A new flux-limiting approach–based kinetic scheme for the Euler equations of gas dynamics

This paper proposes a new kinetic-theory-based high-resolution scheme for the Euler equations of gas dynamics. The scheme uses the well-known connection that the Euler equations are suitable moments of the collisionless Boltzmann equation of kinetic theory. The collisionless Boltzmann equation is discretized using Sweby's flux-limited method and the moment of this Boltzmann level formulation gives a Euler level scheme. It is demonstrated how conventional limiters and an extremum-preserving limiter can be adapted for use in the scheme to achieve a desired effect. A simple total variation diminishing criteria relaxing parameter results in improving the resolution of the discontinuities in a significant way. A 1D scheme is formulated first and an extension to 2D on Cartesian meshes is carried out next. Accuracy analysis suggests that the scheme achieves between first- and second-order accuracy as is expected for any second-order flux-limited method. The simplicity and the explicit form of the conservative numerical fluxes add to the efficiency of the scheme. Several standard 1D and 2D test problems are solved to demonstrate the robustness and accuracy.     

Sodium phenoxy­acetate hemihydrate

The structure of the hemihydrate of sodium phenoxy­acetate, Na⁺·C₈H₇O₃⁻·0.5H₂O, has been redetermined at low temperature (160 K). The structure consists of ribbons containing octahedral NaO₆ units, and half of the Na₂O₂ squares within the ribbon are bridged by water mol­ecules which lie across twofold rotation axes in C2/c. The phenyl substituents lie on the outside of the ribbon.     

Ion dynamics in ultrafast laser ablation of copper target

We investigate the angular distribution and average kinetic energy of ions produced during ultrafast laser ablation （ULA） of a copper target in high vacuum. Laser produced plasma （LPP） is induced by irradiating the target with Ti：Sapphire laser pulses of -50 fs and 800 nm at an angle of incidence of 45°. An ion probe is moved along a circular path around the ablation spot, thereby allowing characterization of the time-of-flight （TOF） of ions at different angles relative to the normal target. The angular distribution of the ion flux is well-described by an adiabatic and isentropic expansion model of a plume produced by solid-target laser ablation （LA）. The angular width of the ion flux becomes narrower with increasing laser fluence. Moreover, the ion average kinetic energy is forward-peaked and shows a stronger dependence on the laser pulse fluence than on the ion flux. Such results can be ascribed to space charge effects that occur during the early stages of LPP formation.     

Condensed two- and three-dimensional aromatic systems: a theoretical study on the relative stabilities of isomers of CB19H16+, B20H15Cl, and B20H14Cl2 and comparison to B12H10Cl22-, C6H4Cl2, C10H7Cl, and C10H6Cl2

DFT studies (B3LYP/6-31G) on mono- and dichloro derivatives of benzene, naphthalene, B12H12(2-), four-atom-sharing condensed systems B20H16, and monocarborane isomers of B20H16 are used to compare the variation of relative stability and aromaticity between condensed aromatics. The trends in the variation of the relative energies and aromaticity in these two- and three-dimensional systems are similar. Aromaticity, estimated by NICS values, does not change considerably with condensation or substitution. The minor variation in the relative energies of the isomers of chloro derivatives is explained by the topological charge stabilization rule of Gimarc. The compatibility of the cap and ring orbitals decides the relative stability of CB19H16+.     

Strong Coupling of Chiral Frenkel Exciton for Intense,Bisignate Circularly Polarized Luminescence

We show that chiral Frenkel excitons yield intense circularly polarized luminescence with an intrinsic dissymmetry factor in emission g_lum as high as 0.08. This outstanding value is measured through thin films of cyanine J-aggregates that form twisted bundles. Our measurements, obtained by a Mueller polarization analysis, are artifact-free and reveal a quasi-perfect correlation between the dissymmetry factors in absorption, g_abs, and in emission g_lum. We interpret the bisignate dissymmetry factors as the signature of a strong coupling between chiral Frenkel excitons longitudinally excited along the bundles. We further resolve by polarimetry analysis the split in energy between the excited states with a Davydov splitting as small as 28 meV. We finally show the anti-Kasha nature of the chiral emission bands with opposite optical chirality. These mirror-imaged emissive chiroptical features emerge from the structural rigidity of the bundles that preserves the ground- and excited-state chirality.     

