Transition between strong and weak disorder regimes for the optimal path

Sameet Sreenivasan; Tomer Kalisky; Lidia A. Braunstein; Sergey V. Buldyrev; Shlomo Havlin; H. Eugene Stanley

doi:10.1016/j.physa.2004.08.064

Transition between strong and weak disorder regimes for the optimal path

Sameet Sreenivasan, Tomer Kalisky, Lidia A. Braunstein, Sergey V. Buldyrev, Shlomo Havlin, H. Eugene Stanley

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path ℓ_opt in a disordered Erdos-Rényi (ER) random network and scale-free (SF) network. Each link i is associated with a weight T_i ≡ exp(ar _i). where r_i is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder. We find that for any finite a, there is a crossover network size N*(a) such that for N ≪ N*(a) the scaling behavior of ℓ_opt is in the strong disorder regime, while for N ≫ N*(a) the scaling behavior is in the weak disorder regime. We derive the scaling relation between N*(a) and a with the help of simulations and also present an analytic derivation of the relation.

Original language	English
Pages (from-to)	174-182
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	346
Issue number	1-2 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.physa.2004.08.064
State	Published - 1 Feb 2005

Bibliographical note

Funding Information:
The authors are grateful to Wein-Bastion (Ulm, Germany) for providing white and red wine samples. They appreciate Christine Stöcker, Simone Ott und Barbara Scheitler (University of Bayreuth) for help with laboratory work. The financial support of J. H. H. comes from the Swiss National Science Foundation Ambizione fellowship (PZ00P2_122212). K. N. H. is supported by a fellowship from the Intramural Research Program of the National Institute of Diabetes Digestive and Kidney Diseases of the National Institutes of Health.

Funding

We thank the Office of Naval Research and ONR-Global, the Israel Science Foundation, and the Israeli Center for Complexity Science for financial support.

Funders	Funder number
Israeli Center for Complexity Science
ONR-Global
Israel Science Foundation
Office of Naval Research

Keywords

Networks
Optimal path
Strong disorder

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10.1016/j.physa.2004.08.064

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abstract = "We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path ℓopt in a disordered Erdos-R{\'e}nyi (ER) random network and scale-free (SF) network. Each link i is associated with a weight Ti ≡ exp(ar i). where ri is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder. We find that for any finite a, there is a crossover network size N*(a) such that for N ≪ N*(a) the scaling behavior of ℓopt is in the strong disorder regime, while for N ≫ N*(a) the scaling behavior is in the weak disorder regime. We derive the scaling relation between N*(a) and a with the help of simulations and also present an analytic derivation of the relation.",

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note = "Funding Information: The authors are grateful to Wein-Bastion (Ulm, Germany) for providing white and red wine samples. They appreciate Christine St{\"o}cker, Simone Ott und Barbara Scheitler (University of Bayreuth) for help with laboratory work. The financial support of J. H. H. comes from the Swiss National Science Foundation Ambizione fellowship (PZ00P2_122212). K. N. H. is supported by a fellowship from the Intramural Research Program of the National Institute of Diabetes Digestive and Kidney Diseases of the National Institutes of Health.",

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AU - Kalisky, Tomer

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AU - Buldyrev, Sergey V.

AU - Havlin, Shlomo

AU - Stanley, H. Eugene

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N2 - We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path ℓopt in a disordered Erdos-Rényi (ER) random network and scale-free (SF) network. Each link i is associated with a weight Ti ≡ exp(ar i). where ri is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder. We find that for any finite a, there is a crossover network size N*(a) such that for N ≪ N*(a) the scaling behavior of ℓopt is in the strong disorder regime, while for N ≫ N*(a) the scaling behavior is in the weak disorder regime. We derive the scaling relation between N*(a) and a with the help of simulations and also present an analytic derivation of the relation.

AB - We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path ℓopt in a disordered Erdos-Rényi (ER) random network and scale-free (SF) network. Each link i is associated with a weight Ti ≡ exp(ar i). where ri is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder. We find that for any finite a, there is a crossover network size N*(a) such that for N ≪ N*(a) the scaling behavior of ℓopt is in the strong disorder regime, while for N ≫ N*(a) the scaling behavior is in the weak disorder regime. We derive the scaling relation between N*(a) and a with the help of simulations and also present an analytic derivation of the relation.

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Transition between strong and weak disorder regimes for the optimal path

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