scholarly journals COUPLED GROWING NETWORKS

2003 ◽  
Vol 06 (04) ◽  
pp. 507-514 ◽  
Author(s):  
DAFANG ZHENG ◽  
GÜLER ERGÜN
Keyword(s):  
Strong Coupling ◽  
Weak Coupling ◽  
Citation Network ◽  
Power Laws ◽  
Coupling Case ◽  
Coupled Networks ◽  
Growing Networks ◽  
Sexual Contacts ◽  
Cross Links ◽  
The Web

We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in both networks. The model segregates the links in the networks as intra-links, cross-links and mix-links. The corresponding degree distributions of these links are found to be power-laws with exponents having coupled parameters for intra- and cross-links. In the weak coupling case, the model reduces to a simple citation network. As for the strong coupling, it mimics the mechanism of the web of human sexual contacts.

scholarly journals Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
X. Wei ◽  
M. F. Randrianandrasana ◽  
M. Ward ◽  
D. Lowe
Keyword(s):  
Strong Coupling ◽  
Internal Resonance ◽  
Weak Coupling ◽  
Response Pattern ◽  
Coupled System ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Periodically Driven ◽  
Coupling Case ◽  
The Stability

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

THE RELATION BETWEEN CHIRAL SYMMETRY SPONTANEOUSLY BREAKING AND CONFINEMENT IN QED

2001 ◽  
Vol 16 (12) ◽  
pp. 2253-2266
Author(s):  
KOU SU-PENG
Keyword(s):  
Strong Coupling ◽  
Chiral Symmetry ◽  
Dimensional Reduction ◽  
Weak Coupling ◽  
Coupling Phase ◽  
Fermion Pairs ◽  
Two Phases

In this paper, we use Parisi and Sourlas dimensional reduction to show that QED has two phases, the strong coupling phase and weak coupling phase. Because chiral symmetry is spontaneously broken, particles with fractional charges are confined in the strong coupling phase by the condensation of topological configurations, and particles with integer charges are screened by fermion pairs.

FUNCTIONAL INTEGRALS AND PHASE STRUCTURES IN SINE-GORDON–THIRRING MODEL

2012 ◽  
Vol 26 (27) ◽  
pp. 1250178 ◽  
Author(s):  
JUN YAN
Keyword(s):  
Strong Coupling ◽  
Finite Temperature ◽  
Thirring Model ◽  
Attractive Potential ◽  
Functional Integrals ◽  
One Dimensional ◽  
Phase Structures ◽  
Coexistence Phase ◽  
Coupling Case ◽  
The Stability

The phase structures of one-dimensional quantum sine-Gordon–Thirring model with N-impurities coupling are studied in this paper. The effective actions at finite temperature are derived by means of the perturbation and non-perturbation functional integrals method. The stability of coexistence phase is analyzed respectively in the weak and strong coupling case. It is shown that the coexistence phase is not stable when fermions have an attractive potential g < 0, and the stable coexistence phase can form when fermions have an exclude potential g > 0.

Localization of Vibration in Disordered Multi-Span Beams With Damping

1993 ◽  
Author(s):  
Djamel Bouzit ◽  
Christophe Pierre
Keyword(s):  
Weak Coupling ◽  
Normal Modes ◽  
Structural Damping ◽  
Coupling Case ◽  
Effects Of Disorder ◽  
Transfer Matrix Approach ◽  
Modes Of Vibration ◽  
Comparable Magnitude ◽  
Localization Of Vibration ◽  
Statistical Perturbation

Abstract The combined effects of disorder and structural damping on the dynamics of a multi-span beam with slight randomness in the spacing between supports are investigated. A wave transfer matrix approach is chosen to calculate the free and forced harmonic responses of this nearly periodic structure. It is shown that both harmonic waves and normal modes of vibration that extend throughout the ordered, undamped beam become spatially attenuated if either small damping or small disorder is present in the system. The physical mechanism which causes this attenuation, however, is one of energy dissipation in the case of damping but one of energy confinement in the case of disorder. The corresponding rates of spatial exponential decay are estimated by applying statistical perturbation methods. It is found that the effects of damping and disorder simply superpose for a multi-span beam with strong interspan coupling, but interact less trivially in the weak coupling case. Furthermore, the effect of disorder is found to be small relative to that of damping in the case of strong interspan coupling, but of comparable magnitude for weak coupling between spans. The adequacy of the statistical analysis to predict accurately localization in finite disordered beams with boundary conditions is also examined.

Weak Coupling Strategy for Multi-Physics CFD Simulation in Engineering Problems

2011 ◽  
Author(s):  
Makoto Yamamoto ◽  
Masaya Suzuki
Keyword(s):  
Strong Coupling ◽  
Time Scale ◽  
Weak Coupling ◽  
Particle Deposition ◽  
Cfd Simulation ◽  
The Other ◽  
Cfd Simulations ◽  
Sand Erosion ◽  
Coupling Strategy ◽  
The Difference

Multi-Physics CFD Simulation will be one of key technologies in various engineering fields. There are two strategies to simulate a multi-physics phenomenon. One is “Strong Coupling”, and the other is “Weak Coupling”. Each can be employed, based on time-scales of physics embedded in a problem. That is, when a time-scale of one physics is nearly same as that of the other physics, we have to use Strong Coupling to take into account the interaction between two physics. On the other hand, when one time-scale is quite different from the other one, Weak Coupling can be applied. Considering the present computer performance, Strong Coupling is difficult to be used in engineering design processes now. Therefore, we are focusing on Weak Coupling, and it has been applied to a number of multi-physics CFD simulations in engineering. We have successfully simulated sand erosion, ice accretion, particle deposition, electro-chemical machining and so on, with using Weak Coupling method. In the present study, the difference between strong and weak couplings is briefly described, and two examples of our multi-physics CFD simulations are expressed. The numerical results indicate that Weak Coupling strategy is promising in a lot of multi-physics CFD simulations.

scholarly journals RECIPROCITY AND THE EMERGENCE OF POWER LAWS IN SOCIAL NETWORKS

2006 ◽  
Vol 17 (07) ◽  
pp. 1067-1076 ◽  
Author(s):  
MICHAEL SCHNEGG
Keyword(s):  
Social Networks ◽  
Power Laws ◽  
Scaling Exponent ◽  
Policy Makers ◽  
Public Health Programs ◽  
Scale Free ◽  
The Past ◽  
Naturally Occurring ◽  
Growing Networks ◽  
Law Degree

Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.

scholarly journals Phases of a strongly coupled four-fermion theory

2018 ◽  
Vol 175 ◽  
pp. 03004 ◽  
Author(s):  
David Schaich ◽  
Simon Catterall
Keyword(s):  
Strong Coupling ◽  
Weak Coupling ◽  
Strongly Coupled ◽  
Coupling Phase ◽  
Long Range Correlations ◽  
Mass Gap ◽  
Narrow Region ◽  
Lattice Field ◽  
Lattice Symmetry ◽  
Lattice Fermion

We present ongoing investigations of a four-dimensional lattice field theory with four massless reduced staggered fermions coupled through an SU(4)-invariant fourfermion interaction. As in previous studies of four-fermion and Higgs–Yukawa models with different lattice fermion discretizations, we observe a strong-coupling phase in which the system develops a mass gap without breaking any lattice symmetry. This symmetric strong-coupling phase is separated from the symmetric weak-coupling phase by a narrow region of four-fermi coupling in which the system exhibits long-range correlations.

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