Nonequilibrium Roughening Transition in a Simple Model of Fungal Growth in <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi></mi><mo>+</mo><mi></mi><mn>1</mn></math></span> Dimensions

Juan M. López; Henrik Jeldtoft Jensen

doi:10.1103/PhysRevLett.81.1734

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Nonequilibrium Roughening Transition in a Simple Model of Fungal Growth in $1 + 1$ Dimensions

Juan M. López and Henrik Jeldtoft Jensen

Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, United Kingdom

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Phys. Rev. Lett. 81, 1734 – Published 24 August, 1998

DOI: https://doi.org/10.1103/PhysRevLett.81.1734

Abstract

We introduce a simple model of yeastlike growth of fungi colonies, which exhibits a continuous roughening transition far from equilibrium from a smooth ( $α = 0$ ) to a rough phase ( $α = 1 / 2$ ) in $1 + 1$ dimensions. At the transition some scaling exponents are calculated by mapping the problem onto a directed percolation process. The model reproduces the roughening transition observed in some experiments of fungal growth.

References (24)

Fractal Geometry in Biological Systems, P. M. Iannaccone and M. Khokha (CRS Press, Boca Raton, FL, 1996).
A. L. Cooper et al., Proc. R. Soc. London B 171, 175 (1968); ibid.A. L. Cooper 175, 95 (1970).
E. Ben-Jacob, Contemp. Phys. 38, 205 (1997).
E. Ben-Jacob and P. Garik, Nature (London) 343, 523 (1990).
E. Ben-Jacob et al., Nature (London) 368, 46 (1994).
D. A. Kessler and H. Levine, Phys. Rev. E 48, 4801 (1993).
T. Vicsek et al., Physica (Amsterdam) 167A, 315 (1990).
M. Matsushita and H. Fujikawa, Physica (Amsterdam) 168A, 12 294 (1990).
S. Matsuura and S. Miyazima, Physica (Amsterdam) 191A, 30 (1992); see also Fractals 1, 336 (1993).
T. Matsuyama and M. Matsushita, in Ref. [[1]].
J. Wakita et al., J. Phys. Soc. Jpn. 63, 1205 (1994).
T. Sams et al., Phys. Rev. Lett. 79, 313 (1997).
M. J. Carlile and S. C. Watkinson, The Fungi (Academic Press, London, 1994).
A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, England, 1995).
Thomas Sams (private communication).
R. Savit and R. Ziff, Phys. Rev. Lett. 55, 2515 (1985).
J. Kertész and D. E. Wolf, Phys. Rev. Lett. 62, 2571 (1989).
U. Alon et al., Phys. Rev. Lett. 76, 2746 (1996).
S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London A 381, 17 (1982).
J. M. López and H. J. Jensen (to be published).
F. Family and T. Vicsek, J. Phys. A 18, L75 (1985).
W. Kinzel, in Percolation Structures and Processes, G. Deutscher , Annals of the Israel Physical Society Vol. 5 (Hilger, Bristol, 1983).
The maximal velocity in our model is given by one vertical lattice spacing per unit time.
M. R. Evans et al., Phys. Rev. Lett. 74, 208 (1995).

[c1] Fractal Geometry in Biological Systems, P. M. Iannaccone and M. Khokha (CRS Press, Boca Raton, FL, 1996).

[c2] A. L. Cooper et al., Proc. R. Soc. London B 171, 175 (1968); ibid.A. L. Cooper 175, 95 (1970).

[c3] E. Ben-Jacob, Contemp. Phys. 38, 205 (1997).

[c4] E. Ben-Jacob and P. Garik, Nature (London) 343, 523 (1990).

[c5] E. Ben-Jacob et al., Nature (London) 368, 46 (1994).

[c6] D. A. Kessler and H. Levine, Phys. Rev. E 48, 4801 (1993).

[c7] T. Vicsek et al., Physica (Amsterdam) 167A, 315 (1990).

[c8] M. Matsushita and H. Fujikawa, Physica (Amsterdam) 168A, 12 294 (1990).

[c9] S. Matsuura and S. Miyazima, Physica (Amsterdam) 191A, 30 (1992); see also Fractals 1, 336 (1993).

[c10] T. Matsuyama and M. Matsushita, in Ref. [[1]].

[c11] J. Wakita et al., J. Phys. Soc. Jpn. 63, 1205 (1994).

[c12] T. Sams et al., Phys. Rev. Lett. 79, 313 (1997).

[c13] M. J. Carlile and S. C. Watkinson, The Fungi (Academic Press, London, 1994).

[c14] A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, England, 1995).

[c15] Thomas Sams (private communication).

[c16] R. Savit and R. Ziff, Phys. Rev. Lett. 55, 2515 (1985).

[c17] J. Kertész and D. E. Wolf, Phys. Rev. Lett. 62, 2571 (1989).

[c18] U. Alon et al., Phys. Rev. Lett. 76, 2746 (1996).

[c19] S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London A 381, 17 (1982).

[c20] J. M. López and H. J. Jensen (to be published).

[c21] F. Family and T. Vicsek, J. Phys. A 18, L75 (1985).

[c22] W. Kinzel, in Percolation Structures and Processes, G. Deutscher , Annals of the Israel Physical Society Vol. 5 (Hilger, Bristol, 1983).

[c23] The maximal velocity in our model is given by one vertical lattice spacing per unit time.

[c24] M. R. Evans et al., Phys. Rev. Lett. 74, 208 (1995).

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Nonequilibrium Roughening Transition in a Simple Model of Fungal Growth in $1 + 1$ Dimensions

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Nonequilibrium Roughening Transition in a Simple Model of Fungal Growth in 1+1 Dimensions

Abstract

References (24)

Nonequilibrium Roughening Transition in a Simple Model of Fungal Growth in $1 + 1$ Dimensions