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Diffusion-limited aggregation, a kinetic critical phenomenon
A model for random aggregates is studied by computer simulation. The model is applicable to a metal-particle aggregation process whose correlations have been measured previously. Density correlations… Expand
Diffusion-limited aggregation (DLA) is an idealization of the process by which matter irreversibly combines to form dust, soot, dendrites, and other random objects in the case where the rate-limiting… Expand
Diffusion-limited aggregation: A kinetic critical phenomenon?
- L. Sander
- 1 July 2000
Diffusion-limited aggregation (DLA) is a model which represents noisy growth limited by diffusion. This process is quite common in nature and the simple algorithm gives a good representation of the… Expand
Lithium inhibits invasion of glioma cells; possible involvement of glycogen synthase kinase-3.
Therapies targeting glioma cells that diffusely infiltrate normal brain are highly sought after. Our aim was to identify novel approaches to this problem using glioma spheroid migration assays.… Expand
A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment.
Glioblastoma, the most malignant form of brain cancer, is responsible for 23% of primary brain tumors and has extremely poor outcome. Confounding the clinical management of glioblastomas is the… Expand
Fractal growth processes
- L. Sander
- Physics, Materials Science
- 28 August 1986
The methods of fractal geometry allow the classification of non-equilibrium growth processes according to their scaling properties. Expand
Extinction Times for Birth-Death Processes: Exact Results, Continuum Asymptotics, and the Failure of the Fokker-Planck Approximation
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which defines a threshold. Expand
The micromechanics of three-dimensional collagen-I gels
We study the micromechanics of collagen-I gel with the goal of bridging the gap between theory and experiment in the study of biopolymer networks. Expand
Percolation on heterogeneous networks as a model for epidemics.
- L. Sander, C. Warren, I. Sokolov, C. Simon, J. Koopman
- Geography, Medicine
- Mathematical biosciences
- 1 November 2002
We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and… Expand
Growth patterns of microscopic brain tumors.
- L. Sander, T. Deisboeck
- Biology, Medicine
- Physical review. E, Statistical, nonlinear, and…
- 18 June 2002
Highly malignant brain tumors such as glioblastoma multiforme form complex growth patterns in vitro in which invasive cells organize in tenuous branches. Here, we formulate a chemotaxis model for… Expand