Showing papers by "Albert-László Barabási published in 1999"
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
33,771 citations
TL;DR: The World-Wide Web becomes a large directed graph whose vertices are documents and whose edges are links that point from one document to another, which determines the web's connectivity and consequently how effectively the authors can locate information on it.
Abstract: Despite its increasing role in communication, the World-Wide Web remains uncontrolled: any individual or institution can create a website with any number of documents and links. This unregulated growth leads to a huge and complex web, which becomes a large directed graph whose vertices are documents and whose edges are links (URLs) that point from one document to another. The topology of this graph determines the web's connectivity and consequently how effectively we can locate information on it. But its enormous size (estimated to be at least 8×108 documents1) and the continual changing of documents and links make it impossible to catalogue all the vertices and edges.
4,135 citations
TL;DR: In this article, the authors use local connectivity measurements to construct a topological model of the world wide web, allowing them to explore and characterize its large scale properties, such as the topology of the Web.
Abstract: Despite its increasing role in communication, the world wide web remains the least controlled medium: any individual or institution can create websites with unrestricted number of documents and links. While great efforts are made to map and characterize the Internet's infrastructure, little is known about the topology of the web. Here we take a first step to fill this gap: we use local connectivity measurements to construct a topological model of the world wide web, allowing us to explore and characterize its large scale properties.
2,663 citations
TL;DR: A mean-field method is developed to predict the growth dynamics of the individual vertices of the scale-free model, and this is used to calculate analytically the connectivity distribution and the scaling exponents.
Abstract: Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-eld method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-eld method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling. c 1999 Elsevier Science B.V. All rights reserved.
2,167 citations
TL;DR: In this paper, it was shown that a system of self-propelled particles exhibits spontaneous symmetry breaking and self-organization in one dimension, in contrast with previous analytical predictions.
Abstract: We demonstrate that a system of self-propelled particles exhibits spontaneous symmetry breaking and self-organization in one dimension, in contrast with previous analytical predictions. To explain this surprising result we derive a new continuum theory that can account for the development of the symmetry broken state and belongs to the same universality class as the discrete self-propelled particle model.
264 citations
TL;DR: In this paper, the authors studied the drag force acting on an object moving with low velocity through a granular medium and found that it is linearly dependent on the cylinder diameter, quadratically dependent on depth of insertion, and independent of velocity.
Abstract: We have studied the drag force acting on an object moving with low velocity through a granular medium. Although the drag force is a dynamic quantity, its behavior in this regime is dominated by the inhomogeneous distribution of stress in static granular media. We find experimentally that the drag force on a vertical cylinder is linearly dependent on the cylinder diameter, quadratically dependent on the depth of insertion, and independent of velocity. An accompanying analytical calculation based on the static distribution of forces arrives at the same result, demonstrating that the local theory of stress propagation in static granular media can be used to predict this bulk dynamic property.
255 citations
TL;DR: In this article, it was shown that the application of analternating current to a superconductor patterned with an asymmetric pinning potential can induce vortex motion whose direction is determined only by the asymmetry of the pattern.
Abstract: A serious obstacle impeding the application of low- and high-temperature superconductor devices is the presence of trapped magnetic flux1,2: flux lines or vortices can be induced by fields as small as the Earth's magnetic field. Once present, vortices dissipate energy and generate internal noise, limiting the operation of numerous superconducting devices2,3. Methods used to overcome this difficulty include the pinning of vortices by the incorporation of impurities and defects4, the construction of flux ‘dams’5, slots and holes6, and magnetic shields2,3 which block the penetration of new flux lines in the bulk of the superconductor or reduce the magnetic field in the immediate vicinity of the superconducting device. The most desirable method would be to remove the vortices from the bulk of the superconductor, but there was hitherto no known phenomenon that could form the basis for such a process. Here we show that the application of analternating current to a superconductor patterned with an asymmetric pinning potential can induce vortex motion whose direction is determined only by the asymmetry of the pattern. The mechanism responsible for this phenomenon is the so-called ‘ratchet effect’7,8,9,10, and its working principle applies to both low- and high-temperature superconductors. We demonstrate theoretically that, with an appropriate choice of pinning potential, the ratchet effect can be used to remove vortices from low-temperature superconductors in the parameter range required for various applications.
200 citations
TL;DR: In this article, a phase diagram for island shape as a function of volume and surface energy is presented, showing how surface energy can control the sequence of island shapes with increasing volume.
Abstract: Strained islands formed in heteroepitaxy sometimes change shape during growth. Here we show that there is typically a first-order shape transition with island size, with the discontinuous introduction of steeper facets at the island edge. We present a phase diagram for island shape as a function of volume and surface energy, showing how surface energy controls the sequence of island shapes with increasing volume. The discontinuous chemical potential at the shape transition drastically affects island coarsening and size distributions. [S0031-9007(99)08789-X]
183 citations
TL;DR: In this article, the impact of nonlinear terms on the morphology of sputter eroded surfaces was analyzed and the morphological transitions induced by the nonlinear effects can be detected by monitoring the surface width and the erosion velocity.
