Leidenfrost Effect as a Directed Percolation Phase Transition

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.

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Sharpness of the Phase Transition for the Orthant Model

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-021-09408-z ◽

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.

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Active–absorbing-state phase transition beyond directed percolation: A class of exactly solvable models

Physical Review E ◽

10.1103/physreve.79.041143 ◽

2009 ◽

Vol 79 (4) ◽

Cited By ~ 27

Author(s):

Urna Basu ◽

P. K. Mohanty

Keyword(s):

Phase Transition ◽

Directed Percolation ◽

Exactly Solvable Models ◽

Solvable Models ◽

Absorbing State ◽

Exactly Solvable

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Directed percolation phase transition at the onset of STI in an inhomogeneous coupled map lattice

Physics Letters A ◽

10.1016/j.physleta.2018.11.005 ◽

2019 ◽

Vol 383 (5) ◽

pp. 421-431 ◽

Cited By ~ 3

Author(s):

Sujay Biswas ◽

Alaka Das

Keyword(s):

Phase Transition ◽

Coupled Map Lattice ◽

Directed Percolation

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.597 ◽

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.

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Criticality between cortical states

10.1101/454934 ◽

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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Directed percolation phase transition to sustained turbulence in Couette flow

Nature Physics ◽

10.1038/nphys3675 ◽

2016 ◽

Vol 12 (3) ◽

pp. 254-258 ◽

Cited By ~ 95

Author(s):

Grégoire Lemoult ◽

Liang Shi ◽

Kerstin Avila ◽

Shreyas V. Jalikop ◽

Marc Avila ◽

...

Keyword(s):

Phase Transition ◽

Couette Flow ◽

Directed Percolation

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CRITICAL EXPONENTS OF THE CONTINUOUS PHASE TRANSITION IN ZIFF–GULARI–BARSHAD MODEL

International Journal of Modern Physics B ◽

10.1142/s0217979204024008 ◽

2004 ◽

Vol 18 (06) ◽

pp. 859-866

Author(s):

DA-YIN HUA ◽

YUE-JIN ZHU ◽

YU-QIANG MA

Keyword(s):

Phase Transition ◽

Monte Carlo Simulation ◽

Critical Exponents ◽

Surface Reaction ◽

Universality Class ◽

Continuous Phase ◽

Reaction Model ◽

Directed Percolation ◽

Continuous Phase Transition ◽

Surface Reaction Model

A simple irreversible surface reaction model first introduced by Ziff, Gulari and Barshad has been studied using Monte Carlo simulation. We determine the static critical exponents accurately which are in excellent agreement with those of directed percolation universality class.

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Microstructure of laser-irradiated, conducting Kapton polyimide

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100138889 ◽

1995 ◽

Vol 53 ◽

pp. 502-503

Author(s):

D. L. Callahan ◽

Z. Ball ◽

H. M. Phillips ◽

R. Sauerbrey

Keyword(s):

Electron Microscopy ◽

Phase Transition ◽

Transmission Electron Microscopy ◽

Cross Section ◽

Film Surface ◽

Cross Sectional ◽

General Utility ◽

Transmission Electron ◽

Considerable Debate ◽

Potential Applications

Ultraviolet laser-irradiation can be used to induce an insulator-to-conductor phase transition on the surface of Kapton polyimide. Such structures have potential applications as resistors or conductors for VLSI applications as well as general utility electrodes. Although the percolative nature of the phase transformation has been well-established, there has been little definitive work on the mechanism or extent of transformation. In particular, there has been considerable debate about whether or not the transition is primarily photothermal in nature, as we propose, or photochemical. In this study, cross-sectional optical microscopy and transmission electron microscopy are utilized to characterize the nature of microstructural changes associated with the laser-induced pyrolysis of polyimide.Laser-modified polyimide samples initially 12 μm thick were prepared in cross-section by standard ultramicrotomy. Resulting contraction in parallel to the film surface has led to distortions in apparent magnification. The scale bars shown are calibrated for the direction normal to the film surface only.

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The structure of membranes and membrane proteins embedded in amorphous ice

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100122563 ◽

1992 ◽

Vol 50 (1) ◽

pp. 432-433

Author(s):

Uwe Lücken ◽

Joachim Jäger

Keyword(s):

Phase Transition ◽

Transition Temperature ◽

Membrane Proteins ◽

Phase Transition Temperature ◽

Lipid Vesicles ◽

Freezing Stress ◽

Amorphous Ice ◽

Different Temperatures ◽

Band Pass ◽

Lipid Polymorphism

TEM imaging of frozen-hydrated lipid vesicles has been done by several groups Thermotrophic and lyotrophic polymorphism has been reported. By using image processing, computer simulation and tilt experiments, we tried to learn about the influence of freezing-stress and defocus artifacts on the lipid polymorphism and fine structure of the bilayer profile. We show integrated membrane proteins do modulate the bilayer structure and the morphology of the vesicles.Phase transitions of DMPC vesicles were visualized after freezing under equilibrium conditions at different temperatures in a controlled-environment vitrification system. Below the main phase transition temperature of 24°C (Fig. 1), vesicles show a facetted appearance due to the quasicrystalline areas. A gradual increase in temperature leads to melting processes with different morphology in the bilayer profile. Far above the phase transition temperature the bilayer profile is still present. In the band-pass-filtered images (Fig. 2) no significant change in the width of the bilayer profile is visible.

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