Two-parameter Quantum Affine Algebra Ur,s(sln^)U_{r,s}(\widehat{\frak {sl}_n}), Drinfel'd Realization and Quantum Affine Lyndon Basis

We further define two-parameter quantum affine algebra $U_{r,s}(\widehat{\frak {sl}_n})$ $(n>2)$ after the work on the finite cases (see [BW1], [BGH1], [HS] & [BH]), which turns out to be a Drinfel'd double. Of importance for the quantum {\it affine} cases is that we can work out the compatible two-parameter version of the Drinfel'd realization as a quantum affinization of $U_{r,s}(\frak{sl}_n)$ and establish the Drinfel'd isomorphism Theorem in the two-parameter setting, via developing a new combinatorial approach (quantum calculation) to the quantum {\it affine} Lyndon basis we present (with an explicit valid algorithm based on the use of Drinfel'd generators).Comment: 31 page

Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.Comment: 22 page

Non-magnetic impurity scattering in a dx2−y2d_{x^2 - y^2} superconductor near a van Hove point: Zn versus Ni in the cuprates

We consider the effect of non-magnetic impurities in a $d_{x^2 - y^2}$ superconductor with \ef close to a van Hove singularity. It is shown that the non-trivial density of states (DOS) allows for resonant scattering already at intermediate potential strengths $|u| \approx 1-2$eV. The residual DOS at \ef, and the \tc suppression rate are found to strongly depend on the carrier concentration. Quantitative agreement with experiments on Zn and Ni doped cuprates is obtained by adjusting a single parameter, $u$.Comment: 4 pages uuencoded compressed Postscript (Minor changes

Disparate MgII Absorption Statistics towards Quasars and Gamma-Ray Bursts : A Possible Explanation

We examine the recent report by Prochter et al. (2006) that gamma-ray burst (GRB) sight lines have a much higher incidence of strong MgII absorption than quasar sight lines. We propose that the discrepancy is due to the different beam sizes of GRBs and quasars, and that the intervening MgII systems are clumpy with the dense part of each cloudlet of a similar size as the quasars, i.e. < 10^16 cm, but bigger than GRBs. We also discuss observational predictions of our proposed model. Most notably, in some cases the intervening MgII absorbers in GRB spectra should be seen varying, and quasars with smaller sizes should show an increased rate of strong MgII absorbers. In fact, our prediction of variable MgII lines in the GRB spectra has been now confirmed by Hao et al. (2007), who observed intervening FeII and MgII lines at z=1.48 to be strongly variable in the multi-epoch spectra of z=4.05 GRB060206.Comment: 12 pages, 2 figures; substantially revised model calculation; accepted for publication in Astrophysics & Space Science as a Lette

Pseudogap formation of four-layer BaRuO3_3 and its electrodynamic response changes

We investiaged the optical properties of four-layer BaRuO$_{3}$, which shows a fermi-liquid-like behavior at low temperature. Its optical conductivity spectra clearly displayed the formation of a pseudogap and the development of a coherent peak with decreasing temperature. Temperature-dependences of the density $n$ and the scattering rate $1/\tau$ of the coherent component were also derived. As the temperature decreases, both $n$ and $1/\tau$ decrease for four-layer BaRuO$_{3}$. These electrodynamic responses were compared with those of nine-layer BaRuO$_{3}$, which also shows a pseudogap formation but has an insulator-like state at low temperature. It was found that the relative rates of change of both $n$ and $1/\tau$ determine either metallic or insulator-like responses in the ruthenates. The optical properties of the four-layer ruthenate were also compared with those of other pseudogap systems, such as high $T_{c}$ cuprates and heavy electron systems.Comment: 7 figures. submitted to Phys. Rev.

Glauber Dynamics for the mean-field Potts Model

We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\beta_s(q)$ strictly lower than the critical $\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\beta<\beta_s(q)$ the mixing time is asymptotically $C(\beta, q) n \log n$ and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order $n$. At $\beta=\beta_s(q)$ the dynamics no longer exhibits cutoff and its mixing obeys a power-law of order $n^{4/3}$. For $\beta>\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\beta \uparrow \beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\beta_s$. These results form the first complete analysis of mixing around the critical dynamical temperature --- including the critical power law --- for a model with a first order phase transition.Comment: 45 pages, 5 figure

Structure and properties of composite Ni–Co–Mn coatings on metal interconnects by electrodeposition

In order to obtain the high conductivity values and wide spinel stability region for solid oxide fuel cell interconnect, several multilayer Ni, Co and Mn coatings are electroplated and then oxidized in air to form spinel oxide layers. Potentiodynamic polarization curves in different simple solutions are tested to analyze the deposition behavior of Co and Mn. Microstructures and compositions of Ni–Co–Mn multi-layers by adjusting the thickness and deposition parameters are analyzed by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The results show that area specific resistance value of sample B–Ni/Co after oxidation at 750 °C for 500h is the lowest among the coatings, and the resistance values at 700 °C and 800 °C are 35.3 and 31.7 mΩ‧cm2, respectively. When the Ni transition layer in the vicinity of coating/substrate interface is thick, it will lead to the outward diffusion and aggregation of element Fe to form Fe-rich oxide intermediate layer, which will affect the high-temperature performance of the coating. Pure Co and CoMn alloy coatings with a certain thickness can effectively prevent the inward diffusion of oxygen and the outward diffusion of Fe and Cr at high temperature. The thin Ni transition layer combined with the thick Co layer or CoMn layer has the best element diffusion inhibition and high temperature electrical properties during the long-term high-temperature oxidation process

Hole concentration and phonon renormalization in Ca-doped YBa_2Cu_3O_y (6.76 < y < 7.00)

In order to access the overdoped regime of the YBa_2Cu_3O_y phase diagram, 2% Ca is substituted for Y in YBa_2Cu_3O_y (y = 7.00,6.93,6.88,6.76). Raman scattering studies have been carried out on these four single crystals. Measurements of the superconductivity-induced renormalization in frequency (Delta \omega) and linewidth (\Delta 2\gamma) of the 340 cm^{-1} B_{1g} phonon demonstrate that the magnitude of the renormalization is directly related to the hole concentration (p), and not simply the oxygen content. The changes in \Delta \omega with p imply that the superconducting gap (\Delta_{max}) decreases monotonically with increasing hole concentration in the overdoped regime, and \Delta \omega falls to zero in the underdoped regime. The linewidth renormalization \Delta 2\gamma is negative in the underdoped regime, crossing over at optimal doping to a positive value in the overdoped state.Comment: 18 pages; 5 figures; submitted to Phys. Rev. B Oct. 24, 2002 (BX8292

Well-Posedness of Nematic Liquid Crystal Flow in Luloc3(R3)L^3_{\hbox{uloc}}(\R^3)

In this paper, we establish the local well-posedness for the Cauchy problem of the simplified version of hydrodynamic flow of nematic liquid crystals (\ref{LLF}) in $\mathbb R^3$ for any initial data $(u_0,d_0)$ having small $L^3_{\hbox{uloc}}$-norm of $(u_0,\nabla d_0)$. Here $L^3_{\hbox{uloc}}(\mathbb R^3)$ is the space of uniformly locally $L^3$-integrable functions. For any initial data $(u_0, d_0)$ with small $\displaystyle |(u_0,\nabla d_0)|_{L^3(\mathbb R^3)}$, we show that there exists a unique, global solution to (\ref{LLF}) which is smooth for $t>0$ and has monotone deceasing $L^3$-energy for $t\ge 0$.Comment: 29 page