scholarly journals Directed percolation phase transition to sustained turbulence in Couette flow

2016 ◽  
Vol 12 (3) ◽  
pp. 254-258 ◽  
Author(s):  
Grégoire Lemoult ◽  
Liang Shi ◽  
Kerstin Avila ◽  
Shreyas V. Jalikop ◽  
Marc Avila ◽  
...  
Keyword(s):  
Phase Transition ◽  
Couette Flow ◽  
Directed Percolation

Nonsteady properties of couette flow of a liquid under the conditions of a phase transition

1986 ◽  
Vol 27 (1) ◽  
pp. 78-83
Author(s):  
S. V. Maklakov ◽  
K. V. Pribytkova ◽  
A. M. Stolin ◽  
S. I. Khudyaev
Keyword(s):  
Phase Transition ◽  
Couette Flow

scholarly journals Subsampled Directed-Percolation Models Explain Scaling Relations Experimentally Observed in the Brain

2021 ◽  
Vol 14 ◽  
Author(s):  
Tawan T. A. Carvalho ◽  
Antonio J. Fontenele ◽  
Mauricio Girardi-Schappo ◽  
Thaís Feliciano ◽  
Leandro A. A. Aguiar ◽  
...  
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Branching Process ◽  
Mean Field ◽  
Universality Class ◽  
Experimental Results ◽  
Scaling Relations ◽  
Directed Percolation ◽  
Specific Level ◽  
The Brain

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.

scholarly journals Sharpness of the Phase Transition for the Orthant Model

2021 ◽  
Vol 24 (4) ◽  
Author(s):  
Thomas Beekenkamp
Keyword(s):  
Phase Transition ◽  
Random Walk ◽  
Critical Value ◽  
Percolation Model ◽  
Critical Threshold ◽  
Directed Percolation ◽  
Sharp Threshold ◽  
Shape Theorem ◽  
Exponentially Small

AbstractThe orthant model is a directed percolation model on $\mathbb {Z}^{d}$ ℤ d , in which all clusters are infinite. We prove a sharp threshold result for this model: if p is larger than the critical value above which the cluster of 0 is contained in a cone, then the shift from 0 that is required to contain the cluster of 0 in that cone is exponentially small. As a consequence, above this critical threshold, a shape theorem holds for the cluster of 0, as well as ballisticity of the random walk on this cluster.

scholarly journals Laminar–turbulent coexistence in annular Couette flow

2019 ◽  
Vol 879 ◽  
pp. 579-603 ◽  
Author(s):  
Kohei Kunii ◽  
Takahiro Ishida ◽  
Yohann Duguet ◽  
Takahiro Tsukahara
Keyword(s):  
Phase Transition ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Couette Flow ◽  
Pipe Flow ◽  
Turbulent Structures ◽  
Coaxial Cylinders ◽  
Turbulent Fluctuations ◽  
Axial Translation ◽  
Planar Shear

Annular Couette flow is the flow between two coaxial cylinders driven by the axial translation of the inner cylinder. It is investigated using direct numerical simulation in long domains, with an emphasis on the laminar–turbulent coexistence regime found for marginally low values of the Reynolds number. Three distinct flow regimes are demonstrated as the radius ratio $\unicode[STIX]{x1D702}$ is decreased from 0.8 to 0.5 and finally to 0.1. The high-$\unicode[STIX]{x1D702}$ regime features helically shaped turbulent patches coexisting with laminar flow, as in planar shear flows. The moderate-$\unicode[STIX]{x1D702}$ regime does not feature any marked laminar–turbulent coexistence. In an effort to discard confinement effects, proper patterning is, however, recovered by artificially extending the azimuthal span beyond $2\unicode[STIX]{x03C0}$. Eventually, the low-$\unicode[STIX]{x1D702}$ regime features localised turbulent structures different from the puffs commonly encountered in transitional pipe flow. In this new coexistence regime, turbulent fluctuations are surprisingly short-ranged. Implications are discussed in terms of phase transition and critical scaling.

scholarly journals A statistical mechanical phase transition to turbulence in a model shear flow

2017 ◽  
Vol 830 ◽  
pp. 1-4
Author(s):  
Nigel Goldenfeld
Keyword(s):  
Phase Transition ◽  
Shear Flow ◽  
Stokes Equations ◽  
Equilibrium Phase ◽  
Transition To Turbulence ◽  
Crystalline Lattice ◽  
Navier Stokes ◽  
Directed Percolation ◽  
Statistical Mechanical ◽  
Non Equilibrium

It is becoming increasingly clear that the strong spatial and temporal fluctuations observed in a narrow Reynolds number regime around the laminar–turbulent transition in shear flows can best be understood using the concepts and techniques from a seemingly unrelated discipline – statistical mechanics. During the last few years, a consensus has begun to emerge that these phenomena reflect an underlying non-equilibrium phase transition exhibited by a model of interacting particles on a crystalline lattice, directed percolation, that seems very far from fluid mechanics. Now, Chantry et al. (J. Fluid Mech., vol. 824, 2017, R1) have developed a truncated-mode computation of a model shear flow, capable of simulating systems far larger and longer than any previous study and have for the first time generated enough statistical data that a high-precision test of theory is feasible. The results broadly confirm the theory, extending the class of flows for which the directed percolation scenario holds and removing any remaining doubts that non-equilibrium statistical mechanical critical phenomena can be exhibited by the Navier–Stokes equations.

scholarly journals Criticality between cortical states

2018 ◽  
Author(s):  
Antonio J. Fontenele ◽  
Nivaldo A. P. de Vasconcelos ◽  
Thaís Feliciano ◽  
Leandro A. A. Aguiar ◽  
Carina Soares-Cunha ◽  
...  
Keyword(s):  
Phase Transition ◽  
Cerebral Cortex ◽  
Critical Exponents ◽  
Slow Wave Sleep ◽  
Mean Field ◽  
Universality Class ◽  
Directed Percolation ◽  
Intermediate Value ◽  
Neuronal Avalanches ◽  
The Brain

Since the first measurements of neuronal avalanches [1], the critical brain hypothesis has gained traction [2]. However, if the brain is critical, what is the phase transition? For several decades it has been known that the cerebral cortex operates in a diversity of regimes [3], ranging from highly synchronous states (e.g. slow wave sleep [4], with higher spiking variability) to desynchronized states (e.g. alert waking [5], with lower spiking variability). Here, using independent signatures of criticality, we show that a phase transition occurs in an intermediate value of spiking variability. The critical exponents point to a universality class different from mean-field directed percolation (MF-DP). Importantly, as the cortex hovers around this critical point [6], it follows a linear relation between the avalanche exponents that encompasses previous experimental results from different setups [7, 8] and is reproduced by a model.

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