%0 Book Section %1 statphys23_0608 %A Lee, S. %A Yook, S.H. %A Kim, Y. %A Yoon, S. %A Kim, H. %A Lee, D. %A Ko, Y. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K capture diffusive network process scale-free statphys23 topic-11 %T Diffusive capture process on scale-free networks %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=608 %X We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the scale-free networks with various sizes of $N$. We find that the life time $łeft<T\right>$ of a lamb scales as $łeft<T\right>N$ and the survival probability $S(Nınfty,t)$ becomes finite on scale-free networks with degree exponent $\gamma>3$. However, $S(N,t)$ for $\gamma<3$ has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. It suggests that the second moment of degree distribution $łeft<k^2\right>$ is the relevant factor for the dynamical properties in diffusive capture process. We numerically find that the normalized number of capture events at a node with degree $k$, $n(k)$, decreases as $n(k)k^-\sigma$. When $\gamma<3$, $n(k)$ still increases anomalously for $kk_max$, where $k_max$ is the maximum value of $k$ of given networks with size $N$. We analytically show that $n(k)$ satisfies the relation $n(k)k^2P(k)$ for any degree distribution $P(k)$ and the total number of capture events $N_tot$ is proportional to $łeft<k^2\right>$, which causes the $\gamma$ dependent behavior of $S(N,t)$ and $łeft<T\right>$

@incollection{statphys23_0608, abstract = {We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the scale-free networks with various sizes of $N$. We find that the life time $\left<T\right>$ of a lamb scales as $\left<T\right>\sim N$ and the survival probability $S(N\rightarrow \infty,t)$ becomes finite on scale-free networks with degree exponent $\gamma>3$. However, $S(N,t)$ for $\gamma<3$ has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. It suggests that the second moment of degree distribution $\left<k^2\right>$ is the relevant factor for the dynamical properties in diffusive capture process. We numerically find that the normalized number of capture events at a node with degree $k$, $n(k)$, decreases as $n(k)\sim k^{-\sigma}$. When $\gamma<3$, $n(k)$ still increases anomalously for $k\approx k_{max}$, where $k_{max}$ is the maximum value of $k$ of given networks with size $N$. We analytically show that $n(k)$ satisfies the relation $n(k)\sim k^2P(k)$ for any degree distribution $P(k)$ and the total number of capture events $N_{tot}$ is proportional to $\left<k^2\right>$, which causes the $\gamma$ dependent behavior of $S(N,t)$ and $\left<T\right>$}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Lee, S. and Yook, S.H. and Kim, Y. and Yoon, S. and Kim, H. and Lee, D. and Ko, Y.}, biburl = {https://www.bibsonomy.org/bibtex/249216bf652ed72e451cd308462b6b0a6/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {0d57c5e925ea3fffbe86fc1b9b95e065}, intrahash = {49216bf652ed72e451cd308462b6b0a6}, keywords = {capture diffusive network process scale-free statphys23 topic-11}, month = {9-13 July}, timestamp = {2007-06-20T10:16:24.000+0200}, title = {Diffusive capture process on scale-free networks}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=608}, year = 2007 }