The dynamical
renormalization group calculations for distortive structural phase transitions report [[rho].sub.[sigma]] = (zv + [[alpha].sub.[sigma]]), where [[alpha].sub.[sigma]] = [alpha] + 2([phi] - 1)(1 - [[delta].sub.[sigma],1)], where z, v,[phi], and are [alpha] are the dynamical, correlation length, heat capacity, and crossover critical exponents, respectively.
In this paper, we investigate the
renormalization group theory for the 2D generalized sine-Gordon model by using the dimensional regularization method to regularize the divergence [50-52].
The nonlinear extension of Balser-Kostov summability method has been requested by our investigation of
renormalization group (RG) flow equation over probability measures [[sigma].sup.N] in [R.sup.N] as N goes to [infinity].
For resolving the turbulent flows in cylinder, the
Renormalization Group (RNG) k-e turbulence model [17] was used.
SCHOLLWOCK, The density-matrix
renormalization group in the age of matrix product states, Ann.
[5], compared eight modified (k- [epsilon]) models and concluded that the
Renormalization Group (RNG) k-[epsilon] model performs best among all the eddyviscosity models tested for mixed convection flow.
The twopoint correlation function that was used was obtained from Monte Carlo simulations [3, 4] for linear chains that agreed with
renormalization group calculations [5].
(5) This is the conclusion of fundamental theoretical analysis based upon
renormalization group methods, (6) empirically validated quantitatively for predictions of geographical locations of violence and peaceful coexistence in Yugoslavia, India, Yemen, and Switzerland.