Retail Bottle Pricing at the Border: Evidence of Cross-Border Shopping, Fraudulent Redemptions, and Use Tax Evasion

This paper examines the pattern of retail prices for deposit eligible goods near Michigan’s borders. Michigan’s unique bottle redemption system and lower sales tax generate incentives for various potentially illegal household responses. Such incentives and behavior should be capitalized in the prices of affected goods. I empirically quantify the spatial price effects and find patterns consistent with theoretical predictions. Michigan’s border prices are higher (lower) for goods with higher (lower) per unit costs by up to 38%. Price-distance trends reflect the waning of these effects away from the border

Self-consistent relativistic quasiparticle random-phase approximation and its applications to charge-exchange excitations and β\beta-decay half-lives

The self-consistent quasiparticle random-phase approximation (QRPA) approach is formulated in the canonical single-nucleon basis of the relativistic Hatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study the isobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Sn isotopes as examples. It is found that self-consistent treatment of the particle-particle residual interaction is essential to concentrate the IAS in a single peak for open-shell nuclei and the Coulomb exchange term is very important to predict the IAS energies. For the GTR, the isovector pairing can increase the calculated GTR energy, while the isoscalar pairing has an important influence on the low-lying tail of the GT transition. Furthermore, the QRPA approach is employed to predict nuclear $\beta$-decay half-lives. With an isospin-dependent pairing interaction in the isoscalar channel, the RHFB+QRPA approach almost completely reproduces the experimental $\beta$-decay half-lives for nuclei up to the Sn isotopes with half-lives smaller than one second. Large discrepancies are found for the Ni, Zn, and Ge isotopes with neutron number smaller than $50$, as well as the Sn isotopes with neutron number smaller than $82$. The potential reasons for these discrepancies are discussed in detail.Comment: 34 pages, 14 figure

Nuclear β+\beta^+/EC decays in covariant density functional theory and the impact of isoscalar proton-neutron pairing

Self-consistent proton-neutron quasiparticle random phase approximation based on the spherical nonlinear point-coupling relativistic Hartree-Bogoliubov theory is established and used to investigate the $\beta^+$/EC-decay half-lives of neutron-deficient Ar, Ca, Ti, Fe, Ni, Zn, Cd, and Sn isotopes. The isoscalar proton-neutron pairing is found to play an important role in reducing the decay half-lives, which is consistent with the same mechanism in the $\beta$ decays of neutron-rich nuclei. The experimental $\beta^+$/EC-decay half-lives can be well reproduced by a universal isoscalar proton-neutron pairing strength.Comment: 12 pages, 4 figure

Investigating the in-/through-plane effective diffusivities of dry and partially-saturated gas diffusion layers

In this study, the effective oxygen diffusivity in the dry or partially-saturated gas diffusion layer (GDL) is numerically investigated by an oxygen diffusion model in GDLs reconstructed by a stochastic method. The predicted effective diffusivity in dry GDLs is compared with various diffusivity models from literatures. Reasonable agreements with other models were obtained. The effect of the PTFE loading in the dry Toray carbon paper is also investigated and compared with recent experimental data. It is found that the effective diffusivity becomes lower under higher PTFE loading due to the decreased pore volume, as expected. The relative effective oxygen diffusivity in partially-saturated GDLs is calculated using the two-phase volume of fluid (VOF) model and an oxygen diffusion model. The effects of different local water profiles and porosity distribution on the effective oxygen diffusivity in both the through-plane (TP) and in-plane (IP) directions are investigated and compared with a lattice Boltzmann model and experimental data. The present results are in good agreement with other studies. It is found that local water profile has significant impacts on the effective diffusivity in partially-saturated GDLs and the diffusivity in the TP direction is more sensitive to the water distribution than the IP direction

H ∞ sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach

Copyright @ 2012 John Wiley & SonsIn this paper, the H ∞  sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time-delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete-time SMO such that the asymptotic stability as well as the H ∞  performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete-time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme

High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position sensitive detection

We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position sensitive detector. The high rotational speed of the technique, $10^3$ to $10^4$ times larger than existing methods, permits precise measurements of the crystallographic and electronic symmetries of samples by averaging over low frequency laser power, beam pointing, and pulse width fluctuations. We demonstrate the sensitivity of our technique by resolving the bulk four-fold rotational symmetry of GaAs about its [001] axis using second harmonic generation

Test of quantum chemistry in vibrationally-hot hydrogen molecules

Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The $v=12, J=0-3$ rovibrational levels of H$_2$ ($X^1\Sigma_g^+$), lying only $2000$ cm$^{-1}$ below the first dissociation limit, were populated by photodissociation of H$_2$S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on $v=12$ level energies with the best \textit{ab initio} calculations shows good agreement, where the present experimental accuracy of $3.5 \times10^{-3}$ cm$^{-1}$ is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.Comment: 5 pages, 4 figures, and 2 table