Breakdown of Universality in Transitions to Spatiotemporal Chaos

Bohr, Tomas; Hecke, Martin van; Mikkelsen, René; Ipsen, Mads

doi:10.1103/physrevlett.86.5482

Cited by 48 publications

(33 citation statements)

References 27 publications

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“…Experiments tell us that, in the cases studied so far, it is first-order and thus deprived of any universality (correlation lengths remain finite at threshold). Abstract models considered up to now have been designed on lattices with local couplings and display both kinds of transitions in both one or two dimensions [20][21][22][23]. The problem with this picture -solved by our (semi-)realistic Navier-Sokes modeling of pCf-is that couplings of hydrodynamic origin may have non-local effects linked to pressure, which makes size an important issue.…”

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confidence: 99%

“…STI has been much studied within the framework of critical phenomena in statistical physics, especially in view of its universality [20]. Coupled map lattices in different spatial dimensions were used to test STI's properties [21,22]. In two dimensions, such an abstract minimal model was found to display a discontinuous first-order like transition as the control parameter was varied [23], which was subsequently used for comparison with transitional pCf [14, b].…”

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Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Manneville

2009

Phys. Rev. E

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Using a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent → laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number R low , whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond R low . PACS: 47.20.Ft, 47.27.Cn, 05.45.Jn The transition to turbulence in flows lacking linear instability modes, such as Poiseuille pipe flow driven by a pressure gradient along a circular tube (Ppf) and plane Couette flow driven by two plates moving parallel to each other in opposite directions (pCf), is particularly delicate to understand owing to its abrupt character, without the usual cascade seen in the globally super-critical case, as for e.g. convection. A recent general presentation of the issues is given in [1]. These globally sub-critical flows become turbulent through the nucleation and growth or decay of turbulent domains called puffs (Ppf) or spots (pCf), see, e.g., [2] and [3] for Ppf and pCf, respectively. Most of the work on the transition problem has dealt with special nonlinear solutions (exact coherent structures [4, b]) to the Navier-Stokes equations and their dynamics in the phase space spanned by them. Such solutions, obtained within the so-called Minimal Flow Unit (MFU) assumption [5], have been found at moderate values of the Reynolds number R in Ppf, [6], pCf [4,[7][8][9], and also in plane Poiseuille flow [8,10]. (In pCf, R is defined as Uh/ν where U is the speed of the plates driving the flow, 2h the gap petween the plates, and ν the kinematic viscosity of the fluid.) These solutions are all unstable and, together with their stable and unstable manifolds, they form the skeleton of the turbulent flow at a local scale. The reason why turbulence can be sustained only at much higher values of R (about a factor of two to three higher) is however not clear [2].

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Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Manneville

2009

Phys. Rev. E

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“…In systems with spatial structure, phase transitions to an absorbing state, as exemplified by the contact process [3,4], are widely studied in connection with self-organized criticality [5], the transition to turbulence [6], and issues of universality in nonequilibrium critical phenomena [7,8,9,10]. Interest in such transitions should continue to grow in the wake of experimental confirmation in a liquid crystal system [11].…”

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Absorbing-state phase transitions: Exact solutions of small systems

Dickman

2008

Phys. Rev. E

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I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents z and β/ν ⊥ ) with an accuracy of better than 0.1%; for the exponent ν ⊥ the accuracy is about 0.5%. Good results are also obtained for the pair contact process.

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“…In autocatalytic processes (in lasers, chemical reactions, or surface catalysis, for example), and population models, a population of n ≥ 0 individuals goes extinct when the absorbing state, n = 0, is reached. Phase transitions to an absorbing state in spatially extended systems, exemplified by the contact process [4,5], are currently of great interest in connection with selforganized criticality [6], the transition to turbulence [7], and issues of universality in nonequilibrium critical phenomena [8][9][10]. Such models are frequently studied using deterministic mean-field equations, Monte Carlo simulation, and renormalization group analyses.…”

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How to simulate the quasistationary state

2005

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For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasi-stationary (QS) regime. We propose a practical simulation method for studying quasi-stationary properties, based on the equation of motion governing the QS distribution. The method is tested in applications to the contact process. At the critical point, our method is about an order of magnitude more efficient than conventional simulation.

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Breakdown of Universality in Transitions to Spatiotemporal Chaos

Cited by 48 publications

References 27 publications

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Absorbing-state phase transitions: Exact solutions of small systems

How to simulate the quasistationary state

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