SCALING OF FLOW DISTANCE IN RANDOM SELF-SIMILAR CHANNEL NETWORKS

Fractals ◽  
2005 ◽  
Vol 13 (04) ◽  
pp. 265-282 ◽  
Author(s):  
BRENT M. TROUTMAN
Keyword(s):  
Drainage Basin ◽  
Empirical Studies ◽  
Rooted Tree ◽  
Network Size ◽  
Channel Networks ◽  
Tree Graphs ◽  
Affine Structures ◽  
Self Similar ◽  
Function Number ◽  
Behavior Characteristic

Natural river channel networks have been shown in empirical studies to exhibit power-law scaling behavior characteristic of self-similar and self-affine structures. Of particular interest is to describe how the distribution of distance to the outlet changes as a function of network size. In this paper, networks are modeled as random self-similar rooted tree graphs and scaling of distance to the root is studied using methods in stochastic branching theory. In particular, the asymptotic expectation of the width function (number of nodes as a function of distance to the outlet) is derived under conditions on the replacement generators. It is demonstrated further that the branching number describing rate of growth of node distance to the outlet is identical to the length ratio under a Horton-Strahler ordering scheme as order gets large, again under certain restrictions on the generators. These results are discussed in relation to drainage basin allometry and an application to an actual drainage network is presented.

scholarly journals Crossover from Self-Similar to Self-Affine Structures in Percolation

1994 ◽  
Vol 26 (6) ◽  
pp. 413-418 ◽  
Author(s):  
E Frey ◽  
U. C Täuber ◽  
F Schwabl
Keyword(s):  
Affine Structures ◽  
Self Similar

Optimal Flow Control and Single Split Architecture Exploration for Fluid-Based Thermal Management

2018 ◽  
Author(s):  
Satya R. T. Peddada ◽  
Daniel R. Herber ◽  
Herschel C. Pangborn ◽  
Andrew G. Alleyne ◽  
James T. Allison
Keyword(s):  
Flow Control ◽  
Thermal Management ◽  
High Performance ◽  
Dynamic Models ◽  
Cooling System ◽  
Rooted Tree ◽  
Modeling Framework ◽  
System Architectures ◽  
Tree Graphs ◽  
Heat Loads

High-performance cooling is often necessary for thermal management of high power density systems. Both human intuition and vast experience may not be adequate to identify optimal thermal management designs as systems increase in size and complexity. This paper presents a design framework supporting comprehensive exploration of a class of single phase fluid-based cooling architectures. The candidate cooling system architectures are represented using labeled rooted tree graphs. Dynamic models are automatically generated from these trees using a graph-based thermal modeling framework. Optimal performance is determined by solving an appropriate fluid flow control problem, handling temperature constraints in the presence of exogenous heat loads. Rigorous case studies are performed in simulation, with components having variable sets of heat loads and temperature constraints. Results include optimization of thermal endurance for an enumerated set of 4,051 architectures. In addition, cooling system architectures capable of steady-state operation under a given loading are identified.

scholarly journals FINITE SELF-SIMILAR p-GROUPS WITH ABELIAN FIRST LEVEL STABILIZERS

2011 ◽  
Vol 21 (01n02) ◽  
pp. 355-364 ◽  
Author(s):  
ZORAN ŠUNIĆ
Keyword(s):  
Cyclic Group ◽  
Abelian Subgroup ◽  
Rooted Tree ◽  
Split Extension ◽  
Similar Action ◽  
Self Similar

We determine all finite p-groups that admit a faithful, self-similar action on the p-ary rooted tree such that the first level stabilizer is abelian. A group is in this class if and only if it is a split extension of an elementary abelian p-group by a cyclic group of order p. The proof is based on use of virtual endomorphisms. In this context the result says that if G is a finite p-group with abelian subgroup H of index p, then there exists a virtual endomorphism of G with trivial core and domain H if and only if G is a split extension of H and H is an elementary abelian p-group.

scholarly journals Structure of sexual networks determines the operation of sexual selection

