The importance of being discrete: life always wins on the surface.
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The microscopic granularity insures the emergence of macroscopic localized subpopulations with collective adaptive properties that allow their survival and development in two dimensions "life" (the localized proliferating phase) always prevails.Abstract:
Many systems in chemistry, biology, finance, and social sciences present emerging features that are not easy to guess from the elementary interactions of their microscopic individual components. In the past, the macroscopic behavior of such systems was modeled by assuming that the collective dynamics of microscopic components can be effectively described collectively by equations acting on spatially continuous density distributions. It turns out that, to the contrary, taking into account the actual individual/discrete character of the microscopic components of these systems is crucial for explaining their macroscopic behavior. In fact, we find that in conditions in which the continuum approach would predict the extinction of all of the population (respectively the vanishing of the invested capital or the concentration of a chemical substance, etc.), the microscopic granularity insures the emergence of macroscopic localized subpopulations with collective adaptive properties that allow their survival and development. In particular it is found that in two dimensions “life” (the localized proliferating phase) always prevails.read more
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References
More filters
Journal ArticleDOI
Absence of Diffusion in Certain Random Lattices
TL;DR: In this article, a simple model for spin diffusion or conduction in the "impurity band" is presented, which involves transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites.
Journal ArticleDOI
Evolutionary games and computer simulations
TL;DR: It is shown that the results of digital simulations regarding territoriality and cooperation differ greatly when time is discrete as opposed to continuous, which casts doubt on the implications of cellular automata-type simulations for the study of cooperation in social systems.
Book
Mathematical Ideas in Biology
TL;DR: In this article, the authors discuss the consequences of scale on the genetics of a population and its consequences in the context of regulation and control, and the role of families in these consequences.
Book
Annual Reviews of Computational Physics VII
TL;DR: A tutorial on advanced dynamic Monte Carlo methods for systems with Discrete State State State Spaces (M A Novotny et al. as discussed by the authors ) and beyond Navier-Stokes: Burnett Equations for Flow Simulations in the Contunuum Transition Regimes (R K Agarwal et al.).
Journal ArticleDOI
Non-hermitian localization and population biology
David R. Nelson,Nadav M. Shnerb +1 more
TL;DR: This work proposes a delocalization transition for the steady state of the nonlinear problem at a critical convection threshold separating localized and extended states, and describes singular scaling behavior described by a $(d\ensuremath{-}1)$-dimensional generalization of the noisy Burgers' equation.