@article{doddsreview,
        title = {Scaling, Universality, and Geomorphology},
        author = {Peter Sheridan Dodds and Daniel H. Rothman},
        journal = {Annual Review of Earth and Planetary Sciences},
        number = 1,
        pages = {571-610},
        volume = 28,
        year = 2000,
        url = {http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.earth.28.1.571},
        doi = {10.1146/annurev.earth.28.1.571},
	eprint = {http://arjournals.annualreviews.org/doi/pdf/10.1146/annurev.earth.28.1.571},
	abstract = {Theories of scaling apply wherever similarity exists across many
scales. This similarity may be found in geometry and in dynamical processes. Uni-
versality arises when the qualitative character of a system is sufficient to quantitatively
predict its essential features, such as the exponents that characterize scaling laws.
Within geomorphology, two areas where the concepts of scaling and universality have
found application are the geometry of river networks and the statistical structure of
topography. We begin this review with a pedagogical presentation of scaling and
universality. We then describe recent progress made in applying these ideas to net-
works and topography. This overview leads to a synthesis that attempts a classification
of surface and network properties based on generic mechanisms and geometric con-
straints. We also briefly review how scaling and universality have been applied to
related problems in sedimentology—specifically, the origin of stromatolites and the
relation of the statistical properties of submarine-canyon topography to the size dis-
tribution of turbidite deposits. Throughout the review, our intention is to elucidate not
only the problems that can be solved using these concepts, but also those that cannot.
},
	biburl = {http://www.bibsonomy.org/bibtex/205edcf21b57ebc1e88e0f5207cb8f612/andreab},
	keywords = {rivernetworks geomorphology earth fractal review imported 2000 scaling}
}

@article{banavar:4522,
        title = {Sculpting of a Fractal River Basin},
        author = {Jayanth R. Banavar and Francesca Colaiori and Allesandro Flammini and Achille Giacometti and Amos Maritan and Andrea Rinaldo},
        journal = {Physical Review Letters},
        number = 23,
        pages = {4522-4525},
        publisher = {APS},
        volume = 78,
        year = 1997,
        url = {http://link.aps.org/abstract/PRL/v78/p4522},
        abstract = {The principle of reparametrization invariance is used to derive a dynamical equation for the erosion of the landscape of the drainage basin of river networks. The stationary solutions of the equation are found to have scaling behavior that is consistent with observational data. Our analytic prediction of the main stream profile is confirmed by numerical results and is amenable to direct observational verification.},
	biburl = {http://www.bibsonomy.org/bibtex/255983b1b3af5ddb694c176e3af0e644f/andreab},
	keywords = {model physics erosion rivernetworks theory network river statistical}
}

@article{colaiori2001,
        title = {Scaling, Optimality, and Landscape Evolution},
        author = {Jayanth R. Banavar and Francesca Colaiori and Alessandro Flammini and Amosd Maritan and Andreae Rinaldo},
        journal = {Journal of Statistical Physics},
        number = 1,
        pages = {1-48},
        volume = 104,
        year = 2001,
        description = {Banavar, Colaiori et al. paper on river network and landscape evolution.},
	abstract = {A nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation. The equation, already in wide use among geomorphologists and in that context obtained phenomenologically, is here derived by reparametrization invariance arguments and exactly solved in dimension d=1. Results of numerical simulations in d=2 show that the model is able to reproduce the critical scaling characterizing landscapes associated with natural river basins. We show that configurations minimizing the rate of energy dissipation (optimal channel networks) are stationary solutions of the equation describing the landscape evolution. Numerical simulations show that a careful annealing of the equation in the presence of additive noise leads to configurations very close to the global minimum of the dissipated energy, characterized by mean field exponents. We further show that if one considers generalized river network configurations in which splitting of the flow (i.e., braiding) and loops are allowed, the minimization of the dissipated energy results in spanning loopless configurations, under the constraints imposed by the continuity equations. This is stated in the form of a general theorem applicable to generic networks, suggesting that other branching structures occurring in nature may possibly arise as optimal structures minimizing a cost function.},
	biburl = {http://www.bibsonomy.org/bibtex/21116c03c4e127f16a232e13bdb93d4e3/andreab},
	keywords = {models physics rivernetworks modeling review statistical}
}