On the nature of the lightest scalar resonances

We briefly review the recent progresses in the new unitarization approach being developed by us. Especially we discuss the large $N_c$ $\pi\pi$ scatterings by making use of the partial wave $S$ matrix parametrization form. We find that the $\sigma$ pole may move to the negative real axis on the second sheet of the complex $s$ plane, therefore it raises the interesting question that this `$\sigma$' pole may be related to the $\sigma$ in the linear $\sigma$ model.Comment: Talk presented by Zheng at ``Quark Confinement and Hadron Spectroscopy VI'', 21--25 Sept. 2004, Cagliari, Italy. 3 pages with 2 figure

Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems

Surface impedance is an important concept in classical wave systems such as photonic crystals (PCs). For example, the condition of an interface state formation in the interfacial region of two different one-dimensional PCs is simply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of the semi-infinite PC on the left- (right-) hand side of the interface. Here, we also show a rigorous relation between the surface impedance of a one-dimensional PC and its bulk properties through the geometrical (Zak) phases of the bulk bands, which can be used to determine the existence or non-existence of interface states at the interface of the two PCs in a particular band gap. Our results hold for any PCs with inversion symmetry, independent of the frequency of the gap and the symmetry point where the gap lies in the Brillouin Zone. Our results provide new insights on the relationship between surface scattering properties, the bulk band properties and the formation of interface states, which in turn can enable the design of systems with interface states in a rational manner

Analyticity and the NcN_c counting rule of SS matrix poles

By studying $\pi\pi$ scattering amplitudes in the large $N_c$ limit, we clarify the $N_c$ dependence of the $S$ matrix pole position. It is demonstrated that analyticity and the $N_c$ counting rule exclude the existence of $S$ matrix poles with ${\cal M}, \Gamma\sim O(1)$. Especially the properties of $\sigma$ and $f_0(980)$ with respect to the $1/N_c$ expansion are discussed. We point out that in general tetra-quark resonances do not exist.Comment: This paper replaces hep-ph/0412175. The latter is withdraw

Excitation of nonlinear ion acoustic waves in CH plasmas

Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $k\lambda_{De}$ increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $T_i/T_e < 0.2$ in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with $k\lambda_{De}$ increasing. When $k\lambda_{De}$ is not large, such as $k\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when $k\lambda_{De}$ is large, such as $k\lambda_{De}=0.7$, the linear frequency can not be applied to exciting the nonlinear IAW, while the frequency calculated by the dispersion relation with no damping can be applied to exciting the nonlinear IAW.Comment: 10 pages, 9 figures, Accepted by POP, Publication in August 1

Recent Developments In Computational Fracture Mechanics At Cardiff

The following most recent developments in computational fracture mechanics at Cardiff University are reviewed: hybrid crack element (HCE) which can give directly the stress intensity factor (SIF) as well as the coefficients of higher order terms in the plane linear elastic crack tip asymptotic field; extended finite element method (XFEM) which avoids using a mesh conforming with the crack as is the case with the traditional FEM and gives highly accurate crack tip fields; penalty function technique for handling point loads; and compressed sparse row (CSR) storage scheme for efficient implementation of the above techniques. Possible future improvements are also discussed

Is the f0(600)f_0(600) meson a dynamically generated resonance? -- a lesson learned from the O(N) model and beyond

O(N) linear $\sigma$ model is solvable in the large $N$ limit and hence provides a useful theoretical laboratory to test various unitarization approximations. We find that the large $N_c$ limit and the $m_\sigma\to \infty$ limit do not commute. In order to get the correct large $N_c$ spectrum one has to firstly take the large $N_c$ limit. We argue that the $f_0(600)$ meson may not be described as generated dynamically. On the contrary, it is most appropriately described at the same level as the pions, i.e, both appear explicitly in the effective lagrangian. Actually it is very likely the $\sigma$ meson responsible for the spontaneous chiral symmetry breaking in a lagrangian with linearly realized chiral symmetry.Comment: 15 pages, 3 figurs; references added; discussions slightly modified; revised version accepted by IJMP

Anti-Stokes scattering and Stokes scattering of stimulated Brillouin scattering cascade in high-intensity laser-plasmas interaction

The anti-Stokes scattering and Stokes scattering in stimulated Brillouin scattering (SBS) cascade have been researched by the Vlasov-Maxwell simulation. In the high-intensity laser-plasmas interaction, the stimulated anti-Stokes Brillouin scattering (SABS) will occur after the second stage SBS rescattering. The mechanism of SABS has been put forward to explain this phenomenon. And the SABS will compete with the SBS rescattering to determine the total SBS reflectivity. Thus, the SBS rescattering including the SABS is an important saturation mechanism of SBS, and should be taken into account in the high-intensity laser-plasmas interaction.Comment: 6 pages, 5 figure