Magnetic-field effect on the diamagnetic susceptibility of hydrogenic impurities in quantum well-wires

We have studied the magnetic field effects on the diamagnetic susceptibility and binding energy of a hydrogenic impurity in a quantum well-wire by taking into account spatially dependent screening. Using the effective-mass approximation within a variational scheme, binding energy and diamagnetic susceptibility of donor are obtained as a function of the magnetic field, length of the square quantum well-wire for different impurity positions. It is shown that the magnetic field effects on diamagnetic susceptibility can be more important for donors in quantum well-wires over a large range of wire dimensions.     

磁场对乙基纤维素胆甾型液晶相的影响

高分子胆甾型液晶相是一个在高分子和液晶领域都引起广泛兴趣的课题,不仅因为自然界中的多种生物大分子,如纤维素,多肽,DNA等可以形成胆甾型液晶相;而且由于胆甾相具有特殊的螺旋结构(如图1所示),能产生一些特殊的光学性能,如强烈的旋光性,圆二色性和选择性反射光性能等;并带来相应的应用,正是由于高分子胆甾相材料的性能和应用,使得高分子胆甾相液晶的相态转变和结构变化也一直倍受关注。     

Diamagnetic repulsion—A versatile tool for label-free particle handling in microfluidic devices

We report the exploration of diamagnetic repulsion forces for the selective manipulation of microparticles inside microfluidic devices. Diamagnetic materials such as polymers are repelled from magnetic fields, an effect greatly enhanced by suspending a diamagnetic object in a paramagnetic Mn²⁺ solution. The versatility of diamagnetic repulsion is demonstrated for the trapping, focussing and deflection of polystyrene particles for three example applications. Firstly, magnet pairs with unlike poles facing each other were arranged along a microcapillary to trap plugs of differently functionalised particles for a simultaneous surface-based assay in which biotin was selectively bound to a plug of streptavidin coated particles utilising only 22 nL of reagent. Secondly, by slightly modifying the magnetic field design, the rapid focussing of particles into a narrow central stream at a flow rate of 650 μm s⁻¹ was accomplished for particle pre-concentration. In a third application, 5 and 10 μm polystyrene particles were separated from each other in continuous flow by passing the particle mixture through a microfluidic chamber with a perpendicular magnetic field, a method termed diamagnetophoresis. The separation was investigated between flow rates of 20–100 μL h⁻¹, with full resolution of the particle populations being achieved at 20 μL h⁻¹. These experiments show the potential of diamagnetic repulsion for simple, label-free manipulation of particles and other diamagnetic objects such as cells for a range of bioanalytical techniques.     

XTOR-2F: A fully implicit Newton–Krylov solver applied to nonlinear 3D extended MHD in tokamaks

XTOR-2F solves a set of extended magnetohydrodynamic (MHD) equations in toroidal tokamak geometry. In the original XTOR code, the time stepping is handled by a semi-implicit method 1, 2 and 3. Moderate changes were necessary to transform it into a fully implicit one using the NITSOL library with Newton–Krylov methods of solution for nonlinear system of equations [4]. After addressing the sensitive issue of preconditioning and time step tuning, the performances of the semi-implicit and the implicit methods are compared for the nonlinear simulation of an internal kink mode test case within the framework of resistive MHD including anisotropic thermal transport. A convergence study comparing the semi-implicit and the implicit schemes is presented. Our main conclusion is that on one hand the Newton–Krylov implicit method, when applied to basic one fluid MHD is more computationally costly than the semi-implicit one by a factor 3 for a given numerical accuracy. But on the other hand, the implicit method allows to address challenging issues beyond MHD. By testing the Newton–Krylov method with diamagnetic modifications on the dynamics of the internal kink, some numerical issues, to be addressed further, are emphasized.     

Diamagnetic susceptibilities of some substituted anisoles and thioanisoles. Evidence for steric enhancement of resonance

Evidence for steric enhancement of resonance in some benzene derivatives is obtained from their diamagnetic susceptibilities. Conjugative interaction of substituents in the benzene ring results in a decrease in diamagnetic susceptibility. For 2-methyl-4-nitroanisole and 2-halogeno-4-nitroanisoles the observed diamagnetic susceptibilities are significantly lower than the expected value, indicating that the 2-substituent in these compounds enhances the resonance interaction of the 1,4-substituents. Interestingly, the diamagnetic susceptibility data also show steric inhibition of resonance in 2,6-disubstituted-4-nitroanisoles. 2-Methyl-4-nitrothioanisole seems to exhibit a behaviour similar to that of its oxygen analogue, though the evidence for steric enhancement of resonance in this case is not beyond doubt. 2,6-Dimethyl-4-nitrothioanisole, however, convincingly shows the expected steric inhibition of resonance. The diamagnetic susceptibilities of 3-substituted-4-methoxyacetophenones also furnish further evidence for steric enhancement of resonance.     

Stabilization of the trivalent oxidation state of copper by tridentate imine–oxime–amine ligands

Two tridentate imine–oxime–amine ligands have been synthesized and their corresponding copper(II) complexes have been isolated. These copper(II) complexes are readily oxidized both chemically and electrochemically to give relatively stable copper(III) complexes. In the pH range 1.5–3.0 the electron transfer process is electrochemically reversible with ΔE_p = 60 mV and i_pa/i_pc ∼ 1. Plots of E_1/2 versus pH are linear with a slope = −60 indicating the involvement of one proton in the electron transfer process. Aqueous solutions of copper(III) complexes have high molar absorption at λ_max with ε > 10⁴ M⁻¹ cm⁻¹. Solid samples of the complexes are diamagnetic consistent with a d⁸ square planar geometry. It seems that only imine–oxime nitrogens are coordinated to copper(II) with the NH₂ group being free as indicated by i.r. spectra. Substitution of a –CH₃ group on the carbon atom adjacent to the oxime group by the more electron donating group –CH(CH₃)₂ lowers electrode potential by more than 90 mV. This is consistent with an earlier observation that electron-donating substituents on the carbon atom adjacent to the oxime group lower the potential of Cu^III/Cu^II couples and stabilize the higher oxidation state.     

Reduced energy functionals for a three-dimensional fast rotating Bose Einstein condensates

We prove that in the fast rotating regime, the three-dimensional Gross–Pitaevskii energy describing the state of a Bose Einstein condensate can be reduced to a two-dimensional problem and that the vortex lines are almost straight. Additionally, we prove that the minimum of this two-dimensional problem can be sought in a reduced space corresponding to the first eigenspace of an elliptic operator. This space is called the Lowest Landau level and is of infinite dimension     

Inner and outer radial density functions in many-electron atoms

When any two electrons are considered simultaneously, the radial density function D(r) in many-electron atoms is shown to be rigorously separated into inner D _<(r) and outer D _>(r) radial densities. Accordingly, radial properties such as the electron–nucleus attraction energy V _en and the diamagnetic susceptibility χ _d are the sum of the inner and outer contributions. The electron–electron repulsion energy V _ee has an approximate relation with the minus first moment of the outer density D _>(r). For the 102 atoms He through Lr in their ground states, different characteristics of local maxima in the radial densities D _<(r), D _>(r), and D(r) are reported based on the numerical Hartree-Fock wave functions. Relative contributions of the inner and outer components to V _en and are also discussed for these atoms.     

Diamagnetic susceptibility of some organic compounds

The diamagnetic susceptibilities of four aromatic compounds of known structure have been measured and the principal molecular susceptibilities have been deduced from these, knowing the molecular orientations. The anisotropy of the substituted benzene is less than that of the unsubstituted benzene. The delocalization term is greater for molecules with stronger hydrogen bonds.