scholarly journals First-order synchronization transition in a large population of strongly coupled relaxation oscillators

2020 ◽  
Vol 6 (39) ◽  
pp. eabb2637
Author(s):  
Dumitru Călugăru ◽  
Jan Frederik Totz ◽  
Erik A. Martens ◽  
Harald Engel
Keyword(s):  
Large Population ◽  
Network Connectivity ◽  
Emergent Behavior ◽  
Power Grids ◽  
Continuous Transition ◽  
Strongly Coupled ◽  
First Order ◽  
Synchronization Transition ◽  
Relaxation Oscillators ◽  
Reduction Techniques

Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed to the paradigmatic continuous transition expected from the widely used weak coupling theory. The resulting first-order transition is robust with respect to changes in network connectivity and natural frequency distribution. This allows us to identify the relaxation character of the oscillators as the essential parameter that determines the nature of the synchronization transition. We further support this hypothesis by revealing the mechanism of the transition, which cannot be accounted for by standard phase reduction techniques.

scholarly journals Bubble wall velocity at strong coupling

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Francesco Bigazzi ◽  
Alessio Caddeo ◽  
Tommaso Canneti ◽  
Aldo L. Cotrone
Keyword(s):  
Phase Transitions ◽  
Steady State ◽  
Friction Force ◽  
Bubble Velocity ◽  
Strongly Coupled ◽  
First Order ◽  
Black Hole Background ◽  
Different Dimensions ◽  
Holographic Description ◽  
First Order Phase

Abstract Using the holographic correspondence as a tool, we determine the steady-state velocity of expanding vacuum bubbles nucleated within chiral finite temperature first-order phase transitions occurring in strongly coupled large N QCD-like models. We provide general formulae for the friction force exerted by the plasma on the bubbles and for the steady-state velocity. In the top-down holographic description, the phase transitions are related to changes in the embedding of $$ Dq\hbox{-} \overline{D}q $$ Dq ‐ D ¯ q flavor branes probing the black hole background sourced by a stack of N Dp-branes. We first consider the Witten-Sakai-Sugimoto $$ D4\hbox{-} D8\hbox{-} \overline{D}8 $$ D 4 ‐ D 8 ‐ D ¯ 8 setup, compute the friction force and deduce the equilibrium velocity. Then we extend our analysis to more general setups and to different dimensions. Finally, we briefly compare our results, obtained within a fully non-perturbative framework, to other estimates of the bubble velocity in the literature.

TERBIUM MOLYBDATE: GROUP THEORY AND FLUCTUATIONS

1987 ◽  
Vol 01 (05n06) ◽  
pp. 239-244
Author(s):  
SERGE GALAM
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Parameter Space ◽  
Landau Theory ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Theory Analysis ◽  
Continuous Transition ◽  
Dimensional Parameter ◽  
First Order

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

Article

1999 ◽  
Vol 77 (11) ◽  
pp. 1810-1812 ◽  
Author(s):  
Alex D Bain
Keyword(s):  
Spin System ◽  
Coupled System ◽  
Coupled Systems ◽  
Physical Reason ◽  
Strongly Coupled ◽  
System Combination ◽  
First Order ◽  
Weakly Coupled ◽  
Quantum Transitions ◽  
Weakly Coupled Systems

Strongly coupled spin systems provide many curious and interesting effects in NMR spectra, one of which is the presence of unexpected (from a first-order viewpoint) lines. A physical reason is given for the presence of these combination lines. The X part of the spectrum of an ABX spin system is analysed as an example. For an ABX system, it is well known that the AB nuclei give a spectrum consisting of two AB-type spectra, corresponding to the two orientations of the X nucleus. It can also be shown that the X part of the spectrum corresponds to the X nucleus undergoing a transition in the presence of an AB-like spin system. For weakly coupled systems, the four observed lines correspond to the four different orientations of the A and B nuclei. For a strongly coupled system, two additional lines may appear, the combination lines. The resulting six lines correspond to the four spin orientations, plus the two zero-quantum transitions. It is shown that these six lines are such that there is no net excitation of the AB-like spin system associated with the X transitions. There is no AB coherence created directly by a pulse applied to X. AB coherence is created as the system evolves, and this is responsible for many of the curious effects. This is shown to be true for all spin sub-systems, which are weakly coupled to a strongly coupled sub-system.Key words: NMR, strong coupling, second-order spectra, ABX spin system, combination lines, spectral analysis.

scholarly journals Identifying critical higher-order interactions in complex networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mehmet Emin Aktas ◽  
Thu Nguyen ◽  
Sidra Jawaid ◽  
Rakin Riza ◽  
Esra Akbas
Keyword(s):  
Complex Networks ◽  
Higher Order ◽  
Power Grids ◽  
Giant Component ◽  
Centrality Measures ◽  
First Order ◽  
Pairwise Interactions ◽  
Size Of Giant Component ◽  
Novel Method ◽  
Structure And Functions

AbstractDiffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids. The critical interactions in networks play critical roles in diffusion and primarily affect network structure and functions. While interactions can occur between two nodes as pairwise interactions, i.e., edges, they can also occur between three or more nodes, which are described as higher-order interactions. This report presents a novel method to identify critical higher-order interactions in complex networks. We propose two new Laplacians to generalize standard graph centrality measures for higher-order interactions. We then compare the performances of the generalized centrality measures using the size of giant component and the Susceptible-Infected-Recovered (SIR) simulation model to show the effectiveness of using higher-order interactions. We further compare them with the first-order interactions (i.e., edges). Experimental results suggest that higher-order interactions play more critical roles than edges based on both the size of giant component and SIR, and the proposed methods are promising in identifying critical higher-order interactions.

Emergent Behavior in a Population of Thermostatically Controlled Loads With Peer-to-Peer Communication

2019 ◽  
Author(s):  
Ryan Schwartz ◽  
John F. Gardner
Keyword(s):  
Demand Response ◽  
Air Conditioning ◽  
Large Scale ◽  
Large Population ◽  
Agent Based Modeling ◽  
Emergent Behavior ◽  
Peer Communication ◽  
Agent Based ◽  
Thermostatically Controlled Loads ◽  
Residential Air Conditioning

Abstract Thermostatically controlled loads (TCLs) are often considered as a possible resource for demand response (DR) events. However, it is well understood that coordinated control of a large population of previously un-coordinated TCLs may result in load synchronization that results in higher peaks and large uncontrolled swings in aggregate load. In this paper we use agent based modeling to simulate a number of residential air conditioning loads and allow each to communicate a limited amount of information with their nearest neighbors. As a result, we document emergent behavior of this large scale, distributed and nonlinear system. Using the techniques described here, the population of TCLs experienced up to a 30% reduction in peak demand following the DR event. This behavior is shown to be beneficial to the goals of balancing the grid and integrating increasing penetration of variable generators.

scholarly journals Do Brain Oscillations Orchestrate Memory?

2018 ◽  
Vol 4 (1) ◽  
pp. 16-33 ◽  
Author(s):  
Wenhan Luo ◽  
Ji-Song Guan
Keyword(s):  
Brain Activity ◽  
Large Population ◽  
Rhythmic Activity ◽  
Brain Oscillations ◽  
Strongly Coupled ◽  
Specific Memory ◽  
State Dependent ◽  
Neural Communication ◽  
The Brain ◽  
Oscillatory Waves

Rhythmicity and oscillations are common features in nature, and can be seen in phenomena such as seasons, breathing, and brain activity. Despite the fact that a single neuron transmits its activity to its neighbor through a transient pulse, rhythmic activity emerges from large population-wide activity in the brain, and such rhythms are strongly coupled with the state and cognitive functions of the brain. However, it is still debated whether the oscillations of brain activity actually carry information. Here, we briefly introduce the biological findings of brain oscillations, and summarize the recent progress in understanding how oscillations mediate brain function. Finally, we examine the possible relationship between brain cognitive function and oscillation, focusing on how oscillation is related to memory, particularly with respect to state-dependent memory formation and memory retrieval under specific brain waves. We propose that oscillatory waves in the neocortex contribute to the synchronization and activation of specific memory trace ensembles in the neocortex by promoting long-range neural communication.

scholarly journals Universal behavior of cascading failures in interdependent networks

2019 ◽  
Vol 116 (45) ◽  
pp. 22452-22457 ◽  
Author(s):  
Dongli Duan ◽  
Changchun Lv ◽  
Shubin Si ◽  
Zhen Wang ◽  
Daqing Li ◽  
...  
Keyword(s):  
Real World ◽  
Order Type ◽  
Networked Systems ◽  
Power Grids ◽  
Cascading Failures ◽  
World Systems ◽  
Epidemic Spreading ◽  
Systematic Analysis ◽  
First Order ◽  
Regulatory Dynamics

Catastrophic and major disasters in real-world systems, such as blackouts in power grids or global failures in critical infrastructures, are often triggered by minor events which originate a cascading failure in interdependent graphs. We present here a self-consistent theory enabling the systematic analysis of cascading failures in such networks and encompassing a broad range of dynamical systems, from epidemic spreading, to birth–death processes, to biochemical and regulatory dynamics. We offer testable predictions on breakdown scenarios, and, in particular, we unveil the conditions under which the percolation transition is of the first-order or the second-order type, as well as prove that accounting for dynamics in the nodes always accelerates the cascading process. Besides applying directly to relevant real-world situations, our results give practical hints on how to engineer more robust networked systems.

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