Hierarchical and Self-Similar Growth of Self-Assembled Crystals

2003 ◽  
Vol 42 (4) ◽  
pp. 413-417 ◽  
Author(s):  
Zhengrong R. Tian ◽  
Jun Liu ◽  
James A. Voigt ◽  
Bonnie Mckenzie ◽  
Huifang Xu
Keyword(s):  
Self Similar ◽  
Self Assembled ◽  
Similar Growth

scholarly journals A Population Study of Faint Compact Steep Spectrum Radio Sources: Self-Similar Growth

2003 ◽  
Vol 20 (1) ◽  
pp. 75-78 ◽  
Author(s):  
Wolfgang Tschager ◽  
Richard Schilizzi ◽  
Huub Röttgering ◽  
Ignas Snellen ◽  
George Miley ◽  
...  
Keyword(s):  
Population Study ◽  
Growth Process ◽  
Radio Galaxies ◽  
Radio Sources ◽  
Self Similarity ◽  
Spectrum Radio ◽  
Wide Range ◽  
Self Similar ◽  
Similar Growth ◽  
Intrinsic Characteristic

AbstractThe main topic of this contribution is the investigation of the morphological self-similarity of the growth process during the gigahertz peaked spectrum (GPS) and compact steep spectrum (CSS) phase of evolving radio galaxies. By investigating a new sample of faint CSS radio sources we establish that self-similar evolution must hold for peaked spectrum sources over a wide range of luminosities as well as physical sizes. Thus, we argue that self-similarity should be regarded as an essential, intrinsic characteristic of the growth process of young radio sources, and be treated as such, and not merely as a supplementary constraint for evolution models.

scholarly journals Scaling up real networks by geometric branching growth

2021 ◽  
Vol 118 (21) ◽  
pp. e2018994118
Author(s):  
Muhua Zheng ◽  
Guillermo García-Pérez ◽  
Marián Boguñá ◽  
M. Ángeles Serrano
Keyword(s):  
Finite Size ◽  
Citation Network ◽  
Network Size ◽  
Link Failures ◽  
Practical Applications ◽  
Best Response ◽  
Sequential Addition ◽  
Self Similar ◽  
Similar Growth ◽  
Fundamental Units

Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or species. Here, we provide empirical evidence for self-similar growth of network structure in the evolution of real systems—the journal-citation network and the world trade web—and present the geometric branching growth model, which predicts this evolution and explains the symmetries observed. The model produces multiscale unfolding of a network in a sequence of scaled-up replicas preserving network features, including clustering and community structure, at all scales. Practical applications in real instances include the tuning of network size for best response to external influence and finite-size scaling to assess critical behavior under random link failures.

Sign in / Sign up

Export Citation Format

Share Document