuations. Connoscopy confirms the nematic phase to be uniaxial and optically positive. We observe that in the solid state, the molecules exist as staggered antiparallel pairs as a consequence of the sterically demanding bulky terminal group, and this would also appear to manifest in the hexatic B phase, where the layer spacing was found to be greater than the molecular length. If true, this is an example of pair formation driven by sterics rather than dipole–dipole interactions and suggests that reentrant systems driven purely by steric frustration may be found.     

Combination of cationic surfactant-assisted solid-phase extraction with field-amplified sample stacking for highly sensitive analysis of chlorinated acid herbicides by capillary zone electrophoresis

This report describes a novel online field-amplified sample stacking (FASS) procedure to analyze 16 chlorinated acid herbicides. By using a poly(vinyl alcohol) (PVA)-coated capillary to reduce electroosmotic flow and introducing a methanol-water plug before sample loading, the sample injection time could be very long without loss of sample and separation efficiency. Under the optimized condition, the FASS procedure could provide great sensitivity enhancement (5000-10 000-fold) and satisfactory reproducibility (relative standard deviations of migration times less than 2.4%, relative standard deviations of peak areas less than 8.0%). Combined with cationic surfactant-assisted solid-phase extraction (CSA-SPE), the limit of detection of the herbicides ranged from 0.269 to 20.3 ppt, which are two orders lower than those of the US Environmental Protection Agency standard method 515.1. The CSA-SPE-FASS-CE method was successfully applied to the analysis of local pond water.     

Qmd-plot: a graphical utility for rapid preliminary analysis of time series of fluctuating data, developed in the context of molecular dynamics simulations

Qmd-plot is a utility to obtain rapid information about past or on-going simulations, or real-time data collections, in the form of graphs of recorded variables (x, y, ...), as x-y plots or as a function of simulated or real time. Time series records in the data file must be named. Variable names and their locations in the data file are initially unknown to the program, but are identified in a first scan, in which header records are located on the basis of a predefined key (that can be changed interactively). The names of the time series are then presented in an interactive menu, from which the user can repeatedly specify a graph to be viewed. Qmd-plot has been developed in the context of molecular dynamics simulations. We give examples of time series and x-y plots made from output of the sigma program. Qmd-plot code is a Java application; source and class files can be obtained free from the authors.     

A new acylated triterpene from the roots of Chaenomeles japonica

A new acylated triterpene together with prunasin, (-)-epicatechin, daucosterol, and three triterpenes, ursolic, oleanolic, and pomolic acids was isolated from the root of Chaenomeles japonica (THUNB.) LINDL. (Rosaceae) and determined to be 3-O-(E)-3, 5-dihydroxycinnamoylursolic acid on the basis of NMR and FAB-MS experiments.