19 research outputs found
Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy
The influence of uniaxial small-scale anisotropy on the stability of the
scaling regimes and on the anomalous scaling of the structure functions of a
passive scalar advected by a Gaussian solenoidal velocity field with finite
correlation time is investigated by the field theoretic renormalization group
and operator product expansion within one-loop approximation. Possible scaling
regimes are found and classified in the plane of exponents ,
where characterizes the energy spectrum of the velocity field in the
inertial range , and is related to the
correlation time of the velocity field at the wave number which is scaled
as . It is shown that the presence of anisotropy does not disturb
the stability of the infrared fixed points of the renormalization group
equations which are directly related to the corresponding scaling regimes. The
influence of anisotropy on the anomalous scaling of the structure functions of
the passive scalar field is studied as a function of the fixed point value of
the parameter which represents the ratio of turnover time of scalar field
and velocity correlation time. It is shown that the corresponding one-loop
anomalous dimensions, which are the same (universal) for all particular models
with concrete value of in the isotropic case, are different (nonuniversal)
in the case with the presence of small-scale anisotropy and they are continuous
functions of the anisotropy parameters, as well as the parameter . The
dependence of the anomalous dimensions on the anisotropy parameters of two
special limits of the general model, namely, the rapid-change model and the
frozen velocity field model, are found when and ,
respectively.Comment: revtex, 25 pages, 37 figure
Influence of helicity on scaling regimes in the extended Kraichnan model
We have investigated the advection of a passive scalar quantity by
incompressible helical turbulent flow in the frame of extended Kraichnan model.
Turbulent fluctuations of velocity field are assumed to have the Gaussian
statistics with zero mean and defined noise with finite time-correlation.
Actual calculations have been done up to two-loop approximation in the frame of
field-theoretic renormalization group approach. It turned out that space parity
violation (helicity) of turbulent environment does not affect anomalous scaling
which is peculiar attribute of corresponding model without helicity. However,
stability of asymptotic regimes, where anomalous scaling takes place, strongly
depends on the amount of helicity. Moreover, helicity gives rise to the
turbulent diffusivity, which has been calculated in one-loop approximation.Comment: 16 pages, talk given by M. Hnatich at "Renormalization Group 2005",
Helsinki, Finland 30 August - 3 September 2005. To apear in J. Phys. A: Math.
Ge
Prediction of the existence of an intermediate phase in the antiferromagnetic J
The structure o f the phase diagram of the antiferromagnetic Ising model with the presence of the nearest-neighbor and next-nearest-neighbor interactions on the face-centered cubic lattice is investigated in detail in the framework of the recursive lattice approximation. The existence of an additional well-defined intermediate phase is predicted that separates two standard antiferromagnetic phases of the model. This new phase is realized in the form of a narrow strip in the phase diagram but can be observed for a rather large interval of the frustration parameter of the model. Moreover, analyzing the sublattice magnetization properties of the model, it is shown that transitions between all model phases have the second-order nature. All predicted series of successive phase transitions of the model caused by the presence of the intermediate phase are studied
A general formula for analytic reduction of multi-loop tensor Feynman integrals
AbstractWe prove a general formula for analytic reduction of tensor integrals which appear in calculations of multi-loop Feynman diagrams in quantum field theory models
Presence of the weak ferromagnetism in pure antiferromagnetic systems with octahedral structure: Effective field theory analysis
The recently reported (Jurčišinová E. and Jurčišin M