Modeling Complex Living Systems, 1st Edition by Nicola Bellomo (auth.)

By Nicola Bellomo (auth.)

Using instruments from mathematical kinetic thought and stochastic video game idea, this paintings bargains with the modeling of huge complicated platforms within the technologies, relatively these constructed from numerous interacting members whose dynamics keep on with ideas made up our minds by way of a few prepared, or maybe "intelligent" skill. typically, equipment of mathematical kinetic thought were utilized to version the evolution of enormous platforms of interacting classical or quantum debris. This publication, nonetheless, examines the modeling of dwelling structures in preference to inert systems.

The writer develops new mathematical tools and tools—hopefully a "new" mathematics—toward the modeling of dwelling structures. Such instruments have to be way more advanced than these facing platforms of inert topic. the 1st a part of the e-book offers with deriving common evolution equations that may be custom-made to specific platforms of curiosity within the technologies. the second one a part of the booklet offers with a variety of versions and purposes.

The presentation unfolds utilizing the next universal procedure in each one chapter:

* Phenomenological interpretation of the actual method within the context of mathematical modeling

* Derivation of the mathematical version utilizing tools from mathematical kinetic thought for lively particles

* Simulations, parameter sensitivity research, and demanding inspection of the derived version in the direction of validation

* review of offered rules to enhance present types, with unique emphasis on applications

Specific issues coated include:

* Modeling of the contest among cells of an competitive invasive agent and cells of the immune system

* Modeling of vehicular site visitors flow

* Modeling of swarms and crowd dynamics in complicated geometric environments

* Methodological points on the topic of multiscale modeling of enormous platforms seen as interconnected subsystems

Modeling advanced dwelling Systems is a necessary source for utilized mathematicians, engineers, physicists, biologists, economists, and graduate scholars fascinated about modeling complicated social structures and residing subject in general.

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Additional resources for Modeling Complex Living Systems, 1st Edition

Sample text

N, where each population is characterized by a different way of organizing their peculiar activities and by different interactions with the other populations. 17) of the ith population, while the whole set of distribution functions for all populations is denoted by f = {fi }. Calculations are analogous to those already seen above. For instance, the local size of the ith population is given by ni [fi ](t, x) = Dv ×Du fi (t, x, v, u) dv du . 19) i=1 where f0 = f (t = 0) denotes the initial distribution for all populations.

The contents are presented through the following five addition sections. 2 introduces the the concepts of the microscopic state of active particles and the distribution function. Subsequently, it is shown how the distribution function can be used to compute macroscopic information on the overall state of the system by weighted moments. First a system consisting of one population is presented, subsequently technical generalizations to systems with several interacting populations are developed. 3 derives a mathematical framework for the modeling of microscopic interactions between active particles.

Electromagnetic, are exchanged. , proliferative/destructive encounters occur at short distances, while conservative encounters are effective at long distances. 4 Mathematical Frameworks The mathematical models of interactions at the microscopic scale described in the preceding section are a preliminary step to the derivation of evolution equations, which are used as a formal framework to be properly specialized with reference to specific physical systems. In other words, a detailed analysis (and modeling) of individual interactions generates models suitable to describe the evolution of a class of large systems of interacting active particles.

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