Modeling quark-hadron duality in polarization observables

We apply a model for the study of quark-hadron duality in inclusive electron scattering to the calculation of spin observables. The model is based on solving the Dirac equation numerically for a scalar confining linear potential and a vector color Coulomb potential. We qualitatively reproduce the features of quark-hadron duality for all potentials considered, and discuss the onset of scaling and duality for the responses, spin structure functions, and polarization asymmetries. Duality may be applied to gain access to kinematic regions which are hard to access in deep inelastic scattering, namely for $x_{Bj} \to 1$, and we discuss which observables are most suitable for this application of duality

Z-graded weak modules and regularity

It is proved that if any Z-graded weak module for vertex operator algebra V is completely reducible, then V is rational and C_2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.Comment: 9 page

Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors

We calculate the two-photon exchange corrections to electron-proton scattering with nucleon and $\Delta$ intermediate states. The results show a dependence on the elastic nucleon and nucleon-$\Delta$-transition form factors used as input which leads to significant changes compared to previous calculations. We discuss the relevance of these corrections and apply them to the most recent and precise data set and world data from electron-proton scattering. Using this, we show how the form factor extraction from these data is influenced by the subsequent inclusion of physical constraints. The determination of the proton charge radius from scattering data is shown to be dominated by the enforcement of a realistic spectral function. Additionally, the third Zemach moment from the resulting form factors is calculated. The obtained radius and Zemach moment are shown to be consistent with Lamb shift measurements in muonic hydrogen.Comment: minor changes, added references, version to appear in PR

Numerical simulation of viscous fingering phenomenon in immiscible displacement of two fluids in porous media using Lattice Boltzmann method

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.In the present study, viscous fingering phenomenon, which occurs when a less viscous fluid (e.g. supercritical carbon dioxide) is injected into simplified porous media to displace a more viscous fluid (e.g. crude oil), is investigated by a mesoscopic approach-the lattice Boltzmann method (LBM). Due to its convenience in dealing with complex fluids of different viscosities, the pseudo-potential model is employed to study the effects of the capillary number, Bond number and viscosity ratio between the displaced fluids and displacing fluid; as such effects reflect the competition of viscous force and surface tension and gravity forces during viscous fingering. The numerical procedure is validated against a series of droplet tests, in which surface tension can be determined. By changing the injecting velocity of the displacing fluid and gravitational acceleration, the displacement processes under conditions of different capillary number and Bond number are investigated. The finger pattern is presented in this paper. The effects of capillary number, Bond number and viscosity ratio are discussed in detail. The ability and suitability of the lattice Boltzmann method for simulating multi-component fluids displacement in porous media are proved in our work.This work is supported by China Scholarship Council (CSC)

DOA estimation with known waveforms in the presence of unknown time delays and Doppler shifts

A novel DOA estimation method for known waveform sources with different unknown time delays and Doppler shifts is proposed. Based on the idea of maximum likelihood and the matrix projection theory, a decoupled cost function is first constructed and then the problem of estimating time delay and Doppler shift is transformed into a nonlinear least squares (NLS) problem. To solve the NLS problem efficiently without multidimensional search, a Toeplitz dominant rule is established to perform initial estimates with a reduced dimension. Finally, with the aid of time delay and Doppler shift estimates, DOAs and complex amplitudes of the incoming signals are obtained. Simulation results show that the proposed method can achieve a performance close to CRB at high SNR and with a large number of snapshots

Relationship between the gamma-ray burst pulse width and energy due to the Doppler effect of fireballs

We study in details how the pulse width of gamma-ray bursts is related with energy under the assumption that the sources concerned are in the stage of fireballs. Due to the Doppler effect of fireballs, there exists a power law relationship between the two quantities within a limited range of frequency. The power law range and the power law index depend strongly on the observed peak energy $E_p$ as well as the rest frame radiation form, and the upper and lower limits of the power law range can be determined by $E_p$. It is found that, within the same power law range, the ratio of the $FWHM$ of the rising portion to that of the decaying phase of the pulses is also related with energy in the form of power laws. A platform-power-law-platform feature could be observed in the two relationships. In the case of an obvious softening of the rest frame spectrum, the two power law relationships also exist, but the feature would evolve to a peaked one. Predictions on the relationships in the energy range covering both the BATSE and Swift bands for a typical hard burst and a typical soft one are made. A sample of FRED (fast rise and exponential decay) pulse bursts shows that 27 out of the 28 sources belong to either the platform-power-law-platform feature class or the peaked feature group, suggesting that the effect concerned is indeed important for most of the sources of the sample. Among these bursts, many might undergo an obvious softening evolution of the rest frame spectrum.Comment: Accepted for publication in The Astrophysical Journa