Scaling of critical connectivity of mobile ad hoc communication networks

In this paper, critical global connectivity of mobile ad hoc communication networks (MAHCN) is investigated. We model the two-dimensional plane on which nodes move randomly with a triangular lattice. Demanding the best communication of the network, we account the global connectivity $\eta$ as a function of occupancy $\sigma$ of sites in the lattice by mobile nodes. Critical phenomena of the connectivity for different transmission ranges $r$ are revealed by numerical simulations, and these results fit well to the analysis based on the assumption of homogeneous mixing . Scaling behavior of the connectivity is found as $\eta \sim f(R^{\beta}\sigma)$, where $R=(r-r_{0})/r_{0}$, $r_{0}$ is the length unit of the triangular lattice and $\beta$ is the scaling index in the universal function $f(x)$. The model serves as a sort of site percolation on dynamic complex networks relative to geometric distance. Moreover, near each critical $\sigma_c(r)$ corresponding to certain transmission range $r$, there exists a cut-off degree $k_c$ below which the clustering coefficient of such self-organized networks keeps a constant while the averaged nearest neighbor degree exhibits a unique linear variation with the degree k, which may be useful to the designation of real MAHCN.Comment: 6 pages, 6 figure

Hidden and Generalized Conformal Symmetry of Kerr-Sen Spacetimes

It is recently conjectured that generic non-extremal Kerr black hole could be holographically dual to a hidden conformal field theory in two dimensions. Moreover, it is known that there are two CFT duals (pictures) to describe the charged rotating black holes which correspond to angular momentum $J$ and electric charge $Q$ of the black hole. Furthermore these two pictures can be incorporated by the CFT duals (general picture) that are generated by $SL(2,\mathbb{Z})$ modular group. The general conformal structure can be revealed by looking at charged scalar wave equation in some appropriate values of frequency and charge. In this regard, we consider the wave equation of a charged massless scalar field in background of Kerr-Sen black hole and show in the "near region", the wave equation can be reproduced by the Casimir operator of a local $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetry. We can find the exact agreement between macroscopic and microscopic physical quantities like entropy and absorption cross section of scalars for Kerr-Sen black hole. We then find an extension of vector fields that in turn yields an extended local family of $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetries, parameterized by one parameter. For some special values of the parameter, we find a copy of $SL(2,\mathbb{R})$ hidden conformal algebra for the charged Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the strong deflection limit.Comment: 16 pages, new material and results added, extensive improvements in interpretation of results, references adde

Hidden Conformal Symmetry of Extremal Kerr-Bolt Spacetimes

We show that extremal Kerr-Bolt spacetimes have a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt spacetimes and find in the "near region", the wave equation in extremal limit can be written in terms of the $SL(2,R)$ quadratic Casimir. Moreover, we obtain the microscopic entropy of the extremal Kerr-Bolt spacetimes also we calculate the correlation function of a near-region scalar field and find perfect agreement with the dual 2D CFT.Comment: 13 page

Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities

A quasi-Gaussian approximation scheme is formulated to study the strongly correlated imbalanced fermions thermodynamics, where the mean-field theory is not applicable. The non-Gaussian correlation effects are understood to be captured by the statistical geometric mean of the individual susceptibilities. In the three-dimensional unitary fermions ground state, an {\em universal} non-linear scaling transformation relates the physical chemical potentials with the individual Fermi kinetic energies. For the partial polarization phase separation to full polarization, the calculated critical polarization ratio is $P_C={[1-(1-\xi)^{6/5}]}/{[1+(1-\xi)^{6/5}]}\doteq 0.34$. The $\xi=4/9$ defines the ratio of the symmetric ground state energy density to that of the ideal fermion gas.Comment: Minor changes with typos correcte

Stability of a neural network model with small-world connections

Small-world networks are highly clustered networks with small distances among the nodes. There are many biological neural networks that present this kind of connections. There are no special weightings in the connections of most existing small-world network models. However, this kind of simply-connected models cannot characterize biological neural networks, in which there are different weights in synaptic connections. In this paper, we present a neural network model with weighted small-world connections, and further investigate the stability of this model.Comment: 4 pages, 3 figure

Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems

Entanglement of the ground states in $XXZ$ and dimerized Heisenberg spin chains as well as in a two-leg spin ladder is analyzed by using the spin-spin concurrence and the entanglement entropy between a selected sublattice of spins and the rest of the system. In particular, we reveal that quantum phase transition points/boundaries may be identified based on the analysis on the local extreme of this entanglement entropy, which is illustrated to be superior over the concurrence scenario and may enable us to explore quantum phase transitions in many other systems including higher dimensional ones.Comment: 4 pages, 4 figure

Electron Accumulation and Emergent Magnetism in LaMnO3/SrTiO3 Heterostructures

Emergent phenomena at polar-nonpolar oxide interfaces have been studied intensely in pursuit of next-generation oxide electronics and spintronics. Here we report the disentanglement of critical thicknesses for electron reconstruction and the emergence of ferromagnetism in polar-mismatched LaMnO3/SrTiO3 (001) heterostructures. Using a combination of element-specific X-ray absorption spectroscopy and dichroism, and first-principles calculations, interfacial electron accumulation and ferromagnetism have been observed within the polar, antiferromagnetic insulator LaMnO3. Our results show that the critical thickness for the onset of electron accumulation is as thin as 2 unit cells (UC), significantly thinner than the observed critical thickness for ferromagnetism of 5 UC. The absence of ferromagnetism below 5 UC is likely induced by electron over-accumulation. In turn, by controlling the doping of the LaMnO3, we are able to neutralize the excessive electrons from the polar mismatch in ultrathin LaMnO3 films and thus enable ferromagnetism in films as thin as 3 UC, extending the limits of our ability to synthesize and tailor emergent phenomena at interfaces and demonstrating manipulation of the electronic and magnetic structures of materials at the shortest length scales.Comment: Accepted by Phys. Rev. Let

Quasi-local Energy for Spherically Symmetric Spacetimes

We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface and extremize the energy. This can be done in two ways, which we call programs I (without constraint) and II (with additional constraints). On the other hand, we match the orthonormal 4-frames of the dynamic and the reference spacetimes. Then, if we further specify the observer by requiring the reference displacement to be the timelike Killing vector of the reference, the result is the same as program I, and the energy can be positive, zero, or even negative. If, instead, we require that the Lie derivatives of the two-area along the displacement vector in both the dynamic and reference spacetimes to be the same, the result is the same as program II, and it satisfies the usual criteria: the energies are non-negative and vanish only for Minkowski (or anti-de Sitter) spacetime.Comment: 16 pages, no figure