Diffusion limited aggregation: a paradigm of disorderly cluster growth

The purpose of this talk is to present a brief overview of our group's recent research into dynamic mechanisms of disorderly growth, an exciting new branch of condensed matter physics in which the methods and concepts of modern statistical mechanics are proving to be useful. Our strategy has been to focus on attempting to understand a single model system — diffusion limited aggregation (DLA). This philosophy was the guiding principle for years of research in phase transitions and critical phenomena. For example, by focusing on the Ising model, steady progress was made over a period of six decades and eventually led to understanding a wide range of critical point phenomena, since even systems for which the Ising model was not appropriate turned out to be described by variants of the Ising model (such as the XY and Heisenberg models). So also, we are optimistic that whatever we may learn in trying to “understand” DLA will lead to generic information helpful in understanding general aspects of dynamic mechanisms underlying disorderly growth.

[1]  Stanley,et al.  Phase transition in the multifractal spectrum of diffusion-limited aggregation. , 1988, Physical review letters.

[2]  Hayakawa,et al.  Exactly self-similar left-sided multifractal measures. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[3]  Benoit B. Mandelbrot,et al.  Plane DLA is not self-similar; is it a fractal that becomes increasingly compact as it grows? , 1992 .

[4]  Stanley,et al.  Fractal dimension of the accessible perimeter of diffusion-limited aggregation. , 1989, Physical review. A, General physics.

[5]  Harris,et al.  Scaling of negative moments of the growth probability of diffusion-limited aggregates. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[6]  A. Coniglio,et al.  Novel dynamical scaling in kinetic growth phenomena , 1990 .

[7]  Coniglio,et al.  Growth probability distribution in kinetic aggregation processes. , 1986, Physical review letters.

[8]  Mandelbrot,et al.  Variability of the form and of the harmonic measure for small off-off-lattice diffusion-limited aggregates. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[9]  Witten,et al.  Surfaces, interfaces, and screening of fractal structures. , 1985, Physical review. A, General physics.

[10]  Hiroshi Fujikawa,et al.  Fractal Growth of Bacillus subtilis on Agar Plates , 1989 .

[11]  Stanley,et al.  Analytic solution of the growth-site probability distribution for structural models of diffusion-limited aggregation. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[12]  H. E. Stanley,et al.  Effect of viscosity on neurite outgrowth and fractal dimension , 1992, Neuroscience Letters.

[13]  H. Stanley,et al.  On growth and form : fractal and non-fractal patterns in physics , 1986 .

[14]  Meakin,et al.  Scaling structure of the surface layer of diffusion-limited aggregates. , 1986, Physical review letters.

[15]  Ball,et al.  Exact results on exponential screening in two-dimensional diffusion-limited aggregation. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[16]  Halsey.  Some consequences of an equation of motion for diffusive growth. , 1987, Physical review letters.

[17]  Localization of growth sites in diffusion-limited-aggregation clusters: Multifractality and multiscaling. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Scher,et al.  Occupancy-probability scaling in diffusion-limited aggregation. , 1985, Physical review letters.

[19]  Carl J. G. Evertsz,et al.  Multifractality of the harmonic measure on fractal aggregates, and extended self-similarity , 1991 .

[20]  Hideki Takayasu,et al.  Fractals in the Physical Sciences , 1990 .

[21]  Multifractal fluctuations in the dynamics of disordered systems , 1993 .

[22]  Aharony,et al.  Breakdown of multifractal behavior in diffusion-limited aggregates. , 1989, Physical review letters.

[23]  B. Masters,et al.  Fractal pattern formation in human retinal vessels , 1989 .

[24]  Witten,et al.  Scaling properties for the surfaces of fractal and nonfractal objects: An infinite hierarchy of critical exponents. , 1986, Physical review. A, General physics.

[25]  Eldred,et al.  Physical mechanisms underlying neurite outgrowth: A quantitative analysis of neuronal shape. , 1990, Physical review letters.

[26]  Carl J. G. Evertsz,et al.  Self-similarity of harmonic measure on DLA , 1992 .

[27]  P. Ossadnik.  Multiscaling analysis and width of the active zone of large off-lattice DLA , 1992, cond-mat/9212024.

[28]  Stanley,et al.  Hierarchical model for the multifractality of diffusion-limited aggregation. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[29]  Alstrm,et al.  Exponentially small growth probabilities in diffusion-limited aggregation. , 1990, Physical review. B, Condensed matter.

[30]  H. Stanley,et al.  Multifractal scaling of 3D diffusion-limited aggregation , 1992 .

[31]  T. Vicsek.  Fractal Growth Phenomena , 1989 .

[32]  Stanley,et al.  Distribution of growth probabilities for off-lattice diffusion-limited aggregation. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[33]  Shlomo Havlin,et al.  Dynamic mechanisms of disorderly growth: Recent approaches to understanding diffusion limited aggregation , 1990 .

[34]  Tremblay,et al.  Comment on "Breakdown of multifractal behavior in diffusion-limited aggregates" , 1990, Physical review letters.

[35]  Stanley,et al.  Exact-enumeration approach to multifractal structure for diffusion-limited aggregation. , 1989, Physical review. A, General physics.

[36]  Harry Eugene Stanley,et al.  Correlations and connectivity : geometric aspects of physics, chemistry, and biology , 1990 .

[37]  Carl J. G. Evertsz,et al.  The potential distribution around growing fractal clusters , 1990, Nature.

[38]  Meakin,et al.  Multiscaling in diffusion-limited aggregation. , 1991, Physical review. B, Condensed matter.

[39]  L. Sander,et al.  Diffusion-limited aggregation, a kinetic critical phenomenon , 1981 .

[40]  Pietronero,et al.  Theory of fractal growth. , 1988, Physical review letters.

[41]  Wolf.  Hitting probabilities of diffusion-limited-aggregation clusters. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[42]  H. E. Stanley,et al.  Determination of fractal dimension of physiologically characterized neurons in two and three dimensions , 1995, Journal of Neuroscience Methods.

[43]  B. Mandelbrot.  New “anomalous” multiplicative multifractals: Left sided ƒ(α) and the modelling of DLA , 1990 .

[44]  P. Enders,et al.  An embedding technique for the solution of coupled Riccati equations , 1992 .

[45]  Stanley,et al.  Minimum growth probability of diffusion-limited aggregates. , 1990, Physical review letters.

[46]  B. Mandelbrot,et al.  BEHAVIOUR OF THE HARMONIC MEASURE AT THE BOTTOM OF FJORDS , 1991 .

[47]  Hayakawa,et al.  Scaling structure of the growth-probability distribution in diffusion-limited aggregation processes. , 1987, Physical review. A, General physics.