scholarly journals Diameter in ultra‐small scale‐free random graphs

2018 ◽  
Vol 54 (3) ◽  
pp. 444-498 ◽  
Author(s):  
Francesco Caravenna ◽  
Alessandro Garavaglia ◽  
Remco van der Hofstad
Keyword(s):  
Random Graphs ◽  
Small Scale ◽  
Scale Free

scholarly journals Robustness and Vulnerability of Scale-Free Random Graphs

2004 ◽  
Vol 1 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Béla Bollobás ◽  
Oliver Riordan
Keyword(s):  
Random Graphs ◽  
Scale Free

The Reform of Agricultural Marketing in China Since 1978

1988 ◽  
Vol 113 ◽  
pp. 1-28 ◽  
Author(s):  
Andrew Watson
Keyword(s):  
Agricultural Policy ◽  
Agricultural Production ◽  
Free Market ◽  
Economic Change ◽  
Small Scale ◽  
Free Markets ◽  
Agricultural Marketing ◽  
Scale Free ◽  
Household Level ◽  
Surplus Production

With the proclamation of Document 1, 1983, reform of marketing became one of the major targets of agricultural policy in China. This official emphasis on the need to liberalize the marketing system was, however, little more than a confirmation of a process which was already taking place. The initial reforms of labour management and prices in 1978 had led to a decentralization of economic authority to the household level. The commune system was in decline and the number of small-scale free markets was increasing rapidly as peasants took advantage of their new-found freedom to trade their surplus production as they wished. Responding to the economic stimulus offered by the new structure of prices and to the organizational flexibility offered by the decentralization of management, some households began to plan at least part of their production for sale on the market, there by initiating a process of specialization and commercialization. Once begun, this process fed backwards into production by encouraging further specialization and diversification and forwards into marketing by stimulating the emergence of longdistance trade carried out by specialist merchants and traders. In effect, the free market began to act as an engine of economic change, shaping both the structure of agricultural production and employment and the network of new economic linkages through the emerging hierarchy of market centres.

Galaxy clustering and the dark-matter problem

1986 ◽  
Vol 320 (1556) ◽  
pp. 517-541 ◽  
Keyword(s):  
Dark Matter ◽  
Cold Dark Matter ◽  
Density Fluctuations ◽  
Small Scale ◽  
Galactic Halos ◽  
Galaxy Clustering ◽  
Simple Assumption ◽  
Scale Free ◽  
The Galaxy ◽  
Flat Rotation Curves

Recent observational and theoretical results on galaxy clustering are reviewed. A major difficulty in relating observations to theory is that the former refer to luminous material whereas the latter is most directly concerned with the gravitationally dominant but invisible dark matter. The simple assumption that the distribution of galaxies generally follows that of the mass appears to conflict with evidence suggesting that galaxies of different kinds are clustered in different ways. If galaxies are indeed biased tracers of the mass, then dynamical estimates of the mean cosmic density, which give Ω « 0.2 may underestimate the global value of Ω. There are now several specific models for the behaviour of density fluctuations from very early times to the present epoch. The late phases of this evolution need to be followed by N -body techniques; simulations of scale-free universes and of universes dominated by various types of elementary particles are discussed. In the former case, the models evolve in a self-similar way; the resulting correlations have a steeper slope than that oberved for the galaxy distribution unless the primordial power spectral index n « 2. Universes dominated by light neutrinos acquire a large coherence length at early times. As a result, an early filamentary phase develops into a present day distribution that is more strongly clustered than observed galaxies and is dominated by a few clumps with masses larger than those of any known object. If the dark matter consists of ‘cold’ particles such as photinos or axions, then structure builds up from subgalactic scales in a roughly hierarchical way. The observed pattern of galaxy clustering can be reproduced if either Ω « 0.2 and the galaxies are distributed as the mass, or if Ω — 1, H 0 = 50 km s -1 Mpc -1 and the galaxies form only at high peaks of the smoothed linear density field. The open model, however, is marginally ruled out by the observed small-scale isotropy of the microwave background, whereas the flat one is consistent with such observations. With no further free parameters a flat cold dark-matter universe produces the correct abundance of rich galaxy clusters and of galactic halos; the latter have flat rotation curves with amplitudes spanning the observed range. Preliminary calculations indicate that the properties of voids may be consistent with the data, but the correlations of rich clusters appear to be somewhat weaker than those reported for Abell clusters.

