A Multiscale Cellular Automata Model for Simulating Complex Transportation Systems Artificial Neural Networks Systems Based on DFT Parameters and Molecular Field Analysis - Computational Tools for Prediction of Ethylbenzene Dehydrogenase Reaction Kinetics

We present a new two-level numerical model describing the evolution of transportation network. Two separate but mutually interacting sub-systems are investigated: a starving environment and the network. We assume that the slow modes of the environment growth can be modeled with classical cellular automata (CA) approach. The fast modes representing the transportation network, we approximate by the graph of cellular automata (GCA). This allows the simulation of transportation systems over larger spatio-temporal scales and scrutinizing global interactions between the network and the environment. We show that the model can mimic the realistic evolution of complex river systems. We also demonstrate how the model can simulate a reverse situation. We conclude that the paradigm of this model can be extended further to a general framework, approximating many realistic multiscale transportation systems in diverse fields such as geology, biology and medicine.

[1]  David M Levinson,et al.  The emergence of hierarchy in transportation networks , 2005 .

[2]  William W. L. Glenn,et al.  Thoracic and cardiovascular surgery , 1983 .

[3]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems: Index , 1998 .

[4]  L Preziosi,et al.  Percolation, morphogenesis, and burgers dynamics in blood vessels formation. , 2003, Physical review letters.

[5]  N. Mills,et al.  Atherosclerosis of the ascending aorta and coronary artery bypass. Pathology, clinical correlates, and operative management. , 1991, The Journal of thoracic and cardiovascular surgery.

[6]  Pawel Topa,et al.  Anastomosing Transportation Networks , 2001, PPAM.

[7]  D. Turcotte,et al.  Symmetries in geology and geophysics. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Kramer,et al.  Evolution of river networks. , 1992, Physical review letters.

[9]  J W Baish,et al.  Fractals and cancer. , 2000, Cancer research.

[10]  P. Ineson,et al.  Methods of studying root dynamics in relation to nutrient cycling. , 1990 .

[11]  Janet Rossant,et al.  Endothelial cells and VEGF in vascular development , 2005, Nature.

[12]  Witold Dzwinel,et al.  Consuming Environment with Transportation Network Modelled Using Graph of Cellular Automata , 2003, PPAM.

[13]  B. Makaske Anastomosing rivers: forms, processes and sediments , 1998 .

[14]  C. Paola,et al.  Properties of a cellular braided‐stream model , 1997 .

[15]  A. N. Strahler Quantitative analysis of watershed geomorphology , 1957 .

[16]  Yuen,et al.  A Two-Level, Discrete-Particle Approach for Simulating Ordered Colloidal Structures. , 2000, Journal of colloid and interface science.

[17]  D. Turcotte,et al.  Shapes of river networks and leaves: are they statistically similar? , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[18]  Stanley J. Wiegand,et al.  Vascular-specific growth factors and blood vessel formation , 2000, Nature.

[19]  M. Sahini,et al.  Applications of Percolation Theory , 2023, Applied Mathematical Sciences.

[20]  Donald L. Turcotte,et al.  Applications of statistical mechanics to natural hazards and landforms , 1999 .

[21]  A. Giaccia,et al.  Oncogenic transformation and hypoxia synergistically act to modulate vascular endothelial growth factor expression. , 1996, Cancer research.

[22]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[23]  C. Paola,et al.  A cellular model of braided rivers , 1994, Nature.

[24]  Roeland M. H. Merks,et al.  Dynamic mechanisms of blood vessel growth , 2006, Nonlinearity.

[25]  J. Brickmann B. Mandelbrot: The Fractal Geometry of Nature, Freeman and Co., San Francisco 1982. 460 Seiten, Preis: £ 22,75. , 1985 .

[26]  P. Dodds,et al.  Unified view of scaling laws for river networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  D. Turcotte,et al.  A diffusion-limited aggregation model for the evolution of drainage networks , 1993 .

[28]  D. Yuen,et al.  A Two-Level, Discrete Particle Approach For Large-Scale Simulation Of Colloidal Aggregates , 2000 .

[29]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[30]  C. Stark An invasion percolation model of drainage network evolution , 1991, Nature.

[31]  Derald G. Smith,et al.  Avulsions, channel evolution and floodplain sedimentation rates of the anastomosing upper Columbia River, British Columbia, Canada , 2002 .

[32]  John B Rundle,et al.  Self-organized complexity in the physical, biological, and social sciences , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Albert-László Barabási,et al.  Linked: The New Science of Networks , 2002 .

[34]  R. Marrs,et al.  Nutrient Cycling in Terrestrial Ecosystems, Field Methods, Applications and Interpretation. , 1990 .

[35]  B. Makaske Anastomosing rivers: a review of their classification, origin and sedimentary products , 2001 .

[36]  A. Rinaldo,et al.  Fractal River Basins: Chance and Self-Organization , 1997 .

[37]  A. Brad Murray,et al.  A new quantitative test of geomorphic models, applied to a model of braided streams , 1996 .

[38]  William I. Newman,et al.  Fractal Trees with Side Branching , 1997 .

[39]  R. Horton EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY , 1945 .