2017 ◽  
Vol 115 (1) ◽  
pp. E53-E61 ◽  
Author(s):  
Grant C. McDonald ◽  
Tommaso Pizzari
Keyword(s):  
Sexual Selection ◽  
Mating Success ◽  
Empirical Studies ◽  
Evolutionary Process ◽  
Population Level ◽  
Network Size ◽  
Male Mating ◽  
Male Mating Success ◽  
Sexual Network ◽  
Bateman Gradient

Sexual selection is a fundamental evolutionary process but remains debated, particularly in the complexity of polyandrous populations where females mate with multiple males. This lack of resolution is partly because studies have largely ignored the structure of the sexual network, that is, the pattern of mate sharing. Here, we quantify what we call mating assortment with network analysis to specify explicitly the indirect as well as direct relationships between partners. We first review empirical studies, showing that mating assortment varies considerably in nature, due largely to basic properties of the sexual network (size and density) and partly to nonrandom patterns of mate sharing. We then use simulations to show how variation in mating assortment interacts with population-level polyandry to determine the strength of sexual selection on males. Controlling for average polyandry, positive mating assortment, arising when more polygynous males tend to mate with more polyandrous females, drastically decreases the intensity of precopulatory sexual selection on male mating success (Bateman gradient) and the covariance between male mating success and postcopulatory paternity share. Average polyandry independently weakened some measures of sexual selection and crucially also impacted sexual selection indirectly by constraining mating assortment through the saturation of the mating network. Mating assortment therefore represents a key—albeit overlooked—modulator of the strength of sexual selection. Our results show that jointly considering sexual network structure and average polyandry more precisely describes the strength of sexual selection.

Are channel networks statistically self-similar?

Geology ◽  
1997 ◽  
Vol 25 (12) ◽  
pp. 1063 ◽  
Author(s):  
Anicet A. Beauvais ◽  
David R. Montgomery
Keyword(s):  
Channel Networks ◽  
Self Similar

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.

scholarly journals A multilevel path analysis of social networks and social interaction in the neighbourhood

REGION ◽  
2015 ◽  
Vol 2 (1) ◽  
pp. 55 ◽  
Author(s):  
Pauline Van den Berg ◽  
Harry Timmermans
Keyword(s):  
Social Network ◽  
Path Analysis ◽  
Social Interactions ◽  
Urban Areas ◽  
Empirical Studies ◽  
Network Size ◽  
Household Composition ◽  
Network Ties ◽  
Social Network Size ◽  
Neighbourhood Characteristics

The topic of neighbourhood-based social interactions has gained attention in the last decades in the light of urban policies that aim to deal with problems regarding social segregation and exclusion, quality of life and liveability in urban areas. Social interactions are expected to play an important role in dealing with these problems. However, empirical studies investigating to which extent neighbourhood characteristics can improve social contacts among residents are scarce and inconclusive. Therefore, this paper studies the role of socio-demographics and neighbourhood characteristics in the formation of social network ties and social interactions with neighbours. Based on data collected in 2011 in 70 different neighbourhoods of Eindhoven in the Netherlands in a survey among 751 respondents these relationships are analysed using a multi-level path analysis approach. The results indicate that neighbourhood-based contacts are influenced by personal and household characteristics, such as education, income, work status, ethnicity, household composition, and years at the current address. Neighbourhood characteristics are not found to affect social network size, the share of neighbours in the network or the frequency of interaction with neighbours.

scholarly journals ON FINITE GENERATION OF SELF-SIMILAR GROUPS OF FINITE TYPE

2013 ◽  
Vol 23 (01) ◽  
pp. 69-79 ◽  
Author(s):  
IEVGEN V. BONDARENKO ◽  
IGOR O. SAMOILOVYCH
Keyword(s):  
Finite Group ◽  
Finite Type ◽  
Rooted Tree ◽  
Profinite Group ◽  
Similar Group ◽  
Finitely Generated ◽  
Finite Generation ◽  
Binary Alphabet ◽  
Self Similar

A self-similar group of finite type is the profinite group of all automorphisms of a regular rooted tree that locally around every vertex act as elements of a given finite group of allowed actions. We provide criteria for determining when a self-similar group of finite type is finite, level-transitive, or topologically finitely generated. Using these criteria and GAP computations we show that for the binary alphabet there is no infinite topologically finitely generated self-similar group given by patterns of depth 3, and there are 32 such groups for depth 4.

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