The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.     

Direct numerical simulation of passive scalar in decaying compressible turbulence

1IntroductionDirectnumericalsimulation(DNS)becomesanimportanttoolinrecentresearchofturbulence[1].DNSofcompressibleturbulenceismoredifficultthanthatoftheincompressibleturbulence.WhentheturbulentMachnumberisgreaterthan0.3theshockletsmayappearinthecompressibleturbulentflowfields.Thereasonandmechanismofshockletsexistencearenotclearyet.TheturbulentMachnumberinDNScannotbeveryhighwiththepresentexistingnumericalmethodsandcomputerresource.Fortheproblemofcompressibleisotropicturbulencewiththeinitia…     

A numerical investigation of the evolution of 2-D disturbances in hypersonic boundary layers and the effect on the flow structure due to the existence of shocklets

The evolution of 2-D disturbances in hypersonic boundary layer with Mach number 6,8, and 10 was investigated numerically by three different numerical schemes. At the entrance, second mode T-S waves with different amplitudes were introduced, and the relation between the Mach number and the amplitude of the disturbance when shocklets started to appear was investigated. By comparing the disturbance velocity profiles with those provided by linear stability theory, the effects of shocklets on flow structures were also investigated.     

Heavy alkaline earth metal pyrazolates: synthetic pathways, structural trends, and comparison with divalent lanthanoids

Two series of heavy alkaline earth metal pyrazolates, [M(Ph(2)pz)(2)(thf)(4)] 1 a-c (Ph(2)pz=3,5-diphenylpyrazolate, M=Ca, Sr, Ba; THF=tetrahydrofuran) and [M(Ph(2)pz)(2)(dme)(n)] (M=Ca, 2 a, Sr, 2 b, n=2; M=Ba, 2 c, n=3; DME=1,2-dimethoxyethane) have been prepared by redox transmetallation/ligand exchange utilizing Hg(C(6)F(5))(2). Compounds 1 a and 2 b were also obtained by redox transmetallation with Tl(Ph(2)pz). Alternatively, direct reaction of the alkaline earth metals with 3,5-diphenylpyrazole at elevated temperatures under solventless conditions yielded compounds 1 a-c and 2 a-c upon extraction with THF or DME. By contrast, [M(Me(2)pz)(2)(Me(2)pzH)(4)] 3 a-c (M=Ca, Sr, Ba; Me(2)pzH=3,5-dimethylpyrazole) were prepared by protolysis of [M[N(SiMe(3))(2)](2)(thf)(2)] (M=Ca, Sr, Ba) with Me(2)pzH in THF and by direct metallation with Me(2)pzH in liquid NH(3)/THF. Compounds 1 a-c and 2 a-c display eta(2)-bonded pyrazolate ligands, while 3 a,b exhibit eta(1)-coordination. Complexes 1 a-c have transoid Ph(2)pz ligands and an overall coordination number of eight with a switch from mutually coplanar Ph(2)pz ligands in 1 a,b to perpendicular in 1 c. In eight coordinate 2 a,b the pyrazolate ligands are cisoid, whilst 2 c has an additional DME ligand and a metal coordination number of ten. By contrast, 3 a,b have octahedral geometry with four eta(1)-Me(2)pzH donors, which are hydrogen-bonded to the uncoordinated nitrogen atoms of the two trans Me(2)pz ligands. The application of synthetic routes initially developed for the preparation of lanthanoid pyrazolates provides detailed insight into the similarities and differences between the two groups of metals and structures of their complexes.     

An evaluation of the radial part of numerical integration commonly used in DFT

Recently, Gill and Chien introduced a new radial quadrature for multiexponential integrands (MultiExp grid) to deal with the radial part of the numerical integration. In this article, the MultiExp grid is studied and used to integrate the charge density. The MultiExp grid, along with an optimal pruning scheme, performed very well both in terms of accuracy and efficiency compared to other radial mappings commonly used in Density Functional Theory.     

Steam distillation-solid-phase microextraction for the detection of Ephedra sinica in herbal preparations

A new method involving concurrent solid-phase microextraction combined with continuous hydrodistillation of essential oil was developed. This new methodology allowed for the detection by GC-MS of very small amounts of a diagnostic peak for the authentication of Ephedra sinica, in a short period of time and using only small sample sizes. This diagnostic peak was identified as 4-vinylanisole, and elucidated from the chromatographic profile allowed for the identification of a sample as E. sinica among other species investigated in this study. To the best of our knowledge this is the first report on using continuous solid-phase microextraction coupled to hydrodistillation for the investigation of essential oil components, and the first report of 4-vinylanisole as a marker compound for E. sinica. A total of 46 collections representing 21 species of Ephedra were studied.     

Automated high-capacity sorption probe for extraction of organic compounds in aqueous samples followed by gas chromatographic analysis

An automated high-capacity sorption device for GC analysis of ultra trace components has been developed. The scope of the presented technique was to combine the simplicity of solid-phase microextraction (SPME) with the high extraction efficiency of the stir bar sorptive extraction technology. Sorptive extractions of water samples were performed using polydimethylsiloxane (PDMS) rubber tubing (120 microl) mounted onto a glass rod. The sampling procedure was carried out by a robotic autoinjector. Since the setup is fully automated, unattended and precise time-controlled extraction of samples is possible and makes quantitation with non-equilibrium extractions feasible. The sorption probes are easy to exchange, which facilitates off-line/in-field sampling. The system was evaluated with a test mixture of 44 environmentally hazardous compounds. Detection limits were found to be in the sub-ppt region. The performance of the system was demonstrated with the analysis of polycyclic aromatic hydrocarbons in urban snow.