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BEGIN:VEVENT
DTSTAMP:20261025T114329Z
LAST-MODIFIED:20121116T203436Z
DTSTART:20110902T143000Z
DTEND:20110902T153000Z
UID:event850@bu.edu
URL:http://physics.bu.edu/internal/events/show/850
SUMMARY:Guanliang Li - Departmental Seminar
DESCRIPTION:Featuring Guanliang Li\n\nPart of the Departmental Seminars.\n\
	nTitle: Transport and Percolation Theory in Weighted Resistor Network\n\n D
	issertation Committee:  H.E. Stanley\, William Skocpol\, Karl Ludwig\,
	  Robert Carey\,  Anatoli Polkovnikov\n\n Abstract:\n We study th
	e distribution $P(\sigma)$ of the equivalent conductance $\sigma$ for Erd\H
	{o}s-R\'enyi (ER) and scale-free (SF) weighted resistor networks with $
	N$ nodes. Each link has conductance $g\equive^{-ax}$\, where $x$ is a rando
	m number taken from a uniform distribution between 0 and 1 and the paramete
	r $a$ represents the strength of the disorder. We provide an iterative fast
	 algorithm to obtain $P(\sigma)$ and compare it with the traditional algori
	thm of solving Kirchhoff equations. We find\, both analytically and numeric
	ally\, that $P(\sigma)$ for ER networks exhibits two regimes. (i) A low con
	ductance regime for $\sigma < e^{-ap_c}$ where $p_c=1/\av{k}$ is the critic
	al percolation threshold of the network and $\av{k}$ is average degree of t
	he network.&nbsp; In this regime $P(\sigma)$ is independent of $N$ and foll
	ows the power law $P(\sigma) \sim \sigma^{-\alpha}$\, where $\alpha=1-\av{k
	}/a$.&nbsp; (ii) A high conductance regime for $\sigma >e^{-ap_c}$ in which
	 we find that $P(\sigma)$ has strong $N$ dependence and scales as $P(\sigma
	) \sim f(\sigma\,ap_c/N^{1/3})$.&nbsp; For SF networks with degree distribu
	tion $P(k)\sim k^{-\lambda}$\, $k_{min} \le k \le k_{max}$\, we find numeri
	cally also two regimes\, similar to those found for ER networks.
LOCATION:SCI 352\, 590 Commonwealth Avenue\, 02215
STATUS:CONFIRMED
CLASS:PUBLIC
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