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

The progenitors of Type Ia supernovae with long delay times

The nature of the progenitors of Type Ia supernovae (SNe Ia) is still unclear. In this paper, by considering the effect of the instability of accretion disk on the evolution of white dwarf (WD) binaries, we performed binary evolution calculations for about 2400 close WD binaries, in which a carbon--oxygen WD accretes material from a main-sequence star or a slightly evolved subgiant star (WD + MS channel), or a red-giant star (WD + RG channel) to increase its mass to the Chandrasekhar (Ch) mass limit. According to these calculations, we mapped out the initial parameters for SNe Ia in the orbital period--secondary mass ($\log P^{\rm i}-M^{\rm i}_2$) plane for various WD masses for these two channels, respectively. We confirm that WDs in the WD + MS channel with a mass as low as $0.61 M_\odot$ can accrete efficiently and reach the Ch limit, while the lowest WD mass for the WD + RG channel is $1.0 \rm M_\odot$. We have implemented these results in a binary population synthesis study to obtain the SN Ia birthrates and the evolution of SN Ia birthrates with time for both a constant star formation rate and a single starburst. We find that the Galactic SN Ia birthrate from the WD + MS channel is $\sim$$1.8\times 10^{-3} {\rm yr}^{-1}$ according to our standard model, which is higher than previous results. However, similar to previous studies, the birthrate from the WD + RG channel is still low ($\sim$$3\times 10^{-5} {\rm yr}^{-1}$). We also find that about one third of SNe Ia from the WD + MS channel and all SNe Ia from the WD + RG channel can contribute to the old populations (\ga1 Gyr) of SN Ia progenitors.Comment: 11 pages, 9 figures, 1 table, accepted for publication in MNRA