Showing papers by "Albert-László Barabási published in 1994"
TL;DR: A model of the inflation process in which 'avalanches' of airway openings are seen is developed—with power-law distributions of both the size of avalanches and the time intervals between them—which agree quantitatively with those seen experimentally, and are reminiscent of the power- law behaviour observed for self-organized critical systems.
Abstract: WHEN lungs are emptied during exhalation, peripheral airways close up1 For people with lung disease, they may not reopen for a significant portion of inhalation, impairing gas exchange2,3 A knowledge of the mechanisms that govern reinflation of collapsed regions of lungs is therefore central to the development of ventilation strategies for combating respiratory problems Here we report measurements of the terminal airway resistance, Rt , during the opening of isolated dog lungs When inflated by a constant flow, Rt decreases in discrete jumps We find that the probability distribution of the sizes of the jumps and of the time intervals between them exhibit power-law behaviour over two decades We develop a model of the inflation process in which 'avalanches' of airway openings are seen—with power-law distributions of both the size of avalanches and the time intervals between them—which agree quantitatively with those seen experimentally, and are reminiscent of the power-law behaviour observed for self-organized critical systems4 Thus power-law distributions, arising from avalanches associated with threshold phenomena propagating down a branching tree structure, appear to govern the recruitment of terminal airspaces
266 citations
TL;DR: It is shown that replacing ordinary time derivatives with fractional time derivatives in the constitutive equation of conventional spring-dashpot systems naturally leads to power law relaxation function, the Fourier transform of which is the constant-phase impedance with alpha = 1 - beta.
Abstract: Recent studies indicated that lung tissue stress relaxation is well represented by a simple empirical equation involving a power law, t-beta (where t is time). Likewise, tissue impedance is well described by a model having a frequency-independent (constant) phase with impedance proportional to omega-alpha (where omega is angular frequency and alpha is a constant). These models provide superior descriptions over conventional spring-dashpot systems. Here we offer a mathematical framework and explore its mechanistic basis for using the power law relaxation function and constant-phase impedance. We show that replacing ordinary time derivatives with fractional time derivatives in the constitutive equation of conventional spring-dashpot systems naturally leads to power law relaxation function, the Fourier transform of which is the constant-phase impedance with alpha = 1 - beta. We further establish that fractional derivatives have a mechanistic basis with respect to the viscoelasticity of certain polymer systems. This mechanistic basis arises from molecular theories that take into account the complexity and statistical nature of the system at the molecular level. Moreover, because tissues are composed of long flexible biopolymers, we argue that these molecular theories may also apply for soft tissues. In our approach a key parameter is the exponent beta, which is shown to be directly related to dynamic processes at the tissue fiber and matrix level. By exploring statistical properties of various polymer systems, we offer a molecular basis for several salient features of the dynamic passive mechanical properties of soft tissues.
226 citations
TL;DR: In this article, a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface is proposed, which incorporates deposition, particle and cluster diffusion, and aggregation, inspired by recent thin-film-deposition experiments.
Abstract: We propose a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. The model, which incorporates deposition, particle and cluster diffusion, and aggregation, is inspired by recent thin-film-deposition experiments. We find that as randomly deposited particles diffuse and aggregate they configure themselves into a wide variety of fractal structures characterized by a length scale ${\mathit{L}}_{1}$. We introduce an exponent \ensuremath{\gamma} that tunes the way the diffusion coefficient changes with cluster size: if the values of \ensuremath{\gamma} are very large, only single particles can move, if they are smaller, all clusters can move. The introduction of cluster diffusion dramatically affects the dynamics of film growth. We compare our results with those of several recent experiments on two-dimensional nanostructures formed by diffusion-controlled aggregation on surfaces, and we propose several experimental tests of the model. We also investigate the spanning properties of this model and find another characteristic length scale ${\mathit{L}}_{2}$ (${\mathit{L}}_{2}$\ensuremath{\gg}${\mathit{L}}_{1}$) above which the system behaves as a bond percolation network of the fractal structures each of length scale ${\mathit{L}}_{1}$. Below ${\mathit{L}}_{2}$, the system shows similarities with diffusion-limited aggregation. We find that ${\mathit{L}}_{1}$ scales as the ratio of the diffusion constant over the particle flux to the power 1/4, whereas ${\mathit{L}}_{2}$ scales with another exponent close to 0.9.
141 citations
TL;DR: Numerical evidence is presented that there are two distinct universality classes characterizing driven interface roughening in the presence of quenched disorder, based on the behavior of $\lambda$, the coefficient of the nonlinear term in the growth equation.
Abstract: We present numerical evidence for the existence of two distinct universality classes characterizing driven interface roughening in the presence of quenched disorder. The evidence is based on the behavior of \ensuremath{\lambda}, the coefficient of the nonlinear term in the growth equation. Specifically, for three of the models studied, \ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty} at the depinning transition, while for the two other models, \ensuremath{\lambda}\ensuremath{\rightarrow}0.
57 citations
TL;DR: It is argued that evaporation can be usefully modeled by introducing a gradient in the strength of the disorder, in analogy with the gradient percolation model of Sapoval, and a new critical exponent and a novel scaling relation for the interface width are predicted.
Abstract: We report imbibition experiments investigating the effect of evaporation on the interface roughness and mean interface height. We observe a new exponent characterizing the scaling of the saturated surface width. Further, we argue that evaporation can be usefully modeled by introducing a gradient in the strength of the disorder, in analogy with the gradient percolation model of Sapoval et al. By incorporating this gradient we predict a new critical exponent and a novel scaling relation for the interface width. Both the exponent value and the form of the scaling agree with the experimental results.
25 citations
TL;DR: The model incorporates deposition, diffusion, and aggregation incorporates a wide variety of fractal structures characterized by a common length scale, which scales as the ratio of the diffusion constant over the particle flux to the power 1/4.
Abstract: We propose a model for describing diffusion-controlled aggregation of particles that are continually deposited on a surface. The model incorporates deposition, diffusion, and aggregation. We find that the diffusion and aggregation of randomly deposited particles ``builds'' a wide variety of fractal structures, all characterized by a common length scale ${\mathit{L}}_{1}$. This length ${\mathit{L}}_{1}$ scales as the ratio of the diffusion constant over the particle flux to the power 1/4. We compare our results with several recent experiments on two-dimensional nanostructures formed by diffusion-controlled aggregation on surfaces.
23 citations
TL;DR: In this paper, the authors generalize the conventional model of site percolation by including both continuous deposition of particles on a two-dimensional substrate, and diffusion of these particles in two-dimensions.
Abstract: We generalize the conventional model of two-dimensional site percolation by including both (1) continuous deposition of particles on a two-dimensional substrate, and (2) diffusion of these particles in two-dimensions. This new model is motivated by recent thin film deposition experiments using the low-energy cluster beam deposition (LECBD) technique. Depending on various parameters such as deposition flux, diffusion constant, and system size, we find a rich range of fractal morphologies including diffusion limited aggregation (DLA), cluster-cluster aggregation (CCA), and percolation.
3 citations
TL;DR: In this article, a stochastic nonlinear equation was derived to describe the evolution and scaling properties of surfaces eroded by ion bombardment, and the coefficients appearing in the equation were calculated explicitly in terms of the physical parameters characterizing the sputtering process.
Abstract: In the context of linear cascade theory, we derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation are calculated explicitly in terms of the physical parameters characterizing the sputtering process. We find that transitions may take place between various scaling behaviors when experimental parameters such as the angle of incidence of the incoming ions or their average penetration depth, are varied.