Kirill A. Kazakov

Nonlinear equation for curved stationary flames

A nonlinear equation describing curved stationary flames with arbitrary gas expansion, θ=ρfuel/ρburnt, subject to the Landau–Darrieus instability, is obtained in a closed form without an assumption of weak nonlinearity. It is proved that in the scope of the asymptotic expansion for θ→1, the new equation gives the true solution to the problem of stationary flame propagation with the accuracy of the sixth order in θ−1. In particular, it reproduces the stationary version of the well-known Sivashinsky equation at the second order corresponding to the approximation of zero vorticity production. At higher orders, the new equation describes influence of the vorticity drift behind the flame front on the flame velocity and the flame front structure. Its asymptotic expansion is carried out explicitly, and the resulting equation is solved analytically at the third order. For arbitrary values of θ, the highly nonlinear regime of fast flow burning is investigated, for which case a large flame velocity expansion of the...

On-shell description of stationary flames

The problem of nonperturbative description of stationary flames with arbitrary gas expansion is considered. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral, a simple explicit expression for the vortex mode of the burnt gas flow near the flame front is obtained. Furthermore, a dispersion relation for the potential mode at the flame front is written down, thus reducing the initial system of bulk equations and jump conditions for the flow variables to a set of integrodifferential equations for the flame front position and the flow velocity at the front. The developed approach is applied to the case of thin flames. Finally, an asymptotic expansion of the derived equations is carried out in the case θ→1 where θ is the gas expansion coefficient, and a single equation for the front position is obtained in the second post-Sivashinsky approximation. It is demonstrated, in particular, how the well-known problem of correct norm...

Detailed analysis of the dependence of 1-loop counter-terms on gauge and parametrization in Einstein gravity with a cosmological constant

In this paper, the dependence of the Einstein gravity with the cosmological constant as well as of this theory in the first-order formalism on the gauge and parametrization is been analyzed. The one-loop counterterms off the mass shell have been plainly calculated in arbitrary gauge and parametrization. The tensor package of analytic calculations, written in REDUCE, allowed all the calculations to be carried out. A method of renormalization group functions calculations off shell is discussed. PACS numbers: 04.60.-m, 11.10.Gh, 11.10.Hi 1 E-mail: kalmykov@thsun1.jinr.dubna.su E-mail: kirill@theor.phys.msu.su E-mail: petr@theor.phys.msu.su E-mail: stepan@theor.phys.msu.suThe dependence of Einstein gravity with the cosmological constant on the gauge and parametrization is analysed. The 1-loop counter-terms off the mass shell have been plainly calculated in arbitrary gauge and parametrization. The tensor package of analytic calculations, written in REDUCE, allowed all the calculations to be carried out. A method of renormalization group functions calculations off shell is discussed.

On-shell description of unsteady flames

The problem of a non-perturbative description of unsteady premixed flames with arbitrary gas expansion is addressed in the two-dimensional case. Considering the flame as a surface of discontinuity with arbitrary local burning rate and gas velocity jumps, we show that the flame-front dynamics can be determined without having to solve the flow equations in the bulk. On the basis of the Thomson circulation theorem, an implicit integral representation of the downstream gas velocity is constructed. It is then simplified by a successive stripping of the potential contributions to obtain an explicit expression for the rotational component near the flame front. We prove that the unknown potential component is left bounded and divergence-free by this procedure, and hence can be eliminated using the dispersion relation for its on-shell value (i.e. the value along the flame front). The resulting system of integro-differential equations relates the on-shell fresh-gas velocity and the front position. As limiting cases, these equations contain all the theoretical results on flame dynamics established so far, including the linear equation describing the Darrieus-Landau instability of planar flames, and the nonlinear Sivashinsky-Clavin equation for flames with weak gas expansion.

Gauge and parametrization dependence in higher derivative quantum gravity

The structure of counterterms in higher derivative quantum gravity is reexamined. Nontrivial dependence of charges on the gauge and parametrization is established. Explicit calculations of two-loop contributions are carried out with the help of the generalized renormgroup method demonstrating consistency of the results obtained.

NONLINEAR THEORY OF FLAME FRONT INSTABILITY

Abstract A nonlinear, nonstationary equation describing evolution of weakly curved premixed flames with arbitrary gas expansion, subject to the Landau-Dar-rieus instability, is derived. The new equation respects all the conservation laws to be satisfied across the flame front, correctly taking into account influence of vorticity, generated in the flame, on the flame front structure and flame velocity. Analytical solutions of the derived equation are found.

On the correspondence between classical and quantum gravity

The relationship between classical and quantum theories of gravity is re-examined. The value of the gravitational potential defined with the help of the two-particle scattering amplitudes is shown to be in disagreement with the classical result of general relativity given by the Schwarzschild solution. It is shown also that the potential so defined fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of the 0-order part of the loop corrections is given directly in terms of the effective action. Gauge independence of that part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed.

Analytical study in the mechanism of flame movement in horizontal tubes

The problem of premixed flame propagation in wide horizontal tubes is revisited. Employing the on-shell description of flames with arbitrary gas expansion, a nonlinear second-order differential equation for the front position of steady flame is derived. Solutions to this equation, obtained numerically, reveal two distinct physical regimes of laminar flame propagation controlled by the strong baroclinic effect. They differ by the front shape and flame speed, the ratio of the total consumption rates in the two regimes being 1.4 to 1.8, depending on the value of the gas expansion coefficient. Comparison with the existing experimental data on methane-air flames is made, and explanation of the main trends in the observed flame behavior is given. It is shown, in particular, that the faster (slower) regime of combustion is realized in mixtures close to (far from) the stoichiometric composition, with pronounced changeover in between.

Quantum theory of flicker noise in metal films

Abstract Flicker ( 1 / f γ ) voltage noise spectrum is derived from finite-temperature quantum electromagnetic fluctuations produced by elementary charge carriers in external electric field. It is suggested that deviations of the frequency exponent γ from unity, observed in thin metal films, can be attributed to quantum backreaction of the conducting medium on the fluctuating field of the charge carrier. This backreaction is described phenomenologically in terms of the effective momentum space dimensionality, D . Using the dimensional continuation technique, it is shown that the combined action of the photon heat bath and external field results in a 1 / f γ -contribution to the spectral density of the two-point correlation function of electromagnetic field. The frequency exponent is found to be equal to 1 + δ , where δ = 3 - D is a reduction of the momentum space dimensionality. This result is applied to the case of a biased conducting sample, and a general expression for the voltage power spectrum is obtained which possesses all characteristic properties of observed flicker noise spectra. The range of validity of this expression covers well the whole measured frequency band. Gauge independence of the power spectrum is proved. It is shown that the obtained results naturally resolve the problem of divergence of the total noise power. A detailed comparison with the experimental data on flicker noise measurements in metal films is given.

Gauge dependence of the post-Newtonian radiative corrections and effective gravitational field of black holes

The problem of interpretation of the \hbar^0-order part of radiative corrections to the effective gravitational field is considered. It is shown that variations of the Feynman parameter in gauge conditions fixing the general covariance are equivalent to spacetime diffeomorphisms. This result is proved for arbitrary gauge conditions at the one-loop order. It implies that the gravitational radiative corrections of the order \hbar^0 to the spacetime metric can be physically interpreted in a purely classical manner. As an example, the effective gravitational field of a black hole is calculated in the first post-Newtonian approximation, and the secular precession of a test particle orbit in this field is determined.