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].
turbulence modeling in PowerFLOW this study uses turbulence theory to model only the dissipative and inertial ranges, modeling the dynamics of sub-grid scale turbulence by two additional equations derived from an extended RNG (Renormalization Group
theory) formulation, as following,
For resolving the turbulent flows in cylinder, the Renormalization Group
(RNG) k-e turbulence model  was used.
 adopted standard k-[epsilon], renormalization group
k-[epsilon], and standard k-[omega] turbulence model to simulate the four step arrangements stepped spillways.
SCHOLLWOCK, The density-matrix renormalization group
in the age of matrix product states, Ann.
Kremer, "Universal shape properties of open and closed polymer chains: renormalization group
analysis and Monte Carlo experiments," Journal de Physique I, vol.
, 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
(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.