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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 19 | Number 2 | Year 2015 | Article Id. IJMTT-V19P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V19P513

Scale Invariant Limit and Emergence of Complexity: Applications to Traffic Flow


Anuja Ray Chaudhuri
Abstract

Some novel applications of recently developed analytic formalism involving a nonlinear variations in the usual definition of limit are studied in the context of some simple classically non smooth systems. A Gell-mann-Low type renormalization group equation is derived indicating inherent scale invariance as well as an effective running of scales. A few elementary models of traffic flow are examined as simple prototypes of intelligent systems.

Keywords
Scale invariance, Ultrametric, Renormalization group, Traffic flow
References

[1] D.P.Datta, On a Variation of the Definition of Limit: Some Analytic Consequences, ArXive: 1110.6024v2[math.CA], (to be submitted).
[2] D.P.Datta, S.Raut and A Ray Chaudhuri, Ultrametric Cantor sets and growth of measure, p-adic Numbers, Ultrametic Analysis and Application, 3, (2011), 7-22.
[3] D.P.Datta and A Ray Chaudhuri, Scale invariant analysis and prime number theorem, Fractals, 18, (2010), 171-184.
[4] A.Ray Chaudhuri, Nonlinear Scale invariant Formalism and its Application to Some Differential Equations, IOSR Journal of Mathematics, Vol.4, Issue 4(2014) 27-37.
[5] D.P.Datta and S.Raut, The arrow of time, complexity and the scale free analysis, Chaos, Solitons and Fractals, 28, (2006), 581-589.
[6] S.Maeriovoet and B.D.Moor, Traffic flow theory, ArXive: Physics/0507126v1[Physics.Soc-Phy].
[7] R.C.McOwen, Partial Differential Equations, India, (2005).
[8] S.Weinberg, quantum Theory of Fields (3 vol), Cambridge University Press, (1995).

Citation :

Anuja Ray Chaudhuri, "Scale Invariant Limit and Emergence of Complexity: Applications to Traffic Flow," International Journal of Mathematics Trends and Technology (IJMTT), vol. 19, no. 2, pp. 102-107, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V19P513

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