Hyperuniform Structures Formed by Shearing Colloidal Suspensions (original) (raw)
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Random organization in periodically driven systems
Nature Physics, 2008
Understanding self-organization is one of the key tasks for controlling and manipulating the structure of materials at the micro-and nanoscale. In general, self-organization is driven by interparticle potentials and is opposed by the chaotic dynamics characteristic of many driven non-equilibrium systems. Here we introduce a new model that shows how the irreversible collisions that generally produce diffusive chaotic dynamics can also cause a system to self-organize to avoid future collisions. This can lead to a self-organized non-fluctuating quiescent state, with a dynamical phase transition separating it from fluctuating diffusing states. We apply the model to recent experiments on periodically sheared particle suspensions where a transition from reversible to irreversible behaviour was observed. New experiments presented here exhibit remarkable agreement with this simple model. More generally, the model and experiments provide new insights into how driven systems can self-organize.
Activated dynamics at a non-disordered critical point
Europhysics Letters (EPL), 2003
We present a non-randomly, frustrated lattice model which exhibits activated dynamics at a critical point. The phase transition involves ordering of large-scale structures which occur naturally within the model. Through the construction of a coarse-grained master equation, we show that the time scales diverge exponentially while the static fluctuations exhibit the usual power law divergences. We discuss the relevance of this scenario in the context of the glass transition in supercooled liquids.
International Journal of Modern Physics B, 1998
The study of phenomena such as capillary displacement in porous media, fracture propagation, and interface dynamics in quenched random media has attracted a great deal of interest in the last few years. This class of problems does not seem to be treatable with the standard theoretical methods, and the only analytical results come from scaling theory or mapping, for some of their properties, to other solvable models. In this paper a recently proposed approach to problems with extremal dynamics in quenched disordered media, named run time statistics ͑RTS͒ or quenched-stochastic transformation, is described in detail. This method allows us to map a quenched dynamics such as invasion percolation onto a stochastic annealed process with cognitive memory. By combining RTS with the fixed scale transformation approach, we develop a general and systematic theoretical method to compute analytically the critical exponents of invasion percolation, with and without trapping, and directed invasion percolation. In addition we can also understand and describe quantitatively the self-organized nature of the process. ͓S1063-651X͑96͒07207-8͔
The order–disorder transition in colloidal suspensions under shear flow
Journal of Physics: Condensed Matter, 2007
We study the order-disorder transition in colloidal suspensions under shear flow by performing Brownian dynamics simulations. We characterize the transition in terms of a statistical property of time-dependent maximum value of the structure factor. We find that its power spectrum exhibits the power-law behaviour only in the ordered phase. The power-law exponent is approximately-2 at frequencies greater than the magnitude of the shear rate, while the power spectrum exhibits the 1/f-type fluctuations in the lower frequency regime.
Power laws and self-organized criticality in theory and nature
Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution. Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance. We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real-world phenomena. The complexity of physical and biological scaling phenomena has been found to transcend the explanatory power of individual paradigmal concepts. The interaction between theoretical development and experimental observations has been very fruitful, leading to a series of novel concepts and insights.
Ultrametricity and memory in a solvable model of self-organized criticality
Physical Review E, 1996
Slowly driven dissipative systems may evolve to a critical state where long periods of apparent equilibrium are punctuated by intermittent avalanches of activity. We present a self-organized critical model of punctuated equilibrium behavior in the context of biological evolution, and solve it in the limit that the number of independent traits for each species diverges. We derive an exact equation of motion for the avalanche dynamics from the microscopic rules. In the continuum limit, avalanches propagate via a diffusion equation with a nonlocal, history dependent potential representing memory. This nonlocal potential gives rise to a non-Gaussian ͑fat͒ tail for the subdiffusive spreading of activity. The probability for the activity to spread beyond a distance r in time s decays as ͱ(24/)s Ϫ3/2 x 1/3 exp͓Ϫ3/4x 1/3 ͔ for xϭr 4 /sӷ1. The potential represents a hierarchy of time scales that is dynamically generated by the ultrametric structure of avalanches, which can be quantified in terms of ''backward'' avalanches. In addition, a number of other correlation functions characterizing the punctuated equilibrium dynamics are determined exactly. ͓S1063-651X͑96͒05108-2͔
From Self-Organized to Extended Criticality
Frontiers in Physiology, 2012
We address the issue of criticality that is attracting the attention of an increasing number of neurophysiologists. Our main purpose is to establish the specific nature of some dynamical processes that although physically different, are usually termed as "critical," and we focus on those characterized by the cooperative interaction of many units. We notice that the term "criticality" has been adopted to denote both noise-induced phase transitions and Self-Organized Criticality (SOC) with no clear connection with the traditional phase transitions, namely the transformation of a thermodynamic system from one state of matter to another. We notice the recent attractive proposal of extended criticality advocated by Bailly and Longo, which is realized through a wide set of critical points rather than emerging as a singularity from a unique value of the control parameter. We study a set of cooperatively firing neurons and we show that for an extended set of interaction couplings the system exhibits a form of temporal complexity similar to that emerging at criticality from ordinary phase transitions. This extended criticality regime is characterized by three main properties: (i) In the ideal limiting case of infinitely large time period, temporal complexity corresponds to Mittag-Leffler complexity; (ii) For large values of the interaction coupling the periodic nature of the process becomes predominant while maintaining to some extent, in the intermediate time asymptotic region, the signature of complexity; (iii) Focusing our attention on firing neuron avalanches, we find two of the popular SOC properties, namely the power indexes 2 and 1.5 respectively for time length and for the intensity of the avalanches. We derive the main conclusion that SOC emerges from extended criticality, thereby explaining the experimental observation of Plenz and Beggs: avalanches occur in time with surprisingly regularity, in apparent conflict with the temporal complexity of physical critical points.
Manifestations of the onset of chaos in condensed matter and complex systems
The European Physical Journal Special Topics
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated with the attractors at period-doubling accumulation points and at tangent bifurcations to describe features of glassy dynamics, critical fluctuations and localization transitions. We recall that trajectories pertaining to the routes to chaos form families of time series that are readily transformed into networks via the Horizontal Visibility algorithm, and this in turn facilitates establish connections between entropy and Renormalization Group properties. We discretize the replicator equation of game theory to observe the onset of chaos in familiar social dilemmas, and also to mimic the evolution of high-dimensional ecological models. We describe an analytical framework of nonlinear mappings that reproduce rank distributions of large classes of data (including Zipf's law). We extend the discussion to point out a common circumstance of drastic contraction of configuration space driven by the attractors of these mappings. We mention the relation of generalized entropy expressions with the dynamics along and at the period doubling, intermittency and quasi-periodic routes to chaos. Finally, we refer to additional natural phenomena in complex systems where these conditions may manifest.