Scaling of Anisotropic Flows in Intermediate Energy and Ultra-relativistic Heavy Ion Collisions

Anisotropic flows ($v_2$ and $v_4$) of hadrons and light nuclear clusters are studied by a partonic transport model and nucleonic transport model, respectively, in ultra-relativistic and intermediate energy heavy ion collisions. Both number-of-constituent-quark scaling of hadrons, especially for $\phi$ meson which is composed of strange quarks, and number-of-nucleon scaling of light nuclear clusters are discussed and explored for the elliptic flow ($v_2$). The ratios of $v_4/v_2^2$ of hadrons and nuclear clusters are, respectively, calculated and they show different constant values which are independent of transverse momentum. The above phenomena can be understood, respectively, by the coalescence mechanism in quark-level or nucleon-level.Comment: Proceeding of the 6th China-Japan Joint Nuclear Physics Symposium, Shanghai, China, May 16-20, 2006. 9 pages, 4 figure

Scaling of Anisotropic Flows and Nuclear Equation of State in Intermediate Energy Heavy Ion Collisions

Elliptic flow ($v_2$) and hexadecupole flow ($v_4$) of light clusters have been studied in details for 25 MeV/nucleon $^{86}$Kr + $^{124}$Sn at large impact parameters by Quantum Molecular Dynamics model with different potential parameters. Four parameter sets which include soft or hard equation of state (EOS) with/without symmetry energy term are used. Both number-of-nucleon ($A$) scaling of the elliptic flow versus transverse momentum ($p_t$) and the scaling of $v_4/A^{2}$ versus $(p_t/A)^2$ have been demonstrated for the light clusters in all above calculation conditions. It was also found that the ratio of $v_4/{v_2}^2$ keeps a constant of 1/2 which is independent of $p_t$ for all the light fragments. By comparisons among different combinations of EOS and symmetry potential term, the results show that the above scaling behaviors are solid which do not depend the details of potential, while the strength of flows is sensitive to EOS and symmetry potential term.Comment: 5 pages, 5 figure

Pyrite oxidation under initially neutral pH conditions and in the presence of Acidithiobacillus ferrooxidans and micromolar hydrogen peroxide

Hydrogen peroxide (H2O2) at a micromolar level played a role in the microbial surface oxidation of pyrite crystals under initially neutral pH. When the mineral-bacteria system was cyclically exposed to 50 μM H2O2, the colonization of Acidithiobacillus ferrooxidans onto the mineral surface was markedly enhanced, as compared to the control(no added H2O2). This can be attributed to the effects of H2O2 on increasing the roughness of the mineral surfaces, as well as the acidity and Fe2+ concentration at the mineral-solution interfaces. All of these effects tended to create more favourable nanoto micro-scale environments in the mineral surfaces for the cell adsorption. However, higher H2O2 levels inhibited the attachment of cells onto the mineral surfaces, possibly due to the oxidative stress in the bacteria when they approached the mineral surfaces where high levels of free radicals are present as a result of Fenton-like reactions. The more aggressive nature of H2O2 as an oxidant caused marked surface flaking of the mineral surface. The XPS results suggest that H2O2 accelerated the oxidation of pyrite-S and consequently facilitated the overall corrosion cycle of pyrite surfaces. This was accompanied by pH drop in the solution in contact with the pyrite cubes

A Remark on Soliton Equation of Mean Curvature Flow

In this short note, we consider self-similar immersions $F: \mathbb{R}^n \to \mathbb{R}^{n+k}$ of the Graphic Mean Curvature Flow of higher co-dimension. We show that the following is true: Let $F(x) = (x,f(x)), x \in \mathbb{R}^{n}$ be a graph solution to the soliton equation $$\bar{H}(x) + F^{\bot}(x) = 0.$$ Assume $\sup_{\mathbb{R}^{n}}|Df(x)| \le C_{0} < + \infty$. Then there exists a unique smooth function $f_{\infty}: \mathbb{R}^{n}\to \mathbb{R}^k$ such that $$f_{\infty}(x) = \lim_{\lambda \to \infty}f_{\lambda}(x)$$ and $$f_{\infty}(r x)=r f_{\infty}(x)$$ for any real number $r\not= 0$, where $$f_{\lambda}(x) = \lambda^{-1}f(\lambda x).$$Comment: 6 page