Impacts of the observed theta_{13} on the running behaviors of Dirac and Majorana neutrino mixing angles and CP-violating phases

The recent observation of the smallest neutrino mixing angle $\theta_{13}$ in the Daya Bay and RENO experiments motivates us to examine whether $\theta_{13} \simeq 9^\circ$ at the electroweak scale can be generated from $\theta_{13} = 0^\circ$ at a superhigh-energy scale via the radiative corrections. We find that it is difficult but not impossible in the minimal supersymmetric standard model (MSSM), and a relatively large $\theta_{13}$ may have some nontrivial impacts on the running behaviors of the other two mixing angles and CP-violating phases. In particular, we demonstrate that the CP-violating phases play a crucial role in the evolution of the mixing angles by using the one-loop renormalization-group equations of the Dirac or Majorana neutrinos in the MSSM. We also take the "correlative" neutrino mixing pattern with $\theta_{12} \simeq 35.3^\circ$, $\theta_{23} = 45^\circ$ and $\theta_{13} \simeq 9.7^\circ$ at a presumable flavor symmetry scale as an example to illustrate that the three mixing angles can receive comparably small radiative corrections and thus evolve to their best-fit values at the electroweak scale if the CP-violating phases are properly adjusted.Comment: RevTeX 16 pages, 3 figures, 4 tables, more discussions added, references updated. Accepted for publication in Phys. Rev.

Acyclic orientations on the Sierpinski gasket

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket $SG_{2,b}(n)$ at stage $n$ with $b$ equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants for $SG_{2,b}$ and $d$-dimensional Sierpinski gasket $SG_d$.Comment: 20 pages, 8 figures and 6 table

A high order compact scheme for hypersonic aerothermodynamics

A novel high order compact scheme for solving the compressible Navier-Stokes equations has been developed. The scheme is an extension of a method originally proposed for solving the Euler equations, and combines several techniques for the solution of compressible flowfields, such as upwinding, limiting and flux vector splitting, with the excellent properties of high order compact schemes. Extending the method to the Navier-Stokes equations is achieved via a Kinetic Flux Vector Splitting technique, which represents an unusual and attractive way to include viscous effects. This approach offers a more accurate and less computationally expensive technique than discretizations based on more conventional operator splitting. The Euler solver has been validated against several inviscid test cases, and results for several viscous test cases are also presented. The results confirm that the method is stable, accurate and has excellent shock-capturing capabilities for both viscous and inviscid flows

S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Investigation on dynamic behaviours of liquid and solid phases within non-homogeneous debris flows

The non-homogeneous debris flows, consisting of a wide range of grain size, bulk density and demonstrating non-uniform velocity distributions, are commonly modeled as the two-phase flow. In adopting such an approach, a critical grain diameter to separate the solid and liquid phase, within such debris flows, can be determined through the principles of minimum energy dissipation. In the current study, an improved analytical approach using the resistance formula of water flow and mass conservation law is presented to determine the velocity of the solid and liquid phases within a non-homogeneous debris flow, based on the derived critical grain diameter. Some of the dynamic parameters required in the analysis are validated against the experimental data of a non-homogeneous, two-phase debris flow measured from the Jiangjia gully, Yunnan Province of China. The results show that, for the majority of non-homogeneous debris flows tested, the liquid phase exhibits higher velocity than the solid phase. However, as the bulk density of the debris flow increases, the solid phase tends to have higher velocity than the liquid phase. These findings are shown to have important implications on the vertical grading patterns of the bed deposits in depositional areas. The observations from the field studies indicate that the non-homogeneous debris flows with bulk density being significantly lower, close to and significantly higher than the critical value seem to exhibit normal (i.e. bed-to-surface vertical fining), mixed, and inverse (bed-to-surface vertical coarsening) grading patterns in the alluvial fan deposits

Effect of miR-146a/bFGF/PEG-PEI Nanoparticles on Inflammation Response and Tissue Regeneration of Human Dental Pulp Cells

published_or_final_versio

Application of the methods of limit analysis to the evaluation of the strength of fiber-reinforced composites

Limit analysis of plasticity applied to strength evaluation of fiber reinforced composite

^{59}Co NMR evidence for charge ordering below T_{CO}\sim 51 K in Na_{0.5}CoO_2

The CoO$_{2}$ layers in sodium-cobaltates Na$_{x}$CoO$_{2}$ may be viewed as a spin $S=1/2$ triangular-lattice doped with charge carriers. The underlying physics of the cobaltates is very similar to that of the high $T_{c}$ cuprates. We will present unequivocal $^{59}$Co NMR evidence that below $T_{CO}\sim51 K$, the insulating ground state of the itinerant antiferromagnet Na$_{0.5}$CoO$_{2}$ ($T_{N}\sim 86 K$) is induced by charge ordering.Comment: Phys. Rev. Lett. 100 (2008), in press. 4 figure