Qualitative Short-Time (ST) Dynamical Systems Analysis of Changes in Smoke Patterns with Applications to other ST dynamical Systems in Nature

Michael R. Golinski

Michael R. Golinski Department of Biology, University of New Mexico, USA

Keywords: diffusion, non-linear dynamics, limit cycle, qualitative short-time (ST) dynamical patterns, thermodynamics

Abstract

The smoking of a cigarette is an obvious metaphor for the observation of qualitative short-time (ST) dynamical patterns in life as a function of heat, diffusion, and the eventual death of a system of molecules (i.e., see laws of thermodynamics [4]), which includes particles that make up common ingredients in a cigarette, including nicotine, tobacco, and the associated artificial chemicals used to deliver these materials into the blood stream. I use the basic materials associated with smoking a cigarette as a framework for exploring qualitative patterns observed in ST dynamical systems. The actual process of smoking a cigarette was used to test the following hypotheses: (1) Do the patterns of change over time of smoking a cigarette from start to finish demonstrate ST dynamical patterns that can be analyzed with simple time series (TS) analysis tools? (2) Does the qualitative ST dynamical behavior generated from smoking a cigarette follow a predictable pattern? Next, I place my qualitative observations within a quantitative framework. Lastly, I use results obtained from hypotheses (1) and (2) to propose how change over time in qualitative ST dynamical behavior of the simple act of smoking a cigarette can be applied to other experiments, especially experiments examining the qualitative and quantitative ST dynamics of patterns observed in naturally occurring systems.

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References

Fick, A. Ueber Diffusion, Pogg. Ann. Phys. Chem. 170 (4. Reihe 94), 59-86 (1855)

Weiss, George H. (1994), Aspects and Applications of the Random Walk, Random Materials and Processes, North-Holland Publishing Co., Amsterdam,

Ben-Avraham, D and Havlin, S, (2000), Diffusion and Reactions in Fractals and Disordered Systems, Cambridge University Press.

Perrot, P (1998). A to Z of Thermodynamics. Oxford University Press.

Atkins, P. (2010). The Laws of Thermodynamics: A Very Short Introductions. OUP Oxford, .

Fick, A. (1855). Ann. der. Physik . 94, 59

Crank, J. (1956). The Mathematics of Diffusion. Oxford: Clarendon Press.

Ben-Avraham D.; Havlin S., (2000). Diffusion and Reactions in Fractals and Disordered Systems, Cambridge University Press.

https://www.nascigs.com/modules/Security/Login.aspx

Atkins, P., de Paula, J. (1978/2010). Physical Chemistry, (first edition 1978), ninth edition 2010, Oxford University Press, Oxford UK

Clausius, R. (1850), Annalen der Physik 79: 368–397, 500–524.

Boltzmann, L. (2010.) The Fourth Law of Thermodynamics: The Law of Maximum Entropy Production (LMEP). Volume 22, Issue 1, 2010.

Sujalal, S. and Curtis, S. (2005). Magnetospheric Multiscale Mission:Cross-scale Exploration of Complexity in the Magnetosphere. In Nonequilbirium Phenomena in Plasmas. Edited by A. Sharma and P. Kaw. Springer.

Kuznetsov, A.V.; Avramenko, A.A. (2009). "A macroscopic model of traffic jams in axons". Mathematical Biosciences 218 (2).

S.H. Strogatz. (2001). Nonlinear dynamics and Chaos: Applications to Physics, Biology, Chemistry, and Engineering. Westview Press; Second Edition.

Edelstein, K. (2004). Mathematical Models in Biology. SIAM.

Murray, J.D. Mathematical Biology. (2002) .Springer-Verlag, 3rd ed. in 2 vols.: Mathematical Biology: I. An Introduction.

Segal, Lee A. (1984). Modeling Dynamic Phenomena in Molecular and Cellular Biology. Cambridge University Press, USA.

Fick, A. (1995). On liquid diffusion, Poggendorffs Annalen. 94, 59 (1855) - reprinted in Journal of Membrane Science, vol. 100 pp. 33-38.

Rose, M.R. (2012). Quantitative Ecological Theory: An Introduction to Basic Models. Springer US.

Koch A. J and Meinhar, H. (1994). Biological Pattern Formation : from Basic Mechanisms to Complex Structures. Rev. Modern Physics 66, 1481-1507.

Hurlbert, Stuart H. (1990). "Spatial Distribution of the Montane Unicorn". Oikos 58 (3): 257–271.

Durrett, Rick (2010). Probability: Theory and Examples (Fourth ed.). Cambridge: Cambridge University Press.

Gause, G.F. (1934). The struggle for existence. Baltimore, MD: Williams & Wilkins.

Freedman, H. I. (1980). Deterministic Mathematical Models in Population Ecology. New York: Marcel Dekker.

Varon, M., Zeigler, B.P. (1978). Bacterial predator-prey interaction at low prey density. Applied and Environmental Microbiology. 36(1):11-7