Universal scaling behavior of polymer chains at the percolation threshold

Soft Matter ◽  
2018 ◽  
Vol 14 (41) ◽  
pp. 8249-8252 ◽  
Author(s):  
Piotr Polanowski ◽  
Andrzej Sikorski
Keyword(s):  
Percolation Threshold ◽  
Scaling Behavior ◽  
Polymer Chains ◽  
Universal Scaling

A universal scaling behavior of chain size at the percolation threshold is presented.

Universal scaling behavior of entropy and conductivity in ionic liquids

2020 ◽  
Vol 316 ◽  
pp. 113824 ◽  
Author(s):  
S. Cheng ◽  
M. Musiał ◽  
Z. Wojnarowska ◽  
K.L. Ngai ◽  
J. Jacquemin ◽  
...  
Keyword(s):  
Ionic Liquids ◽  
Scaling Behavior ◽  
Universal Scaling

Universal Scaling Behavior of Dielectric Dispersion and Its Breakdown in Glycerol, Propyleneglycol and Trimethyleneglycol

1994 ◽  
Vol 63 (11) ◽  
pp. 4200-4205 ◽  
Author(s):  
Ryuji Abe ◽  
Masakiyo Horioka ◽  
Izumi Sakumiya ◽  
Satoshi Nakamura
Keyword(s):  
Dielectric Dispersion ◽  
Scaling Behavior ◽  
Universal Scaling

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 behavior under pressure in the heavy-fermion antiferromagnet CeRh2Si2 : Si29 NMR study

2021 ◽  
Vol 103 (8) ◽  
Author(s):  
H. Sakai ◽  
Y. Matsumoto ◽  
Y. Haga ◽  
Y. Tokunaga ◽  
S. Kambe
Keyword(s):  
Heavy Fermion ◽  
Scaling Behavior ◽  
Universal Scaling ◽  
Nmr Study
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