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

Measuring the Fourth Generation b --> s Quadrangle at the LHC

We show that simultaneous precision measurement of the CP-violating phase in time-dependent Bs --> J/psi phi study and the Bs --> mu+ mu- rate, together with measuring m_t' by direct search at the LHC, would determine V_{t's}^*V_{t'b} and therefore the b --> s quadrangle in the four-generation standard model. The forward-backward asymmetry in B --> K* l+ l- provides further discrimination.Comment: 6 pages, 7 figures, revised based on LHC results released in this summer, to appear in PR

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

Adventures in Friedmann Cosmology: An Educationally Detailed Expansion of the Cosmological Friedmann Equations

The general relativistic cosmological Friedmann equations which describe how the scale factor of the universe evolves are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the Friedmann equations when dominated by a single, isotropic, stable, static, perfect-fluid energy form is discussed for different values of its gravitational pressure to density ratio $w$. These energy forms include phantom energy ($w<-1$), cosmological constant ($w=-1$), domain walls ($w = -2/3$), cosmic strings ($w = -1/3$), normal matter ($w = 0$), radiation and relativistic matter ($w = 1/3$), and a previously little-discussed form of energy called "ultralight" ($w>1/3$). A brief history and possible futures of Friedmann universes dominated by a single energy form are discussed.Comment: 32 pages, 4 tables; modified version accepted for publication in the American Journal of Physic

Spins of the supermassive black hole in M87: new constraints from TeV observations

The rapid TeV $\gamma-$ray variability detected in the well-known nearby radio galaxy M87 implies an extremely compact emission region (5-10 Schwarzschild radii) near the horizon of the supermassive black hole in the galactic center. TeV photons are affected by dilution due to interaction with the radiation field of the advection-dominated accretion flow (ADAF) around the black hole, and can thus be used to probe the innermost regions around the black hole. We calculate the optical depth of the ADAF radiation field to the TeV photons and find it strongly depends on the spin of the black hole. We find that transparent radii of 10 TeV photons are of $5R_{\rm S}$ and $13R_{\rm S}$ for the maximally rotating and non-rotating black holes, respectively. With the observations, the calculated transparent radii strongly suggest the black hole is spinning fast in the galaxy. TeV photons could be used as a powerful diagnostic for estimating black hole spins in galaxies in the future.Comment: 4 pages, 4 figures. to appear in ApJ

Scaling in the time-dependent failure of a fiber bundle with local load sharing

We study the scaling behaviors of a time-dependent fiber-bundle model with local load sharing. Upon approaching the complete failure of the bundle, the breaking rate of fibers diverges according to $r(t)\propto (T_f-t)^{-\xi}$, where $T_f$ is the lifetime of the bundle, and $\xi \approx 1.0$ is a quite universal scaling exponent. The average lifetime of the bundle $$ scales with the system size as $N^{-\delta}$, where $\delta$ depends on the distribution of individual fiber as well as the breakdown rule.Comment: 5 pages, 4 eps figures; to appear in Phys. Rev.

Ultrastable Synergistic Tetravalent RNA Nanoparticles for Targeting to Cancers

One of the advantages of nanotechnology is the feasibility to construct therapeutic particles carrying multiple therapeutics with defined structure and stoichiometry. The field of RNA nanotechnology is emerging. However, controlled assembly of stable RNA nanoparticles with multiple functionalities which retain their original role is challenging due to refolding after fusion. Herein, we report the construction of thermodynamically stable X-shaped RNA nanoparticles to carry four therapeutic RNA motifs by self-assembly of reengineered small RNA fragments. We proved that each arm of the four helices in the X-motif can harbor one siRNA, ribozyme, or aptamer without affecting the folding of the central pRNA-X core, and each daughter RNA molecule within the nanoparticle folds into their respective authentic structures and retains their biological and structural function independently. Gene silencing effects were progressively enhanced as the number of the siRNA in each pRNA-X nanoparticles gradually increased from one to two, three, and four. More importantly, systemic injection of ligand-containing nanoparticles into the tail-vein of mice revealed that the RNA nanoparticles remained intact and strongly bound to cancers without entering the liver, lung or any other organs or tissues, while remaining in cancer tissue for more than 8 h

Parker Instability in a Self-Gravitating Magnetized Gas Disk: I. Linear Stability Analysis

To be a formation mechanism of such large-scale structures as giant molecular clouds (GMCs) and HI superclouds, the classical Parker instability driven by external gravity has to overcome three major obstacles: The convective motion accompanying the instability generates thin sheets than large condensations. The degree of density enhancement achieved by the instability is too low to make dense interstellar clouds. The time and the length scales of the instability are significantly longer and larger than the estimated formation time and the observed mean separation of the GMCs, respectively. This paper examines whether a replacement of the driving agent from the external to the self gravity might remove these obstacles by activating the gravitational instability in the Galactic ISM disk. The self gravity can suppress the convective motions, and a cooperative action of the Jeans and the Parker instabilities can remove all the obstacles confronting the classical version of the Parker instability. The mass and mean separation of the structures resulting from the odd-parity undular mode solution are shown to agree better with the HI superclouds than with the GMCs. We briefly discuss how inclusions of the external gravity and cosmic rays would modify behaviors of the odd-parity undular mode solution.Comment: 53 pages, 21 figure

A Practical Guide for X-Ray Diffraction Characterization of Ga(Al, In)N Alloys

Ga(In, Al)N alloys are used as an active layer or cladding layer in light emitting diodes and laser diodes. x-ray diffraction is extensively used to evaluate the crystalline quality, the chemical composition and the residual strain in Ga(Al,In)N thin films, which directly determine the emission wavelength and the device performance. Due to the minor mismatch in lattice parameters between Ga(Al, In)N alloy and a GaN virtual substrate, x-ray diffraction comes to a problem to separate the signal from Ga(Al,In)N alloy and GaN. We give a detailed comparison on different diffraction planes. In order to balance the intensity and peak separation between Ga(Al,In)N alloy and GaN, (0004) and (1015) planes make the best choice for symmetric scan and asymmetric scan, respectively.Comment: 9 pages, 5 figure

Effect of process parameters on microstructure of 42CrMo steel ball hot skew rolling

Microstructure grain refinement is an effective way to improve the quality of 42CrMo steel ball. A three-dimensional thermal-mechanical-microstructure coupled Finite element model (FEM) of steel ball skew rolling is established in the finite element simulation software. Simufact software was used to simulate the effects of process parameters on the microstructure of steel balls, and the effects of roll Angle, roll temperature and roll speed on the average grain size of rolled pieces were analyzed by single factor variable method. The research results provide some reference for the improvement of 42CrMo steel ball quality