scholarly journals Universal organization of resting brain activity at the thermodynamic critical point

2013 ◽  
Vol 7 ◽  
Author(s):  
Shan Yu ◽  
Hongdian Yang ◽  
Oren Shriki ◽  
Dietmar Plenz
Keyword(s):  
Critical Point ◽  
Brain Activity ◽  
Thermodynamic Critical Point

scholarly journals Critical behaviour of the stochastic Wilson-Cowan model

2021 ◽  
Author(s):  
Antonio De Candia ◽  
Alessandro Sarracino ◽  
Ilenia Apicella ◽  
Lucilla de Arcangelis
Keyword(s):  
Critical Point ◽  
Brain Activity ◽  
Universality Class ◽  
System Size ◽  
Critical Behaviour ◽  
Accurate Analysis ◽  
Scale Free ◽  
Stochastic Version ◽  
Wide Range ◽  
Avalanche Dynamics

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, -3/2 and -2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.

An Analytical Investigation of Forced Convection Heat Transfer to Fluids Near the Thermodynamic Critical Point

1975 ◽  
Vol 97 (2) ◽  
pp. 226-230 ◽  
Author(s):  
V. S. Sastry ◽  
N. M. Schnurr
Keyword(s):  
Heat Transfer ◽  
Critical Point ◽  
Circular Tube ◽  
Convection Heat Transfer ◽  
Analytical Investigation ◽  
Convection Heat ◽  
Thermodynamic Critical Point ◽  
Constant Wall Heat Flux ◽  
Flow Through ◽  
Implicit Finite Difference

A numerical solution is carried out for heat transfer to fluids near the thermodynamic critical point for turbulent flow through a circular tube with constant wall heat flux. An adaptation of the Patankar-Spalding implicit finite difference marching procedure is used. Agreement of the results with experimental data for water and carbon dioxide show the solution to be quite accurate very near the critical point provided the wall temperature at inlet is less than the pseudocritical temperature of the fluid.

Phase Change Mechanisms in Pulsed Laser-Matter Interaction

2004 ◽  
Vol 850 ◽  
Author(s):  
Xianfan Xu
Keyword(s):  
Phase Change ◽  
Critical Point ◽  
Spinodal Decomposition ◽  
Nanosecond Laser ◽  
Micro Machining ◽  
Laser Micro Machining ◽  
Thermodynamic Critical Point ◽  
Matter Interaction ◽  
Explosive Phase ◽  
Change Mechanisms

ABSTRACTLaser micro-machining is finding many applications in materials processing and manufacturing. Various laser techniques are being used to fabricate micro-electronics, optics, and medical components. This paper will mainly deal with the fundamental issues involved in laser-matter interaction. Our studies are focused on laser induced thermal and thermomechanical phenomena and phase change mechanisms that determine the materials removal process during laser micro-machining. It is shown that during nanosecond laser machining, explosive phase change could occur, during which the liquid is superheated to close to the thermodynamic critical point, followed by an explosive, homogeneous phase transformation. On the other hand, it is observed in the experiment that the time needed for nucleation during laser induced phase explosion is on the order of one nanosecond. Thus, when a laser with a pulsewidth of the order of picosecond or less is used, it is likely that the material can be heated above the critical point, and another type of phase change, spinodal decomposition is possible. Molecular dynamics studies showed that with the use of a femtosecond laser pulse, it is possible to superheat the material to above the critical point, and spinodal decomposition is the dominant mechanism for materials removal.

scholarly journals Critical behaviour of the stochastic Wilson-Cowan model

2021 ◽  
Vol 17 (8) ◽  
pp. e1008884
Author(s):  
Antonio de Candia ◽  
Alessandro Sarracino ◽  
Ilenia Apicella ◽  
Lucilla de Arcangelis
Keyword(s):  
Critical Point ◽  
Brain Activity ◽  
Universality Class ◽  
System Size ◽  
Critical Behaviour ◽  
Accurate Analysis ◽  
Scale Free ◽  
Stochastic Version ◽  
Wide Range ◽  
Avalanche Dynamics

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.

scholarly journals Fractal Dimension of Cortical Functional Connectivity Networks Predicts Severity in Disorders of Consciousness

2019 ◽  
Author(s):  
TF. Varley ◽  
M. Craig ◽  
R. Adapa ◽  
P. Finoia ◽  
G. Williams ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Functional Connectivity ◽  
Healthy Volunteers ◽  
Critical Point ◽  
Brain Activity ◽  
Conscious Experience ◽  
Minimally Conscious State ◽  
Disorders Of Consciousness ◽  
Level Of Consciousness ◽  
The Brain

AbstractRecent evidence suggests that the quantity and quality of conscious experience may be a function of the complexity of activity in the brain, and that consciousness emerges in a critical zone on the axes of order/randomness and integration/differentiation. We propose fractal shapes as a measure of proximity to this critical point, as fractal dimension encodes information about complexity beyond simple entropy or randomness, and fractal structures are known to emerge in systems nearing a critical point. To validate this, we tested the several measures of fractal dimension on the brain activity from healthy volunteers and patients with disorders of consciousness of varying severity. We used a Compact Box Burning algorithm to compute the fractal dimension of cortical functional connectivity networks as well as computing the fractal dimension of the associated adjacency matrices using a 2D box-counting algorithm. To test whether brain activity is fractal in time as well as space, we used the Higuchi temporal fractal dimension on BOLD time-series. We found significant decreases in the fractal dimension between healthy volunteers (n=15), patients in a minimally conscious state (n=10), and patients in a vegetative state (n=8), regardless of the mechanism of injury. We also found significant decreases in adjacency matrix fractal dimension and Higuchi temporal fractal dimension, which correlated with decreasing level of consciousness. These results suggest that cortical functional connectivity networks display fractal character and that this is predictive of level of consciousness in a clinically relevant population, with more fractal (i.e. more complex) networks being associated with higher levels of consciousness. This supports the hypothesis that level of consciousness and system complexity are positively associated, and is consistent with previous EEG, MEG, and fMRI studies.

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