Inverse Geometric Approach to the Simulation of the Circular Growth. The Case of Multicellular Tumor Spheroids

We demonstrate the power of the genetic algorithms to construct the cellular automata model simulating the growth of 2-dimensional close-to-circular clusters revealing the desired properties, such as the growth rate and, at the same time, the fractal behavior of their contours. The possible application of the approach in the field of tumor modeling is outlined

Toward a Comprehensive Model of Snow Crystal Growth: 4. Measurements of Diffusion-limited Growth at -15 C

We present measurements of the diffusion-limited growth of ice crystals from water vapor at different supersaturation levels in air at a temperature of -15 C. Starting with thin, c-axis ice needle crystals, the subsequent growth morphologies ranged from blocky structures on the needle tips (at low supersaturation) to thin faceted plates on the needle tips (at high supersaturation). We successfully modeled the experimental data, reproducing both growth rates and growth morphologies, using a cellular-automata method that yields faceted crystalline structures in diffusion-limited growth. From this quantitative analysis of well-controlled experimental measurements, we were able to extract information about the attachment coefficients governing ice growth under different circumstances. The results strongly support previous work indicating that the attachment coefficient on the prism surface is a function of the width of the prism facet. Including this behavior, we created a comprehensive model at -15 C that explains all the experimental data. To our knowledge, this is the first demonstration of a kinetic model that reproduces a range of diffusion-limited ice growth behaviors as a function of supersaturation

A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.Comment: 44 pages, 8 figure

Synchronization universality classes and stability of smooth, coupled map lattices

We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic behavior implies that the synchronization transition belongs to the multiplicative noise universality class, while stable chaos implies that the synchronization transition belongs to the directed percolation universality class.Comment: 6 pages, 7 figure