Abstract Renormalized field theory is a most effective framework to carry out asymptotic analysis of non-equilibrium nearly critical systems, especially in high orders perturbation theory. Here, we review some subtle, slippery and non-conventional aspects this approach. We present construction the field-theoretic representation certain Langevin-type stochastic equations with additive multiplicative random sources as well master various birth–death processes. Application renormalization group...

The field theoretic renormalization group (RG) and the operator-product expansion are applied to model of a transverse (divergence-free) vector quantity, passively advected by "synthetic" turbulent flow with finite (and not small) correlation time. is described stochastic advection-diffusion equation most general form inertial nonlinearity; it contains as special cases kinematic dynamo model, linearized Navier-Stokes (NS) equation, without stretching term that possesses additional symmetries...

Inertial-range scaling behavior of high-order (up to order N=51 ) two-point correlation functions a passively advected vector field has been analyzed in the framework rapid-change model with strong small-scale anisotropy aid renormalization group and operator-product expansion. Exponents power-like asymptotic have calculated one-loop approximation. These exponents are shown depend on parameters such way that specific hierarchy related degree is observed. Deviations from power-law like...

Field theoretic renormalization group and the operator product expansion are applied to a model of passive scalar quantity straight theta(t,x), advected by Gaussian strongly anisotropic velocity field with covariance infinity delta(t-t('))/x-x(')/(epsilon). Inertial-range anomalous scaling behavior is established, explicit asymptotic expressions for structure functions S(n)(r) identical with<[straight theta(t,x+r)-straight theta(t,x)](n)> obtained. They represented superpositions power laws;...

The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we study by means field-theoretic formulation with subsequent renormalization group analysis. We calculate all critical exponents needed for quantitative description corresponding universality class to third order perturbation theory. Using dimensional...

Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field theoretic renormalization group. The mixing are modelled by external Gaussian noise with correlation function $\propto\delta(t-t') k^{4-d-y}$ divergence-free (due incompressibility) velocity field, governed stochastic Navier--Stokes equation force k^{4-d-y'}$. Depending on relations between exponents $y$ $y'$ space dimensionality $d$, model...

The influence of helicity on the stability scaling regimes, effective diffusivity, and anomalous structure functions a passive scalar advected by Gaussian solenoidal velocity field with finite correlation time is investigated theoretic renormalization group operator-product expansion within two-loop approximation. regimes discussed shown in plane exponents epsilon-eta, where epsilon characterizes energy spectrum inertial range E proportional to k(1-2epsilon), eta related at wave number k,...

A liquid crystal optical device made of an optically anisotropic heterostructure is considered. The consists a cholesteric (CLC) layer sandwiched by two phase-shifting layers nematic (NLC). In this structure each the NLC quarterwave plate. problem solved both Ambartsumian method addition and Muller matrix method. peculiarities reflection spectra, eigen polarizations, rotation polarization plane ellipticity are studied. It shown that can work as light modulator or system for obtaining...

In this work the thermotropic liquid crystal 4-(trans-4'-n-hexylcyclohexyl)-isothiocyanato-benzene (6CHBT) was doped with differently shaped magnetic nanoparticles aim to increase sensitivity of on external field. The volume concentration particles 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> . phase transition temperature from isotropic nematic in fields up 12 T monitored by precise capacitance measurements cells filled...

The peculiarities of defect modes and reflection spectra chiral photonic crystals (CPC) with an isotropic for various thicknesses the layer was investigated. density state (DOS) those intensity at center were investigated, too. It shown that there is one more possibility tuning laser emission - by change thickness in CPCs doped dyes (with resonance atoms) defect. given system can work as a tunable narrow-band filter (or mirror) wavelength width location frequency complete transmittance...

In the present paper, we investigate polarization properties of cholesteric liquid crystals (CLCs) with an isotropic/anisotropic defect inside them. Possibilities amplification plane rotation and stabilization light azimuth by these systems are investigated in details.

Presentation of the probability as an intrinsic property nature leads researchers to switch from deterministic stochastic description phenomena. The procedure stochastization one-step process was formulated. It allows write down master equation based on type kinetic equations and assumptions about process. kinetics interaction has recently attracted attention because it often occurs in physical, chemical, technical, biological, environmental, economic, sociological systems. However, there...

The effect of a random velocity field on the kinetics single-species annihilation reaction A+A--> is analyzed near two dimensions with aid perturbative renormalization group. previously found asymptotic behavior induced by density fluctuations only in diffusion-limited shown to be unstable any (including thermal equilibrium) spatial d</=d(c)=2. Four different stable long-time regimes combined and are identified corresponding decay rates calculated leading order.

The spectral distribution of spontaneous emission electrons moving in a plane wiggler with inhomogeneous magnetic field is calculated. We show that do complicated motion consisting slow(strophotron) and fast(undulator) parts. equations are averaged over fast undulator part we obtain for connected motion. It shown, the account inhomogenity leads to appearance additional peaks radiation.

We have investigated the advection of a passive scalar quantity by incompressible helical turbulent flow in frame extended Kraichnan model.Turbulent fluctuations velocity field are assumed to Gaussian statistics with zero mean and defined noise finite time-correlation.Actual calculations been done up two-loop approximation field-theoretic renormalization group approach.It turned out that space parity violation (helicity) environment does not affect anomalous scaling which is peculiar...

The influence of compressibility on the stability scaling regimes passive scalar advected by a Gaussian velocity field with finite correlation time is investigated theoretic renormalization group within two-loop approximation. discussed as function exponents $\epsilon$ and $\eta$, where characterizes energy spectrum in inertial range $E\propto k^{1-2\epsilon}$, $\eta$ related to at wave number $k$ which scaled $k^{-2+\eta}$. restrictions given nonzero regions stable infrared fixed points...

The Renormalization group method (RG) is applied to the investigation of E model critical dynamics, which describes transition from normal superfluid phase in He4. technique “Sector decomposition” with R’ operation used for calculation Feynman diagrams. RG functions, exponents and dynamical exponent z, determines growth relaxation time near point, have been calculated two-loop approximation framework ε-expansion. relevance a fixed point helium, where dynamic scaling weakly violated, briefly...

A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid and velocity fluctuations is proposed. The stochastic Navier-Stokes equation used for generation of the fluctuations. As such this generalizes F critical dynamics. field-theoretic action derived using Martin-Siggia-Rose formalism path integral approach. regime equilibrium analyzed within perturbative renormalization group method. double (ε,δ)-expansion scheme employed, where ε...