We have thus a new D-finite function with integer coefficients and irrational critical exponent
(involving the golden ratio [phi]), but this is not contradicting the G-function theorem, because, due to the multiplication by n
Topics covered include Potts models, dynamic complexity of renormalization transformations, the connectivity of Julia sets, Jordan domains, Fatou components and the critical exponent
of free energy.
Several researchers (6), (31) have studied the critical exponent
(t) values of different polymer nanocomposites systems.
Aloson, Multiplicity of solutions for elliptic problems with critical exponent
or with a nonsymmetric term, Trans.
c]/N is called the critical exponent
(loosely speaking, [alpha] is the "first non zero exponent" appearing in the series, and if [z.
Rocha, Four solutions of an inhomogeneous elliptic equation with critical exponent
and singular term, Nonlinear Anal.
The critical exponent
depends on the dimensionality of the structure and is predicted as [iota] = 2 for a 3-dimensional network (20), (66), (67).
where a, h, f and g are smooth functions on M , N = 2n/n-4 is the critical exponent
, 2 < q < N a real number, [lambda] > 0 a real parameter and [epsilon] > 0 any small real number.
2cr] are the critical volume fractions (the percolation thresholds) at which the components become partially continuous and q is the critical exponent
p] is the loss tangent of the polymer matrix and r = t- 2q is a critical exponent
can be used to describe the viscosity as a function of temperature and extent of reaction by using a temperature and conversion dependent critical exponent
Objective: A paradigm example of precise predictions in complex systems is the universal scaling of correlation functions close to phase transitions, with their associated critical exponents