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BEGIN:VEVENT
DTSTAMP:20260729T090549Z
LAST-MODIFIED:20121116T203436Z
DTSTART:20120912T200000Z
DTEND:20120912T210000Z
UID:event968@bu.edu
URL:http://physics.bu.edu/internal/events/show/968
SUMMARY:TRANSPORT AND PERCOLATION IN COMPLEX NETWORKS 
DESCRIPTION:Featuring Guanliang Li\n\nPart of the PhD Final Oral Exams.\n\n
	Dissertation Committee:  H. Eugene Stanley\, William Skocpol\, Karl Lu
	dwig\, William Klein\, Martin Schmaltz\n \nAbstract: To design complex
	 networks with optimal transport properties such as flow efficiency\, we co
	nsider three approaches to understanding transport and percolation in compl
	ex networks. We analyze the effects of randomizing the strengths of connect
	ions\, randomly adding long-range connections to regular lattices and perco
	lation of spatially constrained networks.  Various real-world networks ofte
	n have links that are differentiated in terms of their strength\, intensity
	\, or capacity. We study the distribution $P(\sigma)$ of the equivalent con
	ductance for Erd\H{o}s-R\'enyi (ER) and scale-free (SF) weighted resistor n
	etworks with $N$ nodes\, for which links are assigned with conductance $\si
	gma_i \equiv e^{-ax_i}$\, where $x_i$ is a random variable with $0<x_i<1$. 
	We find\, both analytically and numerically\, that $P(\sigma)$ for ER netwo
	rks exhibits two regimes: (i) For $\sigma < e^{-ap_c}$\, $P(\sigma)$ is ind
	ependent of $N$ and scales as $P(\sigma) \sim \sigma^{-\delta}$\, where $\d
	elta=1-\frac{1}{ap_c}$. Here $p_c=1/\av{k}$ is the critical percolation thr
	eshold of the network and $\av{k}$ is the average degree of the network. (i
	i) For $ \sigma > e^{-ap_c}$\, $P(\sigma)$ has strong $N$ dependence and sc
	ales as $P(\sigma) \sim f(\sigma\,ap_c/N^{1/3})$.  Transport properties are
	 greatly affected by the topology of networks. We investigate the transport
	 problem in lattices with long-range connections and subject to a cost cons
	traint\, seeking design principles for optimal transport networks. Our netw
	ork is built from a regular $d$-dimensional lattice to be improved by addin
	g long-range connections with probability $P_{ij} \sim r_{ij}^{-\alpha}$\, 
	where $r_{ij}$ is the lattice distance between site $i$ and $j$. We introdu
	ce a cost constraint on the total length of the additional links and find o
	ptimal transport in the system for $ \alpha=d+1 $\, established here for $d
	=1\, 2$ and $3$ for regular lattices and $d_f$ for fractals. Remarkably\, t
	his cost constraint approach remains optimal\, regardless of the strategy u
	sed for transport\, whether based on local or global knowledge of the netwo
	rk structure.  To further understand the role that long-range connections p
	lay in optimizing the transport of complex systems\, we study the percolati
	on of spatially constrained networks. We now consider originally empty latt
	ices embedded in $d$ dimensions by adding long-range connections with the s
	ame power law probability $p(r) \sim r^{-\alpha}$. We find that\, for $\alp
	ha \le d$\, the percolation transition belongs to the universality class of
	 percolation in ER networks\, while for $\alpha >2d$ it belongs to the univ
	ersality class of percolation in regular lattices (for one dimension\, ther
	e is no percolation transition as one-dimensional regular lattice). However
	 for $d <\alpha < 2d$\, the percolation properties show new intermediate be
	havior different from ER networks\, with critical exponents that depend on 
	$\alpha$.  \nPicture1.png\n&nbsp;\nUID>/INBOX>161743?part=1.2&amp;type=imag
	e/png&amp;filename=Picture1.png" alt="" />
LOCATION:SCI 352\, 590 Commonwealth Avenue\, 02215
STATUS:CONFIRMED
CLASS:PUBLIC
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