Two 3-Branes in Randall-Sundrum Setup and Current Acceleration of the Universe

Five-dimensional spacetimes of two orbifold 3-branes are studied, by assuming that {\em the two 3-branes are spatially homogeneous, isotropic, and independent of time}, following the so-called "bulk-based" approach. The most general form of the metric is obtained, and the corresponding field equations are divided into three groups, one is valid on each of the two 3-branes, and the third is valid in the bulk. The Einstein tensor on the 3-branes is expressed in terms of the discontinuities of the first-order derivatives of the metric coefficients. Thus, once the metric is known in the bulk, the distribution of the Einstein tensor on the two 3-branes is uniquely determined. As applications, we consider two different cases, one is in which the bulk is locally $AdS_{5}$, and the other is where it is vacuum. In some cases, it is shown that the universe is first decelerating and then accelerating. The global structure of the bulk as well as the 3-branes is also studied, and found that in some cases the solutions may represent the collision of two orbifold 3-branes. The applications of the formulas to the studies of the cyclic universe and the cosmological constant problem are also pointed out.Comment: revtex4, 14 figures, published in Nucl. Phys. B797 (2008) 395 - 43

Thermodynamic Geometry and Critical Behavior of Black Holes

Based on the observations that there exists an analogy between the Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black holes and the van der Waals-Maxwell liquid-gas system, in which a correspondence of variables is $(\phi, q) \leftrightarrow (V,P)$, we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN-AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes. Our result for the RN-AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.Comment: Revtex, 18 pages including 4 figure

Dryland maize yields and water use efficiency in response to tillage and nutrient management practices in China

Rainfed crop production in northern China is constrained by low and variable rainfall. This study explored the effects of tillage and nutrient management practices on maize (Zea mays L.) yield and water use efficiency (WUE), at Shouyang Dryland Farming Experimental Station in northern China during 2003-2008. The experiment was set-up using a split-plot design with 3 tillage methods as main treatments: conventional, reduced (till with crop residue incoperated in fall but no-till in spring), and no-till. Sub-treatments were 3 NP fertilizer rates: 105-46, 179-78 and 210-92 kg N and P ha. -1 Maize grain yields were greatly influenced by the amount of growing season rainfall, and by soil water contents at sowing. Mean grain yields over the 6-year period in response to tillage treatments were 5604, 5347 and 5185 kg ha, under reduced, no-till and conventional tillage, respectively. Mean WUE was 13.7, 13.6 and 12.6 kg ha mm under reduced, no-till, and conventional tillage, respectively. Mean soil water contents at sowing and at harvest were significantly influenced by tillage treatments. At harvest time, the no-till treatment had ~8-12% more water in the soil than the conventional and reduced tillage treatments. Under conventional tillage, grain yields increased with NP fertilizer application rates. However, under reduced tillage, grain yields were highest with lowest NP fertilizer application rate. In conclusion, grain yields and WUE were highest under reduced tillage at modest NP fertilizer application rates of 105 kg N and 46 kg P per ha. No-till increased soil water storage by 8-12% and improved WUE compared to conventional tillage

A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In particular, it is shown that the rate of convergence between the estimator and the true $s$-sparse precision matrix under the spectral norm is $s\sqrt{\log p/n}$ when the population distribution has either exponential-type tails or polynomial-type tails. Convergence rates under the elementwise $L_{\infty}$ norm and Frobenius norm are also presented. In addition, graphical model selection is considered. The procedure is easily implementable by linear programming. Numerical performance of the estimator is investigated using both simulated and real data. In particular, the procedure is applied to analyze a breast cancer dataset. The procedure performs favorably in comparison to existing methods.Comment: To appear in Journal of the American Statistical Associatio

The Cardy-Verlinde formula and entropy of Topological Reissner-Nordstr\"om black holes in de Sitter spaces

In this paper we discuss the question of whether the entropy of cosmological horizon in Topological Reissner-Nordstr\"om- de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. Furthermore, we find that the entropy of black hole horizon can also be rewritten in terms of the Cardy-Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. Our result is in favour of the dS/CFT correspondence.Comment: 6 pages, accepted for publication in IJMP

Light-like noncommutativity and duality from open strings/branes

In this paper we perform some non-trivial tests for the recently obtained open membrane/D-brane metrics and `generalized' noncommutativity parameters using Dp/NS5/M5-branes which have been deformed by light-like fields. The results obtained give further evidence that these open membrane/D-brane metrics and `generalized' noncommutativity parameters are correct. Further, we use the open brane data and supergravity duals to obtain more information about non-gravitational theories with light-like noncommutativity, or `generalized' light-like noncommutativity. In particular, we investigate various duality relations (strong coupling limits). In the light-like case we also comment on the relation between open membrane data (open membrane metric etc.) in six dimensions and open string data in five dimensions. Finally, we investigate the strong coupling limit (high energy limit) of five dimensional NCYM with \Theta^{12}=\Theta^{34}. In particular, we find that this NCYM theory can be UV completed by a DLCQ compactification of M-theory.Comment: 24 pages, Latex. v2:Comments and references added. v3:Version published in JHE

Interaction of a Nanomagnet with a Weak Superconducting Link

We study electromagnetic interaction of a nanomagnet with a weak superconducting link. Equations that govern coupled dynamics of the two systems are derived and investigated numerically. We show that the presence of a small magnet in the proximity of a weak link may be detected through Shapiro-like steps caused by the precession of the magnetic moment. Despite very weak magnetic field generated by the weak link, a time-dependent bias voltage applied to the link can initiate a non-linear dynamics of the nanomagnet that leads to the reversal of its magnetic moment. We also consider quantum problem in which a nanomagnet interacting with a weak link is treated as a two-state spin system due to quantum tunneling between spin-up and spin-down states.Comment: 7 pages, 4 figure