An efficient HOC scheme for transient convection-diffusion-reaction equations with discontinuous coefficients and singular source terms

In this paper, we propose a new methodology for numerically solving one-dimensional (1D) transient convection-diffusion-reaction equations with discontinuous coefficients and singular source terms on nonuniform space grids. This Higher Order Compact (HOC) formulation is at least third order accurate at regular grid points and exactly third order accurate at points just next to the discontinuity. We conduct numerous numerical studies on a number of problems and compare our results with those obtained with immersed interface and other well-known methods. In all cases our formulation is found to produce better results on relatively coarser grids. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Quantum Chemical Study on the Enormously Large Nonlinear Optical Response of Doped Endohedral Superalkali Na2F and Superhalogens MF4 (M = B,Al) with CNT (C56H16) Cage

In the present communication, the interaction of single-wall carbon nanotubes (SWCNTs) CNT (C56H16) with endohedral doped superhalogens (MF₄:M = B, Al) placed outside of CNT cage and superalkali (Na₂F) placed inside the cage has been studied by using a combination of DFT/B3LYP method and 6–311G(d, p) basis set. The geometry and stability of MF₄@CNT-Li₂F have been studied using optimization parameters, highest occupied molecular orbit (HOMO), lowest unoccupied molecular orbital (LUMO), vibration frequencies, and thermodynamic parameters of absorption reactions. The quantum theory in atoms in molecules (QTAIM) analysis is used to analyze the nature of interactions between MF₄ (M = B, Al) and Na₂F@CNT. Several electronic parameters are computed by using HOMO–LUMO energy. The dipole moment, polarizability, hyperpolarizability, order parameters, anisotropic polarizability, and molar refractivity of MF4@CNT-Li₂F (M = Al, B) are used to calculate the nonlinear optical parameters (MR). The NBO analysis is used to calculate the transfer of charge to stabilized system. The calculated hyperpolarizability of Na₂F@CNT-BF₄/Na₂F@CNT-AlF₄ is nearly 81 times that of reference material urea (40 a.u.). The intramolecular charge transfer (ICT) moment of π electron cloud is responsible for the nonlinear optical behavior of the system.     

Why do we need probability distributions with fat tails to describe the surface strain evolution in reinforced concrete flexural members?

This paper, for the first time, justifies the use of alpha-stable distribution (a fat tailed distribution) for describing the statistical variations in surface strains in reinforced concrete flexural members. Justification is provided by viewing the cracking process in these members, that affects the strain evolution, as an emergent structure (in thermodynamical sense, Prigogine and Stengers in Order out of chaos: man’s new dialogue with nature, 1984; Carpinteri in J. Mech. Phys. Solids 37(5):567–582, 1989; van Mier et al. in Comput. Meth. Appl. Mech. Eng. 142(1–2):189–201, 1997). The proposal of the alpha-stable distribution is checked by comparing the estimated relevant parameters (namely, location and scale parameters which are representative of mean and dispersion) with the mean and standard deviation of experimentally measured surface strains both in extreme compression fibre and at the level of reinforcement (in the flexure zone), at different stages of loading. A satisfactory agreement is obtained between the respective experimental and estimated values. Also, comparison of the tails of estimated CDFs of normal and alpha-stable distributions with the cumulative distribution functions of experimentally observed strains suggested that alpha-stable distribution is able to fit the tails of compression and tensile strains better than normal distribution. For the purpose of the present study, the experimental results of three beams are considered. Also, in the present investigation the strains at the level of reinforcement and at the extreme compression fibre are considered. The practical consequence of the use alpha stable distribution in performance based design and future direction of research are also included.     

Risk and Pitman closeness properties of feasible generalized double k-class estimators in linear regression models with non-spherical disturbances under balanced loss function

In this article, a family of feasible generalized double k-class estimator in a linear regression model with non-spherical disturbances is considered. The performance of this estimator is judged with feasible generalized least-squares and feasible generalized Stein-rule estimators under balanced loss function using the criteria of quadratic risk and general Pitman closeness. A Monte-Carlo study investigates the finite sample properties of several estimators arising from the family of feasible double k-class estimators.