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.

c] symbolizes for the percolation threshold, depends on the lattice in which particles are accommodated and "s" and "t" signify critical exponents.

Several researchers (6), (31) have studied the critical exponent (t) values of different polymer nanocomposites systems.

i]'s), it is not suitable to get general asymptotics from this formula, so we now proceed with another approach, which leads to a nice universal result for the critical exponents, but to the price of a rather technical proof.

The theory of Puiseux expansions (or the theory of G-functions) implies that every algebraic function has a Puiseux series expansion and, thus, the critical exponents are rational numbers.

Jannelli, Critical exponents, critical dimensions and biharmonic operator, Arch.

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.

2000, The role of

critical exponents in blow-up theorems, The sequel, J.

4:00 EXISTENCE THEOREM OF ELLIPTIC SYSTEMS WITH SINGULARITIES INVOLVING SOBOLEV OR SOBOLEV-HARDY

CRITICAL EXPONENTSThis last year has brought new breakthroughs: the jamming

critical exponents can be computed with the theory, which suggests a precise test in a lab.

The calculated values of the

critical exponents q and rare given in Table 1.

Next I will explore links to non-equilibrium phase transitions in other areas of science by determining the

critical exponents and the universality class of the onset of shear flow turbulence.