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Showing papers by "Albert-László Barabási published in 1996"


Journal ArticleDOI
TL;DR: It is found that the treelike structure of the airways, together with the simplest assumptions concerning opening threshold pressures of each airway, is sufficient to explain the existence of power-law distributions observed experimentally.
Abstract: We study a statistical mechanical model for the dynamics of lung inflation which incorporates recent experimental observations on the opening of individual airways by a cascade or avalanche mechanism. Using an exact mapping of the avalanche problem onto percolation on a Cayley tree, we analytically derive the exponents describing the size distribution of the first avalanches and test the analytical solution by numerical simulations. We find that the treelike structure of the airways, together with the simplest assumptions concerning opening threshold pressures of each airway, is sufficient to explain the existence of power-law distributions observed experimentally.

48 citations


Journal ArticleDOI
TL;DR: A new IBP model is introduced that belongs to the same universality class as IBP and generates the minimal energy tree spanning the IBP cluster.
Abstract: Invasion bond percolation (IBP) is mapped exactly into Prim{close_quote}s algorithm for finding the shortest spanning tree of a weighted random graph. Exploring this mapping, which is valid for arbitrary dimensions and lattices, we introduce a new IBP model that belongs to the same universality class as IBP and generates the minimal energy tree spanning the IBP cluster. {copyright} {ital 1996 The American Physical Society.}

44 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a critical discussion on the advantages and disadvantages of kinetic theories and continuum models, two main methods frequently used to study the roughening and scaling of surfaces grown by MBE.

12 citations


Journal ArticleDOI
TL;DR: The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP) as discussed by the authors.
Abstract: The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP) In higher dimensions these models give rise to directed surfaces, which do not belong to the directed percolation universality class We formulate a scaling theory of directed surfaces, and calculate critical exponents numerically, using a cellular automaton that locates the directed surfaces without making reference to the dynamics of the underlying interface growth models

12 citations


Journal ArticleDOI
TL;DR: The scaling properties of a random walker that moves ballistically on a two-dimensional square lattice are introduced and it is shown that this random walk is subdiffusive.
Abstract: We introduce and investigate the scaling properties of a random walker that moves ballistically on a two-dimensional square lattice. The walker is scattered (changes direction randomly) every time it reaches a previously unvisited site, and follows ballistic trajectories between two scattering events. The asymptotic properties of the density of unvisited sites and the diffusion exponent can be calculated using a mean-field theory. The obtained predictions are in good agreement with the results of extensive numerical simulations. In particular, we show that this random walk is subdiffusive. \textcopyright{} 1996 The American Physical Society.

8 citations


Journal ArticleDOI
01 Sep 1996-Fractals
TL;DR: In this paper, the authors review a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface and analyze the effects of small cluster mobility and show that the introduction of cluster diffusion dramatically affects the dynamics of film growth.
Abstract: In this paper, we briefly review a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. This model allows us to understand many experiments of thin film deposition. In the Sec. 1, we describe the model, which incorporates deposition, particle and cluster diffusion, and aggregation. In Sec. 2, we study the dynamical evolution of the model. Finally, we analyze the effects of small cluster mobility and show that the introduction of cluster diffusion dramatically affects the dynamics of film growth. Some of these effects can be tested experimentally.

5 citations


Journal ArticleDOI
10 Oct 1996-EPL
TL;DR: In this paper, the interaction of two nonequilibrium conservative fields was analyzed for the growth of semiconductors. But the coupling between the surfactant thickness and the interface height cannot account for the experimentally observed layered growth, implying that reduced diffusion of the embedded atoms is a key mechanism in the growth.
Abstract: We present an analytical study of the interaction of two nonequilibrium conservative fields. Due to the conservative character of the relaxation mechanism, the scaling exponents can be obtained exactly using dynamic renormalization group. We apply our results to surfactant-mediated growth of semiconductors. We find that the coupling between the surfactant thickness and the interface height cannot account for the experimentally observed layered growth, implying that reduced diffusion of the embedded atoms is a key mechanism in surfactant-mediated growth.

2 citations


Journal ArticleDOI
01 Jan 1996-Fractals
TL;DR: In this article, the authors review the recently introduced Directed Percolation Depinning (DPD) and Self-Organized Depinning(SOD) models for interface roughening with quenched disorder.
Abstract: We review the recently introduced Directed Percolation Depinning (DPD) and Self-Organized Depinning (SOD) models for interface roughening with quenched disorder. The differences in the dynamics of the invasion process in these two models are discussed and different avalanche definitions are presented. The scaling properties of the avalanche size distribution and the properties of active cells are discussed.

1 citations


Journal ArticleDOI
TL;DR: A one-dimensional elastic string is considered as a set of massless beads interacting through springs characterized by anisotropic elastic constants that lead to nonlinear behavior in the equation of motion that is kinematically generated by the motion of the string.
Abstract: We consider a one-dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We find that longitudinal fluctuations lead to nonlinear behavior in the equation of motion that is kinematically generated by the motion of the string. The strength of the nonlinear effects depends on the anisotropy of the medium and the distance from the depinning transition. On the other hand, the consideration of restricted solid-on-solid conditions imposed on the string leads to a nonlinear term with a diverging coefficient at the depinning transition.