The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by external turbulence and the intrinsic flame instability. The analytical formulas for the velocity of flame propagation are obtained. It is demonstrated that the flame instability is of principal importance when the integral turbulent length scale is much larger than the cut off wavelength of the instability. The developed theory is used to analyse recent experiments on turbulent flames propagating in tubes. It is demonstrated that most of the flame velocity increase measured experimentally is provided by the large scale effects like the flame instability, and not by the small-scale external turbulence.

Vitaly Bychkov Vyacheslav Akkerman Arkady Petchenko

Spontaneous flame acceleration leading to explosion triggering in open tubes/channels due to wall friction was analytically and computationally studied. It was first demonstrated that the acceleration is effected when the thermal expansion across the flame exceeds a critical value depending on the combustion configuration. For the axisymmetric flame propagation in cylindrical tubes with both ends open, a theory of the initial (exponential) stage of flame acceleration in the quasi-isobaric limit was developed and substantiated by extensive numerical simulation of the hydrodynamics and combustion with an Arrhenius reaction. The dynamics of the flame shape, velocity, and acceleration rate, as well as the velocity profile ahead and behind the flame, have been determined.

V'yacheslav Akkerman Chung K Law Vitaly Bychkov Lars-Erik Eriksson

The Kelvin-Helmholtz instability in an ionized plasma is considered with a focus on the generation of magnetic field via the Biermann battery mechanisms. The problem is studied through direct numerical simulations of two counter-directed flows in 2D geometry. The simulations demonstrate the formation of eddies and their further interaction resulting in a large single vortex. At early stages, the generated magnetic field evolves due to the baroclinic term in the induction equation, revealing significantly different structures from the vorticity field, despite the fact that magnetic field and vorticity obey identical equations. At later times, the magnetic field exhibits complex behavior and continues to grow even after a hydrodynamic vortex has developed.

Mikhail Modestov Vitaly Bychkov Gert Brodin Mattias Marklund Axel Brandenburg

In our Comment (G.E. Volovik and V.M. Yakovenko, Phys. Rev. Lett. 79 (1997) 3792) to the Letter by W. Apel and Yu.A. Bychkov (Phys. Rev. Lett. 78 (1997) 2188) we questioned the derivation of the Hopf term in the hydrodynamic action for the Skyrmion dynamics in QHE. Our main argument was that the description in terms of Euler angles used by Apel and Bychkov was potentially dangerous since these angles were ill-defined. The Reply (W. Apel and Yu.A. Bychkov, Phys. Rev. Lett. 79 (1997) 3792) to our Comment confirmed our apprehension.

G. E. Volovik

In this Comment on the paper by W. Apel and Yu. A. Bychkov, cond-mat/9610040 and Phys. Rev. Lett. 78, 2188 (1997), we draw attention to our prior microscopic derivations of the Hopf term for various systems and to shortcomings of the Apel-Bychkov derivation. We explain how the value of the Hopt term prefactor $\Theta$ is expressed in terms of a topological invariant in the momentum space and the quantized Hall conductivity of the system. (See also related paper cond-mat/9703195)

G. E. Volovik V. M. Yakovenko

We report on a theoretical approach developed to investigate the influence of Bychkov-Rashba interaction on a few interacting electrons confined in a quantum dot. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Inter-electron interaction causes level crossings in the ground state and a jump in magnetization. As the coupling strength is increased, that jump is shifted to lower magnetic fields. Low-field magnetization will therefore provide a direct probe of the spin-orbit coupling strength in a quantum dot.

Tapash Chakraborty Pekka Pietilainen

A closed-form analytic formula for the magnetoconductivity in the diffusive regime is derived in the presence of Bychkov-Rashba spin-orbit interaction in two dimensions. It is shown that at low fields B << B_{so}, where B_{so} is the characteristic field associated with spin precession, D'yakonov-Perel' mechanism leads to spin relaxation, while for B >> B_{so} spin relaxation is suppressed and the resulting spin precession contributes a Berry phase-like spin phase to the magnetoconductivity. The relative simplicity of the formula greatly facilitates data fitting, allowing for the strength of the spin-orbit coupling to be easily extracted.

Alexander Punnoose

The effects of the spin-orbit interaction on the tunneling magnetoresistance of magnetic tunnel junctions are investigated. A model in which the experimentally observed two-fold symmetry of the anisotropic tunneling magnetoresistance (TAMR) originates from the interference between Dresselhaus and Bychkov-Rashba spin-orbit couplings is formulated. Bias induced changes of the Bychkov-Rashba spin-orbit coupling strength can result in an inversion of the TAMR. The theoretical calculations are in good agreement with the TAMR experimentally observed in epitaxial Fe/GaAs/Au tunnel junctions.

A. Matos-Abiague J. Fabian

We present the generating function for the numbers of isomorphism classes of coverings of the two-dimensional sphere by the genus $g$ compact oriented surface not ramified outside of a given set of $m+1$ points in the target, fixed ramification type over one point, and arbitrary ramification types over the remaining $m$ points. We present the genus expansion of this generating function and prove, that the generating function of coverings of genus $0$ satisfies some system of differential equations. We show that this generating function is a specialization of the function from paper \cite{GJ} and, therefore, satisfies the KP-hierarchy.

Boris Bychkov

We show that in the fundamental groups of closed manifolds without conjugate points centralizers of all elements virtually split.

Sergei Ivanov Vitali Kapovitch