Explosive synchronization: from synthetic to real-world networks (Interdisciplinary Physics)

2021 ◽  
Author(s):  
Atiyeh Bayani ◽  
Sajad Jafari ◽  
Hamed Azarnoush
Keyword(s):  
Real World ◽  
Mean Field Theory ◽  
Mean Field ◽  
Point Of View ◽  
Continuous Transition ◽  
First Order ◽  
Grid Networks ◽  
Structural Framework ◽  
Neuronal Oscillators ◽  
Explosive Synchronization

Abstract Synchronization is a widespread phenomenon in both synthetic and real-world networks. This collective behavior of simple and complex systems has been attracting much research during the last decades. Two different routes to synchrony are defined in networks; first-order, characterized as explosive, and second-order, characterized as continuous transition. Although pioneer researches explained that the transition type is a generic feature in the networks, recent studies proposed some frameworks in which different phase and even chaotic oscillators exhibit explosive synchronization. The relationship between the structural properties of the network and the dynamical features of the oscillators is mainly proclaimed because some of these frameworks show abrupt transitions. Despite different theoretical analyses about the appearance of the first-order transition, studies are limited to the mean-field theory, which cannot be generalized to all networks. There are different real-world and man-made networks whose properties can be characterized in terms of explosive synchronization, e.g., the transition from unconsciousness to wakefulness in the brain and spontaneous synchronization of power-grid networks. In this review article, explosive synchronization is discussed from two main aspects. First, pioneer articles are categorized from the dynamical-structural framework point of view. Then, articles that considered different oscillators in the explosive synchronization frameworks are studied. In this article, the main focus is on the explosive synchronization in networks with chaotic and neuronal oscillators. Also, efforts have been made to consider the recent articles which proposed new frameworks of explosive synchronization.

scholarly journals Miscibility studies of two twist-bend nematic liquid crystal dimers with different average molecular curvatures. A comparison between experimental data and predictions of a Landau mean-field theory for the NTB–N phase transition

2016 ◽  
Vol 18 (6) ◽  
pp. 4394-4404 ◽  
Author(s):  
D. O. López ◽  
B. Robles-Hernández ◽  
J. Salud ◽  
M. R. de la Fuente ◽  
N. Sebastián ◽  
...  
Keyword(s):  
Field Theory ◽  
Experimental Data ◽  
Phase Transition ◽  
Liquid Crystal ◽  
Nematic Phase ◽  
Mean Field Theory ◽  
Mean Field ◽  
Landau Model ◽  
First Order ◽  
Miscibility Studies

We have developed a Landau model that predicts a first order twist-bend nematic–nematic phase transition.

From Spin Glasses to Glasses

1996 ◽  
Vol 455 ◽  
Author(s):  
J. P. Bouchaud ◽  
M. Mezard
Keyword(s):  
Glass Transition ◽  
Spin Glasses ◽  
Mode Coupling ◽  
Random Potential ◽  
Mean Field Theory ◽  
Mean Field ◽  
Coupling Theory ◽  
Aging Effects ◽  
First Order ◽  
Recent Developments

ABSTRACTWe discuss some aspects of the links between the behaviour and theory of spin glasses and that of structural glasses of the fragile type. We review the present status of the conjecture according to which a certain class of spin glass mean field theories (those with first order transitions) could provide a mean field theory for the glass transition. Recent developments pointing in that direction include the existence of spin glasses without disorder, and the general link between Mode-Coupling Theory (MCT) and the motion of a particle in a random potential. This link enables one to generalize the MCT equations for temperatures below the glass transition, and to describe aging effects. We compare these results with those obtained within more phonomonological ‘trap’ models.

Calculation of the thermodynamic quantities of perovskite metal organics DMAKCr and perovskite HyFe close to the weakly first-order relaxor-like structural transformation using the mean field theory

2019 ◽  
Vol 33 (11) ◽  
pp. 1950103 ◽  
Author(s):  
H. Yurtseven ◽  
Ö. Tarı
Keyword(s):  
Field Theory ◽  
Field Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Excess Heat Capacity ◽  
Mean Field Model ◽  
First Order ◽  
Entropy Formula ◽  
Inverse Susceptibility ◽  
The Mean

Weakly first-order or nearly second-order phase transitions occurring in metal–organic frameworks (MOFs), particularly in DMAKCr and perovskite HyFe, are studied under the mean field model by using the observed data from the literature. In this work, mainly thermal and magnetic properties among various physical properties which have been reported in the literature for those MOFs are studied by the mean field theory. By expanding the free energy in terms of the magnetization (order parameter), the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S), latent heat (L), magnetization (M) and the inverse susceptibility ([Formula: see text]) are calculated as a function of temperature close to the weakly first-order phase transition within the Landau phenomenological model which is fitted to the experimental data from the literature for C[Formula: see text] (DMAKCr and perovskite HyFe) and for magnetization M (HyFe). Our predictions of the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S) agree below T[Formula: see text] with the observed data within the temperature intervals studied for DMAKCr and perovskite HyFe. From our predictions, we find that magnetization decreases continuously whereas the inverse susceptibility decreases linearly with increasing temperature toward the transition temperature in those MOFs as expected for a weakly first-order transition from the mean field model.

A FIRST ORDER PHASE TRANSITION IN ISING FERRIMAGNETS

1995 ◽  
Vol 09 (21) ◽  
pp. 1347-1351 ◽  
Author(s):  
HASAN M. AL MUKADAM ◽  
DIMO I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
First Order ◽  
First Order Phase Transition ◽  
Exchange Constants ◽  
The Mean ◽  
First Order Phase ◽  
Ising Spins

The mean field theory is used for the analysis of a two-sublattice system of Ising spins, which describes ferro-, antiferro-, and ferrimagnetic orderings. It is proven that the phase transition in these systems is of a first order when the exchange constants of the sublattices are different. The free energy, the order parameter profiles and the latent heat of the phase transition are calculated for almost equivalent sublattices.

