Phase Structure of Thermal QED Based on the Hard Thermal Loop Improved Ladder Dyson-Schwinger Equation --a "Gauge Invariant" Solution--

Based on the hard-thermal-loop resummed improved ladder Dyson-Schwinger quation for the fermion mass function, we study how we can get the gauge invariant solution in the sense it satisfies the Ward identity. Properties of the ``gauge-invariant'' solutions are discussed.Comment: 3figures, Proceedins of SCGT06 (Nagoya University, Japan, November 2006

Chiral Phase Transitions in QED at Finite Temperature: Dyson-Schwinger Equation Analysis in the Real Time Hard-Thermal-Loop Approximation

In order for clarifying what are the essential thermal effects that govern the chiral phase transition at finite temperature, we investigate, in the real-time thermal QED, the consequences of the Hard-Thermal-Loop (HTL) resummed Dyson-Schwinger equation for the physical fermion mass function $\Sigma_R$. Since $\Sigma_R$ is the mass function of an ``unstable'' quasi-particle in thermal field theories, it necessarily has non-trivial imaginary parts together with non-trivial wave function renormalization constants. In the present analysis we correctly respect this fact, and study, in the ladder approximation, the effect of HTL resummed gauge boson propagator. Our results with the use of numerical analysis, show the two facts; i) The chiral phase transition is of second order, since the fermion mass is dynamically generated at a critical value of the temperature $T_c$, or at the critical coupling constant $\alpha_c$, without any discontinuity, and ii) the critical temperature $T_c$ at fixed value of $\alpha$ is significantly lower than the previous results, namely the restoration of chiral symmetry occurs at lower temperature than previously expected. The second fact shows the importance of correctly taking the essential thermal effect into the analysis of chiral phase transition, which are, in the previous analyses, neglected due to the inappropriate approximations. The procedure how to maximally respect the gauge invariance in the present approximation, is also discussed.Comment: Revtex4 with 6 figures, 11 page

Grey Fuzzy Optimization of Total Nitrogen Load Allocation to Nonpoint Sources in Watershed

Water Resources Planning and Managemen

Preparation of sodium hexatitanate photocatalysts by a flux method for photocatalytic steam reforming of methane

Fine crystals of sodium hexatitanate (Na₂Ti₆O₁₃) were prepared by a flux method for photocatalytic steam reforming of methane (PSRM) to produce hydrogen. The examined parameters for the preparation in this study were the solute concentration in the molten sodium chloride salt and the cooling rate from the molten mixture. As a reference, another sample was prepared by a solid state reaction method, which corresponds to the preparation without the sodium chloride flux. The prepared samples consisted of hexagonal rod-like microcrystals of monoclinic structure with various morphology, particle size, crystallite size, aspect ratio, and specific surface area. The solute concentration affected the length and the aspect ratio of the rod-like structure although the cooling rate did not so much. The samples were loaded with 0.05 wt% of Rh cocatalyst nanoparticles, which was well dispersed oxide species on the surface. The Rh-loaded samples exhibited photocatalytic activity for hydrogen production in the PSRM. It was found that the photocatalytic production rate varied with the various structural parameters, especially correlated with the crystallite size of the rod-like Na₂Ti₆O₁₃ fine crystals

Vanishing Thermal Mass in the Strongly Coupled QCD/QED medium

In this paper we perform a nonperturbative analysis of a thermal quasifermion in thermal QCD/QED by studying its self-energy function through the Dyson-Schwinger equation with the hard-thermal-loop resummed improved ladder kernel. Our analysis reveals several interesting results, some of which may force us to change the image of the thermal quasifermion: (1) The thermal mass of a quasifermion begins to decrease as the coupling gets stronger and finally disappears in the strong coupling region,(2) the imaginary part of the chiral invariant mass function (i.e., the decay width of the quasifermion) persists to have $O(g^2 T \log (1/g))$ behavior. Present results suggest that in the recently produced strongly coupled quark-gluon-plasma, the thermal mass of a quasifermion should vanish. We also briefly comment on evidence of the existence of a massless, or an ultrasoft mode.Comment: 6 pages, 8 figures, Published versio

Nonoxidative Coupling of Ethane with Gold loaded Photocatalysts

Direct and continuous conversion of ethane to yield n-butane and hydrogen at near room temperature (ca. 320 K) was examined with gold loaded gallium oxide and titanium dioxide photocatalysts without the aid of any oxidant in a flow reactor. A Ga₂O₃ photocatalyst produced n-butane and ethene as well as hydrogen with an almost stoichiometric ratio of products from ethane. Loading Au on the Ga₂O₃ sample gave a 12 times higher production rate of n-butane such as 0.65 μmol h−1 with a high selectivity of 89%. Although a bare TiO₂ sample showed very low yield due to poor reduction resistance, the addition of an Au cocatalyst drastically improved the photocatalytic performance of the TiO₂ sample, i.e., the Au(0.2)/TiO₂ sample produced n-butane and ethene continuously at least for 5 h, where the production rate of n-butane, the n-butane selectivity, and the apparent quantum efficiency (AQE) for n-butane formation were 0.92 μmol h⁻¹, 92%, and 0.02%, respectively. The reaction mechanism of n-butane formation as the main reaction was proposed to be the photocatalytic nonoxidative coupling of ethane (NOCE), which is similar to the photocatalytic nonoxidative coupling of methane (NOCM)