Abstract
The tree annual ring is defined and geometrically described by two new physical quantities designated as golden ring cube (GRC) and golden ring volume (GRV). The quantities were used to derive a two-level system dynamical coarse-graining framework for annual rings by applying non-equilibrium equality of free energy differences of dynamical repetitive transitions from earlywood to latewood and vice versa. The scaling properties of growth rings interaction parameter β, GRC and GRV were then numerically quantified and tested for Douglas-fir and white spruce. Although parameter β was different for Douglas-fir and white spruce, its invariant property was tested and found to be the same for both species. The parameter β was thereafter used to derive a novel heterogeneity test criterion that was described and tested. β is an important parameter that provides integrated information for the dependence of the GRV and GRC on species, growth factors, and environmental interaction signals.
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References
Chvosta P, Reineker P, Schulz M (2007) Probability distribution of work done on a two-level system during a nonequilibrium isothermal process. Phys Rev E 75:041124/1–041124/10
Crooks EG (2000) Path-ensemble averages in systems driven far from equilibrium. Phys Rev E 61(3):2361–2366
Garrahan JP, Jack RL, Lecomte V, Pitard E, van Duijvendijk K, vanWijland F (2007) Dynamical first-order phase transition in kinetically constrained models of glasses. Phys Rev Lett 98-195702:1–4
Garrahan JP, Jack RL, Lecomte V, Pitard E, van Duijvendijk K, van Wijland F (2009) First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories. J Phys A Math Theor 42–075007:1–34
Grotta AT, Leichti RJ, Gartner BL, Johnson GR (2005) Effect of growth ring orientation and placement of earlywood and latewood on MOE and MOR of very-small clear Douglas-fir beams. Wood Fibre Sci 37(2):207–212
Hedges LO, Jack RL, Garrahan JP, Chandler D (2009) Dynamic order-disorder in atomistic models of structural glass formers. Science 323:1309–1313
Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78(14):2690–2693
Jozsa LA, Richards JE, Johnson SG (1987) Calibration of Forintek’s direct reading X-ray densitometer. Research report CFS No. 36a. Forintek Canada Corp, Vancouver
Jozsa LA, Munro BD, Gordon JR (1998) Basic wood properties of second-growth Tsuga heterophylla. British Columbia. Forest Practices Branch and Forintek Canada Corp. Special Publication No. Sp–38
Jyske T, Mäkinen H, Saranpää P (2008) Wood density within Norway spruce stems. Silva Fennica 42(3):439–455
Lecomte V, Appert-Rolland C, van Wijland F (2005) Chaotic properties of systems with Markov dynamics. Phys Rev Lett 95:010601–010604
Mäkinen H, Jaakkola T, Piispanen R, Saranpää P (2007) Predicting wood and tracheid properties of Norway spruce. For Ecol Manage 241:175–188
Modén CS, Berglund LA (2008) A two-phase annual ring model of transverse anisotropy in softwoods. Compos Sci Technol 68:3020–3026
Pernestål K, Jonsson B, Larsson B (1995) A simple model for density of annual rings. Wood Sci Technol 29:441–449
Perré P, Turner IW (2008) A mesoscopic drying model applied to the growth rings of softwood: mesh generation and simulation results. Maderas Ciencia y tecnología 10(3):251–274
Ritort F (2004) Work and heat fluctuations in two-state systems: a trajectory thermodynamics formalism. J Stat Mech Theor Exp P10016:1–33
Tekleyohannes AT, Avramidis S (2009) Two-level self-organization of properties of wood. A new paradigm for dimensional analysis and scaling. Wood Sci Technol 44(2):253–268
Williams GP (1997) Chaos theory tamed. Taylor & Francis limited, London
Zobel BJ, van Buijtenen JP (1989) Wood variation–its causes and control. Springer, Verlag
Acknowledgments
The authors would like to express their great appreciations to Mr. Dave Munro of Forintek-FPInnovations for providing densitometry data of Douglas-fir and white spruce. This project was funded by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.
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Tekleyohannes, A.T., Avramidis, S. Two-level system dynamical coarse-graining of annual rings. Wood Sci Technol 46, 473–485 (2012). https://doi.org/10.1007/s00226-011-0419-x
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DOI: https://doi.org/10.1007/s00226-011-0419-x