Abstract: Many morphological features of sputter eroded surfaces are determined by the balance between ion-induced linear instability and surface diffusion. However, the impact of the nonlinear terms on the morphology is less understood. We demonstrate that, while at short times ripple formation is described by the linear theory, after a characteristic time the nonlinear terms determine the surface morphology by either destroying the ripples or generating a new rotated ripple structure. We show that the morphological transitions induced by the nonlinear effects can be detected by monitoring the surface width and the erosion velocity.
169 citations
TL;DR: In this paper, the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities, have been investigated and a mean-field method was developed to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents.
Abstract: Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.
78 citations
TL;DR: This work investigates the effect of interstitial liquid on the physical properties of granular media by measuring the angle of repose as a function of the liquid content, and discusses three distinct regimes in terms of two proposed theories describing the effects of liquid.
Abstract: We investigate the effect of interstitial liquid on the physical properties of granular media by measuring the angle of repose as a function of the liquid content. The resultant adhesive forces lead to three distinct regimes in the observed behavior as the liquid content is increased: a granular regime in which the grains move individually, a correlated regime in which the grains move in correlated clusters, and a plastic regime in which the grains flow coherently. We discuss these regimes in terms of two proposed theories describing the effects of liquid on the physical properties of granular media.
TL;DR: In this paper, the authors demonstrate that stability criteria can be used to calculate the maximum angle of stability, m, of a granular medium composed of spherical particles in three dimensions and circular discs in two dimensions.
Abstract: We demonstrate that stability criteria can be used to calculate the maximum angle of stability, m, of a granular medium composed of spherical particles in three dimensions and circular discs in two dimensions. We apply the results to wet granular material by calculating the dependence of m on the liquid content of the material. The results are in good agreement with our experimental data. c 1999 Elsevier Science B.V. All rights reserved.
TL;DR: In this paper, the surface stress distribution in an ordered quantum dot superlattice was investigated using classical molecular dynamics simulations, and it was shown that the stress field induced by various numbers of Ge islands embedded in a Si~001! substrate is in good agreement with analytical expressions based on pointlike embedded force dipoles, explaining the tendency of layered arrays to form vertically aligned columns.
Abstract: The surface stress distribution in an ordered quantum dot superlattice is investigated using classical molecular dynamics simulations. We find that the surface stress field induced by various numbers~ from 1t o 9! of Ge islands embedded in a Si~001! substrate is in good agreement with analytical expressions based on pointlike embedded force dipoles, explaining the tendency of layered arrays to form vertically aligned columns. The short-ranged nature of this stress field implies that only the uppermost layers affect the surface growth and that their influence decreases rapidly with layer depth. @S0163-1829~99!52028-6#
TL;DR: In this article, the authors show that equilibrium theories can successfully predict the island sizes and densities, the nature and the magnitude of the critical thickness needed to be deposited for SAQD formation, as well as the flux and temperature dependence of the SAQDs.
Abstract: Heteroepitaxial growth of highly strained structures offers the possibility to fabricate islands with very narrow size distribution, coined self-assembling quantum dots (SAQD). In spite of the high experimental interest, the mechanism of SAQD formation is not well understood. We will show that equilibrium theories can successfully predict the island sizes and densities, the nature and the magnitude of the critical thickness needed to be deposited for SAQD formation, as well as the onset of ripening. Furthermore, the flux and temperature dependence of the SAQDs is described using kinetic Monte Carlo simulations.
Book•
01 Jan 1999
TL;DR: The authors brings together an international mix of researchers and scientists to address common themes in epitaxial growth, such as growth mechanisms; characterization; strained systems and novel epitaxy, with contributions by experts in the field enriched by additional mix of student and invited papers.
Abstract: Epitaxial growth is a critical technology in numerous areas ranging from elemental semiconductors to optoelectronic materials, from magnetic multilayers to inorganic insulators, from protein crystals to quantum dots. This book brings together an international mix of researchers and scientists to address common themes in epitaxial growth. Contributions by experts in the field are enriched by the additional mix of student and invited papers. Topics include: growth mechanisms; characterization; strained systems and novel epitaxy.
TL;DR: In this paper, the authors demonstrate that for surfaces that have a nonzero Schwoebel barrier, the application of an ac field parallel to the surface will induce a net electromigration current.
Abstract: We demonstrate that for surfaces that have a nonzero Schwoebel barrier, the application of an ac field parallel to the surface will induce a net electromigration current. Most important, the direction of the net current will be always downhill; i.e. it will point in the step-down direction. The magnitude of this equilibrium current is calculated analytically, and compared with Monte Carlo simulations. A downhill current is known to smooth the surface, thus we suggest that the application of ac fields during annealing might aid the smoothing process and during growth it has the potential to slow or eliminate the Schwoebel barrier induced mound formation
TL;DR: In this paper, the morphological features of sputter eroded surfaces were investigated and it was shown that while ripple formation is described by the linear theory, after a characteristic time the nonlinear terms determine the surface morphology.
Abstract: We investigate the morphological features of sputter eroded surfaces, demonstrating that while at short times ripple formation is described by the linear theory, after a characteristic time the nonlinear terms determine the surface morphology. We also show that the morphological transitions induced by the nonlinear effects can be detected by monitoring the surface width and the erosion velocity.