%0 Book Section %1 statphys23_0268 %A Laurson, L. %A Alava, M.J. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K avalanches criticality imbibition noise plasticity self-organized statphys23 topic-3 %T $1/f$ noise and avalanche scaling: Theory and applications in non-equilibrium systems %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=268 %X Recent developments have made it possible to understand the origin of $1/f$ -noise in several non-equilibrium systems exhibiting avalanches. For Barkhausen noise, it has been shown 1 that the power spectrum exponent $\alpha$ is related to the scaling of average avalanche sizes with their duration. Our work shows that the equality of $\alpha$ to $\gamma_st$, from the size-duration scaling $s(T) \sim T^\gamma_st$, is applicable to a wide class of systems from sandpile models of self-organized criticality (SOC) 2, to dislocation avalanches in plastically deforming crystals 3 to fluid invasion into disordered media 4. In the case of SOC, our observation is that the noise exponent of the activity time series $V(t)$ follows from the avalanche scaling and therefore from the underlying universality class of the model and spatial dimension at hand. This implies that for $d<d_c$ (with $d_c$ the upper critical dimension), the power spectrum $P(f) f^-\alpha$ scales with a non-trivial $\alpha<2$, instead of the long-standing belief that sandpile models should lead to a Lorentzian power spectrum (i.e. $\alpha=2$) independent of $d$ 5,6. For two specific, experimentally relevant applications we consider two apparently very different systems. First, the collective velocity or deformation time series of dislocations in a plastically deforming crystal, as obtained from a simple two-dimensional discrete dislocation dynamics model, is shown to follow $\alpha=\gamma_st$ -scaling as well 3. Second, this conclusion is also found for the fluctuations of a two-phase interface velocity in fluid invasion into disordered, porous media, by simulating a phase-field model of the problem 4.\\ 1) M. C. Kuntz and J. P. Sethna, Phys. Rev. B 62, 11699 (2000).\\ 2) L. Laurson, M. J. Alava, and S. Zapperi, J. Stat. Mech. 0511, L11001 (2005).\\ 3) L. Laurson, M. J. Alava, Phys. Rev. E 74, 066106 (2006).\\ 4) M. Rost, L. Laurson, M. Dubé and M. J. Alava, Phys. Rev. Lett. 98, 054502 (2007).\\ 5) H. J. Jensen, K. Christensen, and H. C. Fogedby, Phys. Rev. B 40, R7425 (1989).\\ 6) J. Kertesz and L. B. Kiss, J. Phys. A: Math. Gen. 23, L433 (1990).

@incollection{statphys23_0268, abstract = {Recent developments have made it possible to understand the origin of $1/f$ -noise in several non-equilibrium systems exhibiting avalanches. For Barkhausen noise, it has been shown [1] that the power spectrum exponent $\alpha$ is related to the scaling of average avalanche sizes with their duration. Our work shows that the equality of $\alpha$ to $\gamma_{st}$, from the size-duration scaling $\langle s(T) \rangle \sim T^{\gamma_{st}}$, is applicable to a wide class of systems from sandpile models of self-organized criticality (SOC) [2], to dislocation avalanches in plastically deforming crystals [3] to fluid invasion into disordered media [4]. In the case of SOC, our observation is that the noise exponent of the activity time series $V(t)$ follows from the avalanche scaling and therefore from the underlying universality class of the model and spatial dimension at hand. This implies that for $d<d_c$ (with $d_c$ the upper critical dimension), the power spectrum $P(f) \sim f^{-\alpha}$ scales with a non-trivial $\alpha<2$, instead of the long-standing belief that sandpile models should lead to a Lorentzian power spectrum (i.e. $\alpha=2$) independent of $d$ [5,6]. For two specific, experimentally relevant applications we consider two apparently very different systems. First, the collective velocity or deformation time series of dislocations in a plastically deforming crystal, as obtained from a simple two-dimensional discrete dislocation dynamics model, is shown to follow $\alpha=\gamma_{st}$ -scaling as well [3]. Second, this conclusion is also found for the fluctuations of a two-phase interface velocity in fluid invasion into disordered, porous media, by simulating a phase-field model of the problem [4].\\ 1) M. C. Kuntz and J. P. Sethna, Phys. Rev. B {\bf 62}, 11699 (2000).\\ 2) L. Laurson, M. J. Alava, and S. Zapperi, J. Stat. Mech. {\bf 0511}, L11001 (2005).\\ 3) L. Laurson, M. J. Alava, Phys. Rev. E {\bf 74}, 066106 (2006).\\ 4) M. Rost, L. Laurson, M. Dub\'e and M. J. Alava, Phys. Rev. Lett. {\bf 98}, 054502 (2007).\\ 5) H. J. Jensen, K. Christensen, and H. C. Fogedby, Phys. Rev. B {\bf 40}, R7425 (1989).\\ 6) J. Kertesz and L. B. Kiss, J. Phys. A: Math. Gen. {\bf 23}, L433 (1990).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Laurson, L. and Alava, M.J.}, biburl = {https://www.bibsonomy.org/bibtex/29af451777e45681ca3a3a1039f66cbfd/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {f8e6c7da5ab7b7e4089dbd14267a76bf}, intrahash = {9af451777e45681ca3a3a1039f66cbfd}, keywords = {avalanches criticality imbibition noise plasticity self-organized statphys23 topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:15.000+0200}, title = {$1/f$ noise and avalanche scaling: Theory and applications in non-equilibrium systems}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=268}, year = 2007 }