scholarly journals Optimal shattering of complex networks

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Nicole Balashov ◽  
Reuven Cohen ◽  
Avieli Haber ◽  
Michael Krivelevich ◽  
Simi Haber
Keyword(s):  
Complex Networks ◽  
Random Graphs ◽  
Polynomial Time ◽  
Optimal Performance ◽  
Regular Graphs ◽  
Scale Free ◽  
Scale Free Networks ◽  
Minimum Number

Abstract We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size.We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality.Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

scholarly journals Scale-free network clustering in hyperbolic and other random graphs

2019 ◽  
Vol 52 (29) ◽  
pp. 295101 ◽  
Author(s):  
Clara Stegehuis ◽  
Remco van der Hofstad ◽  
Johan S H van Leeuwaarden
Keyword(s):  
Random Graphs ◽  
Network Clustering ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

scholarly journals Extreme cavity expansion in soft solids: Damage without fracture

2020 ◽  
Vol 6 (13) ◽  
pp. eaaz0418 ◽  
Author(s):  
Jin Young Kim ◽  
Zezhou Liu ◽  
Byung Mook Weon ◽  
Tal Cohen ◽  
Chung-Yuen Hui ◽  
...  
Keyword(s):  
Phase Separation ◽  
Brittle Materials ◽  
Damage Mechanism ◽  
Cavity Expansion ◽  
Small Scale ◽  
Elastic Solids ◽  
Ductile Metals ◽  
Scale Free ◽  
Soft Solids ◽  
Bond Breakage

Cavitation is a common damage mechanism in soft solids. Here, we study this using a phase separation technique in stretched, elastic solids to controllably nucleate and grow small cavities by several orders of magnitude. The ability to make stable cavities of different sizes, as well as the huge range of accessible strains, allows us to systematically study the early stages of cavity expansion. Cavities grow in a scale-free manner, accompanied by irreversible bond breakage that is distributed around the growing cavity rather than being localized to a crack tip. Furthermore, cavities appear to grow at constant driving pressure. This has strong analogies with the plasticity that occurs surrounding a growing void in ductile metals. In particular, we find that, although elastomers are normally considered as brittle materials, small-scale cavity expansion is more like a ductile process. Our results have broad implications for understanding and controlling failure in soft solids.

scholarly journals Unimodular lattice triangulations as small-world and scale-free random graphs

2015 ◽  
Vol 17 (2) ◽  
pp. 023013 ◽  
Author(s):  
B Krüger ◽  
E M Schmidt ◽  
K Mecke
Keyword(s):  
Random Graphs ◽  
Small World ◽  
Unimodular Lattice ◽  
Scale Free

Some Effects of Upstream Turbulence on the Unsteady Lift Forces Imposed on Prismatic Two Dimensional Bodies

1984 ◽  
Vol 106 (4) ◽  
pp. 418-424 ◽  
Author(s):  
I. S. Gartshore
Keyword(s):  
Small Scale ◽  
Resonant Amplitude ◽  
Scale Free ◽  
Free Stream Turbulence ◽  
Subsequent Decrease ◽  
Scale Turbulence ◽  
Oncoming Stream ◽  
Rms Amplitude ◽  
Stream Direction ◽  
Unsteady Lift

Measurements of fluctuating lift are reported from four fixed rectangular prisms and a fixed circular cylinder, for various intensities of turbulence in the oncoming stream. Variations of unsteady lift with intensity of small scale turbulence are similar to present (and previous) measured variations of mean drag or base pressure. Reasons are suggested for these trends. Observations are also reported of the maximum (resonant) RMS amplitude of two cylinders, one square and the other circular in cross section, free to move in the cross stream direction. Small scale free stream turbulence provided by the wake of a small upstream rod increased the resonant amplitude of motion in both cases, the greater increase (and subsequent decrease) occurring for the square section. Two possible explanations for these observations are advanced.

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