Optimization of robustness of scale-free network to random and targeted attacks

The scale-fee networks, having connectivity distribution $P(k)\sim k^{-\alpha}$ (where $k$ is the site connectivity), is very resilient to random failures but fragile to intentional attack. The purpose of this paper is to find the network design guideline which can make the robustness of the network to both random failures and intentional attack maximum while keeping the average connectivity per node constant. We find that when $=3$ the robustness of the scale-free networks reach its maximum value if the minimal connectivity $m=1$, but when is larger than four, the networks will become more robust to random failures and targeted attacks as the minimal connectivity $m$ gets larger

Optimization of scale-free network for random failures

It has been found that the networks with scale-free distribution are very resilient to random failures. The purpose of this work is to determine the network design guideline which maximize the network robustness to random failures with the average number of links per node of the network is constant. The optimal value of the distribution exponent and the minimum connectivity to different network size are given in this paper. Finally, the optimization strategy how to improve the evolving network robustness is given.Comment: 6 pages, 1 figur

First-principles study of stability and vibrational properties of tetragonal PbTiO_3

A first-principles study of the vibrational modes of PbTiO_3 in the ferroelectric tetragonal phase has been performed at all the main symmetry points of the Brillouin zone (BZ). The calculations use the local-density approximation and ultrasoft pseudopotentials with a plane-wave basis, and reproduce well the available experimental information on the modes at the Gamma point, including the LO-TO splittings. The work was motivated in part by a previously reported transition to an orthorhombic phase at low temperatures [(J. Kobayashi, Y. Uesu, and Y. Sakemi, Phys. Rev. B {\bf 28}, 3866 (1983)]. We show that a linear coupling of orthorhombic strain to one of the modes at Gamma plays a role in the discussion of the possibility of this phase transition. However, no mechanical instabilities (soft modes) are found, either at Gamma or at any of the other high-symmetry points of the BZ.Comment: 8 pages, two-column style with 3 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#ag_pbt

LDA+Gutzwiller Method for Correlated Electron Systems: Formalism and Its Applications

We introduce in detail our newly developed \textit{ab initio} LDA+Gutzwiller method, in which the Gutzwiller variational approach is naturally incorporated with the density functional theory (DFT) through the "Gutzwiller density functional theory (GDFT)" (which is a generalization of original Kohn-Sham formalism). This method can be used for ground state determination of electron systems ranging from weakly correlated metal to strongly correlated insulators with long-range ordering. We will show that its quality for ground state is as high as that by dynamic mean field theory (DMFT), and yet it is computationally much cheaper. In additions, the method is fully variational, the charge-density self-consistency can be naturally achieved, and the quantities, such as total energy, linear response, can be accurately obtained similar to LDA-type calculations. Applications on several typical systems are presented, and the characteristic aspects of this new method are clarified. The obtained results using LDA+Gutzwiller are in better agreement with existing experiments, suggesting significant improvements over LDA or LDA+U.Comment: 20 pages, 11 figure