Holographic Van der Waals phase transition for a hairy black hole

The Van der Waals(VdW) phase transition in a hairy black hole is investigated by analogizing its charge, temperature, and entropy as the temperature, pressure, and volume in the fluid respectively. The two point correlation function(TCF), which is dual to the geodesic length, is employed to probe this phase transition. We find the phase structure in the temperature$-$geodesic length plane resembles as that in the temperature$-$thermal entropy plane besides the scale of the horizontal coordinate. In addition, we find the equal area law(EAL) for the first order phase transition and critical exponent of the heat capacity for the second order phase transition in the temperature$-$geodesic length plane are consistent with that in temperature$-$thermal entropy plane, which implies that the TCF is a good probe to probe the phase structure of the back hole.Comment: Accepted by Advances in High Energy Physics(The special issue: Applications of the Holographic Duality to Strongly Coupled Quantum Systems

Gravitational waves with dark matter minispikes: the combined effect

It was shown that the dark matter(DM) minihalo around an intermediate mass black hole(IMBH) can be redistributed into a cusp, called the DM minispike. We consider an intermediate-mass-ratio inspiral consisting of an IMBH harbored in a DM minispike with nonannihilating DM particles and a small black hole(BH) orbiting around it. We investigate gravitational waves(GWs) produced by this system and analyze the waveforms with the comprehensive consideration of gravitational pull, dynamical friction and accretion of the minispike and calculate the time difference and phase difference caused by it. We find that for a certain range of frequency, the inspiralling time of the system is dramatically reduced for smaller central IMBH and large density of DM. For the central IMBH with $10^5M_\odot$, the time of merger is ahead, which can be distinguished by LISA, Taiji and Tianqin. We focus on the effect of accretion and compare it with that of gravitational pull and friction. We find that the accretion mass is a small quantity compared to the initial mass of the small BH and the accretion effect is inconspicuous compared with friction. However, the accumulated phase shift caused by accretion is large enough to be detected by LISA, Taiji and Tianqin, which indicate that the accretion effect can not be ignored in the detection of GWs.Comment: 10 pages, 14 figure

Correlations and Scaling Laws in Human Mobility

Human mobility patterns deeply affect the dynamics of many social systems. In this paper, we empirically analyze the real-world human movements based GPS records, and observe rich scaling properties in the temporal-spatial patterns as well as an abnormal transition in the speed-displacement patterns. We notice that the displacements at the population level show significant positive correlation, indicating a cascade-like nature in human movements. Furthermore, our analysis at the individual level finds that the displacement distributions of users with strong correlation of displacements are closer to power laws, implying a relationship between the positive correlation of the series of displacements and the form of an individual's displacement distribution. These findings from our empirical analysis show a factor directly relevant to the origin of the scaling properties in human mobility.Comment: 10 pages, 9 figure

Centralizer of fixed point free separating flows

In this paper, we study the centralizer of a separating continuous flow without fixed points. We show that if $M$ is a compact metric space and $\phi_t:M\to M$ is a separating flow without fixed points, then $\phi_t$ has a quasi-trivial centralizer, that is, if a continuous flow $\psi_t$ commutes with $\phi_t$, then there exists a continuous function $A: M\to\mathbb{R}$ which is invariant along the orbit of $\phi_t$ such that $\psi_t(x)=\phi_{A(x)t}(x)$ holds for all $x\in M$. We also show that if $M$ is a compact Riemannian manifold without boundary and $\Phi_u$ is a separating $C^1$ $\mathbb{R}^d$-action on $M$, then $\Phi_u$ has a quasi-trivial centralizer, that is, if $\Psi_u$ is a $\mathbb{R}^d$-action on $M$ commuting with $\Phi_u$, then there is a continuous map $A: M\to\mathcal{M}_{d\times d}(\mathbb{R})$ which is invariant along orbit of $\Phi_u$ such that $\Psi_{u}(x)=\Phi_{A(x)u}(x)$ for all $x\in M$. These improve Theorem 1 of \cite{O} and Theorem 2 of \cite{BRV} respectively