Scaling Laws for Transport, Mechanical and Fracture Properties of Disordered Materials

1990 ◽  
Vol 207 ◽  
Author(s):  
Muhammad Sahimi ◽  
Sepehr Arbabi
Keyword(s):  
Percolation Threshold ◽  
Transport Properties ◽  
Elastic Moduli ◽  
Scaling Laws ◽  
Gumbel Distribution ◽  
Disordered Materials ◽  
Universal Scaling ◽  
Macroscopic Fracture ◽  
Vector Transport ◽  
Fracture Processes

AbstractWe discuss scaling laws for scalar and vector transport properties of, and fracture processes in, disordered materials. Random resistor networks, and elastic and superelastic percolation networks are used to model the disordered material. While scalar transport properties of such systems (e.g. conductivity or diffusivity) obey universal scaling laws near the percolation threshold, vector transport properties (e.g. elastic moduli) may not follow such universal laws, and the critical exponents characterizing such scaling laws may depend on the microscopic force laws of the system. On the other hand, fracture processes in such systems appear to obey universal scaling laws. In particular, the external stress F for the fracture of the system scales with its linear size L as F ˜ Ld-1/(ln L)ψ, where d is the dimensionality of the system and ψ is a small critical exponent (ψ ≃ 0.1). Moreover, as the macroscopic fracture point of the system is approached, the ratio of various elastic moduli of the system approaches a universal fixed point, independent of the microscopic details of the system. Finally, the distribution of fracture strength in a randomly reinforced system, or in a system near its percolation threshold with a broad distribution of elastic constants, is in the form of a Weibull distribution, rather than the recently-proposed Gumbel distribution.

Universal scaling laws and the QCD scale anomaly

1994 ◽  
Vol 242 (4-6) ◽  
pp. 355-361
Author(s):  
Georges Ripka ◽  
Martine Jaminon
Keyword(s):  
Scaling Laws ◽  
Universal Scaling

Universal scaling laws of transients

2002 ◽  
Vol 47 (3) ◽  
pp. 181-183 ◽  
Author(s):  
A. A. Koronovskii ◽  
D. I. Trubetskov ◽  
A. E. Khramov ◽  
A. E. Khramova
Keyword(s):  
Scaling Laws ◽  
Universal Scaling

Transport Phenomena and Properties in Treelike Networks

2016 ◽  
Vol 68 (4) ◽  
Author(s):  
Peng Xu ◽  
Agus Pulung Sasmito ◽  
Boming Yu ◽  
Arun Sadashiv Mujumdar
Keyword(s):  
Transport Properties ◽  
Scaling Laws ◽  
Transport Phenomena ◽  
Transport Processes ◽  
Research Progress ◽  
Transport Systems ◽  
Transport Mechanisms ◽  
Branching Structures ◽  
Flow And Heat Transfer ◽  
Flow Heat

Treelike structures abound in natural as well as man-made transport systems, which have fascinated multidisciplinary researchers to study the transport phenomena and properties and understand the transport mechanisms of treelike structures for decades. The fluid flow and heat transfer in treelike networks have received an increasing attention over the past decade as the highly efficient transport processes observed in natural treelike structures can provide useful hints for optimal solutions to many engineering and industrial problems. This review paper attempts to present the background and research progress made in recent years on the transport phenomenon in treelike networks as well as technological applications of treelike structures. The subtopics included are optimization of branching structures, scaling laws of treelike networks, and transport properties for laminar flow, turbulent flow, heat conduction, and heat convection in treelike networks. Analytical expressions for the effective transport properties have been derived based on deterministic treelike networks, and the effect of branching parameters on the transport properties of treelike networks has also been discussed. Furthermore, numerical simulation results for treelike microchannel networks are presented as well. The proposed transport properties may be beneficial to understand the transport mechanisms of branching structures and promote the applications of treelike networks in engineering and industry.

scholarly journals Universal scaling across biochemical networks on Earth

2019 ◽  
Vol 5 (1) ◽  
pp. eaau0149 ◽  
Author(s):  
Hyunju Kim ◽  
Harrison B. Smith ◽  
Cole Mathis ◽  
Jason Raymond ◽  
Sara I. Walker
Keyword(s):  
Scaling Laws ◽  
Network Size ◽  
Biochemical Networks ◽  
Biochemical Network ◽  
Reaction Networks ◽  
Biochemical Reaction Networks ◽  
Global Database ◽  
Universal Scaling ◽  
Planetary Scale ◽  
Domains Of Life

The application of network science to biology has advanced our understanding of the metabolism of individual organisms and the organization of ecosystems but has scarcely been applied to life at a planetary scale. To characterize planetary-scale biochemistry, we constructed biochemical networks using a global database of 28,146 annotated genomes and metagenomes and 8658 cataloged biochemical reactions. We uncover scaling laws governing biochemical diversity and network structure shared across levels of organization from individuals to ecosystems, to the biosphere as a whole. Comparing real biochemical reaction networks to random reaction networks reveals that the observed biological scaling is not a product of chemistry alone but instead emerges due to the particular structure of selected reactions commonly participating in living processes. We show that the topology of biochemical networks for the three domains of life is quantitatively distinguishable, with >80% accuracy in predicting evolutionary domain based on biochemical network size and average topology. Together, our results point to a deeper level of organization in biochemical networks than what has been understood so far.

scholarly journals Ambiguity in language networks

2015 ◽  
Vol 32 (1) ◽  
Author(s):  
Ricard V. Solé ◽  
Luís F. Seoane
Keyword(s):  
Language Processing ◽  
Network Architecture ◽  
Essential Role ◽  
Scaling Laws ◽  
Network Growth ◽  
Computational Approaches ◽  
Universal Scaling ◽  
Different Levels ◽  
Relevant Component ◽  
Language Network

AbstractHuman language defines the most complex outcomes of evolution. The emergence of such an elaborated form of communication allowed humans to create extremely structured societies and manage symbols at different levels including, among others, semantics. All linguistic levels have to deal with an astronomic combinatorial potential that stems from the recursive nature of languages. This recursiveness is indeed a key defining trait. However, not all words are equally combined nor frequent. In breaking the symmetry between less and more often used and between less and more meaning-bearing units, universal scaling laws arise. Such laws, common to all human languages, appear on different stages from word inventories to networks of interacting words. Among these seemingly universal traits exhibited by language networks, ambiguity appears to be a specially relevant component. Ambiguity is avoided in most computational approaches to language processing, and yet it seems to be a crucial element of language architecture. Here we review the evidence both from language network architecture and from theoretical reasonings based on a least effort argument. Ambiguity is shown to play an essential role in providing a source of language efficiency, and is likely to be an inevitable byproduct of network growth.

Magneto-transport properties of CoFe-Al2O3 granular films in the vicinity of the percolation threshold

2002 ◽  
Vol 242-245 ◽  
pp. 476-478 ◽  
Author(s):  
A.Ya. Vovk ◽  
J.Q. Wang ◽  
A.M. Pogoriliy ◽  
O.V. Shypil’ ◽  
A.F. Kravets
Keyword(s):  
Percolation Threshold ◽  
Transport Properties ◽  
Granular Films
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