Predicting the epidemic threshold of the susceptible-infected-recovered model

Researchers have developed several theoretical methods for predicting epidemic thresholds, including the mean-field like (MFL) method, the quenched mean-field (QMF) method, and the dynamical message passing (DMP) method. When these methods are applied to predict epidemic threshold they often produce differing results and their relative levels of accuracy are still unknown. We systematically analyze these two issues---relationships among differing results and levels of accuracy---by studying the susceptible-infected-recovered (SIR) model on uncorrelated configuration networks and a group of 56 real-world networks. In uncorrelated configuration networks the MFL and DMP methods yield identical predictions that are larger and more accurate than the prediction generated by the QMF method. When compared to the 56 real-world networks, the epidemic threshold obtained by the DMP method is closer to the actual epidemic threshold because it incorporates full network topology information and some dynamical correlations. We find that in some scenarios---such as networks with positive degree-degree correlations, with an eigenvector localized on the high $k$-core nodes, or with a high level of clustering---the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input parameter, performs better than the other two methods. We also find that the performances of the three predictions are irregular versus modularity

Mean-field study of itinerant ferromagnetism in trapped ultracold Fermi gases: Beyond the local density approximation

We theoretically investigate the itinerant ferromagnetic transition of a spherically trapped ultracold Fermi gas with spin imbalance under strongly repulsive interatomic interactions. Our study is based on a self-consistent solution of the Hartree-Fock mean-field equations beyond the widely used local density approximation. We demonstrate that, while the local density approximation holds in the paramagnetic phase, after the ferromagnetic transition it leads to a quantitative discrepancy in various thermodynamic quantities even with large atom numbers. We determine the position of the phase transition by monitoring the shape change of the free energy curve with increasing the polarization at various interaction strengths.Comment: 7 pages, 5 figures; published version in Phys. Rev.

Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality

We consider Einstein-Horndeski-Maxwell gravity, together with a cosmological constant and multiple Horndeski axions. We construct charged AdS planar black holes in general dimensions where the Horndeski anxions span over the planar directions. We analyse the thermodynamics and obtain the black hole volumes. We show that the reverse isoperimetric inequality can be violated, implying that these black holes can store information more efficiently than the Schwarzschild black hole.Comment: Latex, 25 pages, 1 figure, references adde

Black Hole Entropy and Viscosity Bound in Horndeski Gravity

Horndeski gravities are theories of gravity coupled to a scalar field, in which the action contains an additional non-minimal quadratic coupling of the scalar, through its first derivative, to the Einstein tensor or the analogous higher-derivative tensors coming from the variation of Gauss-Bonnet or Lovelock terms. In this paper we study the thermodynamics of the static black hole solutions in $n$ dimensions, in the simplest case of a Horndeski coupling to the Einstein tensor. We apply the Wald formalism to calculate the entropy of the black holes, and show that there is an additional contribution over and above those that come from the standard Wald entropy formula. The extra contribution can be attributed to unusual features in the behaviour of the scalar field. We also show that a conventional regularisation to calculate the Euclidean action leads to an expression for the entropy that disagrees with the Wald results. This seems likely to be due to ambiguities in the subtraction procedure. We also calculate the viscosity in the dual CFT, and show that the viscosity/entropy ratio can violate the $\eta/S\ge 1/(4\pi)$ bound for appropriate choices of the parameters.Comment: 30 pages, no figure, minor revision

The dielectrophoresis of cylindrical and spherical particles submerged in shells and in semi-infinite media

The dielectrophoretic forces acting on and the resulting velocities of cylindrical and spherical particles embedded in perfectly dielectric viscous fluids are calculated analytically. The fluids are confined in cylindrical/spherical shells and in semi-infinite media with prescribed potential distributions along the surfaces of the media. The forces are calculated by evaluating the Maxwell stress tensor. The velocities of the particles are obtained by solving the Stokes equation for creeping flow. The range of validity of force calculations based on the dipole-moment approximation is estimated

Optical rotation of heavy hole spins by non-Abelian geometrical means

A non-Abelian geometric method is proposed for rotating of heavy hole spins in a singly positive charged quantum dot in Voigt geometry. The key ingredient is the delay-dependent non-Abelian geometric phase, which is produced by the nonadiabatic transition between the two degenerate dark states. We demonstrate, by controlling the pump, the Stokes and the driving fields, that the rotations about $y$- and $z$-axes with arbitrary angles can be realized with high fidelity. Fast initialization and heavy hole spin state readout are also possible.Comment: 7 pages, 6 figure

On the translation of a cylinder in a long tube

We study the motion of a cylindrical particle translating slowly in a long tube as a function of the particle\u27s dimensions and placement both in the presence and the absence of external pressure gradients. The cylinder acts as a leaky piston, generating both fluid recirculation and through flow. When the particle is long, analytic expressions are obtained for both the velocity field and the force needed to sustain the particle’s motion as functions of the particle\u27s position and dimensions. When the particle is short, a superposition-based algorithm is outlined to facilitate economical numerical calculations. When the particle is placed off center in the tube, torque will act on the particle. When the particle is unguided, this torque will preclude coaxial motion and cause the particle to follow an oscillatory trajectory