SURFACE ROTATIONAL DISORDERING IN CRYSTALLINE C60

1997 ◽  
Vol 04 (05) ◽  
pp. 859-861 ◽  
Author(s):  
D. PASSERONE ◽  
E. TOSATTI
Keyword(s):  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Rotational Transition ◽  
Layer By Layer ◽  
Energy Term ◽  
First Order ◽  
Potential Energy Term ◽  
Body Potential ◽  
Order Surface

We present a theory of surface rotational disordering of crystalline fullerene. Realistic intermolecular interactions are implemented, in a layer-by-layer mean field theory. The crucial new ingredient turns out to be a one-body potential energy term, or "crystal field," is totally different at the surface, therefore locally frustrating bulk order. This frustration causes a severe surface order parameter reduction, and a first order surface rotational disordering transition, well below the corresponding bulk one. Preliminary results are in agreement with recent experiments, confirming a first order surface rotational transition of C 60(111) at a transition temperature lower than the bulk one.

Notizen: Monte-Carlo Simulation of a Two-dimensional Dipolar Lattice

1977 ◽  
Vol 32 (11) ◽  
pp. 1320-1322 ◽  
Author(s):  
S. Romano
Keyword(s):  
Monte Carlo ◽  
Mean Field Theory ◽  
Mean Field ◽  
Square Lattice ◽  
Electrostatic Energy ◽  
Two Dimensional ◽  
First Order ◽  
First Order Phase Transition ◽  
The Mean ◽  
First Order Phase

Abstract Monte-Carlo calculations were carried out on a system consisting of 256 point-dipoles, whose centres are fixed in a two-dimensional square lattice with the usual boundary con­dition; the Epstein-Ewald-Kornfeld algorithm was used in evaluating the electrostatic energy. No evidence of a first-order phase transition was found, and the results suggest there might be a second-order one. Additional calculations were carrierd out using the mean-field theory, which was found to overestimate the transition temperature by about a factor two.

scholarly journals ORDER VIA NONLINEARITY IN RANDOMLY CONFINED BOSE GASES

2009 ◽  
Vol 19 (08) ◽  
pp. 2745-2753 ◽  
Author(s):  
ROBERT GRAHAM ◽  
AXEL PELSTER
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Particle Number Density ◽  
Ideal Gas ◽  
Einstein Condensation ◽  
Continuous Transition ◽  
Hartree Fock ◽  
Localized State ◽  
Bose Glass ◽  
Bose Einstein

A Hartree–Fock mean-field theory of a weakly interacting Bose-gas in a quenched white noise disorder potential is presented. A direct continuous transition from the normal gas to a localized Bose-glass phase is found which has localized short-lived excitations with a gapless density of states and vanishing superfluid density. The critical temperature of this transition is as for an ideal gas undergoing Bose–Einstein condensation. Increasing the particle-number density a first-order transition from the localized state to a superfluid phase perturbed by disorder is found. At intermediate number densities both phases can coexist.

scholarly journals Quantum Mechanics and Superconductivity in a Magnetic Field

1993 ◽  
Vol 46 (3) ◽  
pp. 333 ◽  
Author(s):  
AH MacDonald ◽  
Hiroshi Akera ◽  
MR Norman
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Magnetic Fields ◽  
Landau Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Point Of View ◽  
Ginzburg Landau ◽  
Accurate Picture ◽  
The Individual

The influence of a magnetic field on superconductivity is usually described either phenomenologically, using Ginzburg-Landau theory, or semiclassically, using Gor'kov theory. In this article we discuss the influence of magnetic fields on the mean-field theory of the superconducting instability from a completely quantum-mechanical point of view. The suppression of superconductivity by an external magnetic field is seen in this more physically accurate picture to be due to the impossibility, in quantum mechanics, of precisely specifying both the centre-of-mass state of a pair and the individual electron kinetic energies. We also discuss the possibility of novel aspects of superconductivity at extremely strong magnetic fields, where recent work has shown that the transition temperature may be enhanced rather than suppressed by a magnetic field and where a quantum treatment is essential.

THE A-C-A PHASE DIAGRAM OF MIXED LIQUID CRYSTALS: A PHOTON TRANSMISSION STUDY

2001 ◽  
Vol 15 (15) ◽  
pp. 2161-2167 ◽  
Author(s):  
HALUK ÖZBEK ◽  
SEVTAP YILDIZ ◽  
ÖNDER PEKCAN ◽  
A. NIHAT BERKER
Keyword(s):  
Phase Diagram ◽  
Mean Field Theory ◽  
Mean Field ◽  
Weight Percentage ◽  
First Order ◽  
Smectic A ◽  
Transmission Technique ◽  
Liquid Crystal System ◽  
Transmission Study ◽  
Visible Photon

Ultraviolet/visible photon transmission technique was applied to study the phase diagram of the BOPDOB-BOPOOB liquid crystal system. It was observed that the nematic-smectic A transition becomes first order, as the weight percentage of BOPDOB in the binary mixture is increased. The smectic A-C-A reentrance disappears when the BOPDOB percentage approaches 100 (pure BOPDOB). We also present the smectic A-C transition temperatures and the critical exponents β of the all samples. The values of the exponent are consistent with mean-field theory.

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