The Topology of Foliations Formed by the Generic K-Orbits of a Subclass of the Indecomposable MD5-Groups

The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideal. In the paper, we give the topological classification of all considered MD5-foliations. A description of these foliations by certain fibrations or suitable actions of $\mathbb{R}^{2}$ and the Connes' C*-algebras of the foliations which come from fibrations are also given in the paper.Comment: 20 pages, no figur

Triangular de Rham Cohomology of Compact Kahler Manifolds

We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle $M\times G$ by the so-called gauge equivalence. We consider the case when M is a compact K\"ahler manifold and G is a solvable complex linear algebraic group of a special class which contains the Borel subgroups of all complex classical groups and, in particular, the group $T_n(\Bbb C)$ of all triangular matrices. In this case, we get a description of the set H^1_{DR}(M,G) in terms of the 1-cohomology of M with values in the (abelian) sheaves of flat sections of certain flat Lie algebra bundles with fibre $\frak g$ (the Lie algebra of G) or, equivalently, in terms of the harmonic forms on M representing this cohomology

Spectral Properties of the Generalized Spin-Fermion Models

In order to account for competition and interplay of localized and itinerant magnetic behaviour in correlated many body systems with complex spectra the various types of spin-fermion models have been considered in the context of the Irreducible Green's Functions (IGF) approach. Examples are generalized d-f model and Kondo-Heisenberg model. The calculations of the quasiparticle excitation spectra with damping for these models has been performed in the framework of the equation- of-motion method for two-time temperature Green's Functions within a non-perturbative approach. A unified scheme for the construction of Generalized Mean Fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation has been generalized in order to include the presence of the two interacting subsystems of localized spins and itinerant electrons. A general procedure is given to obtain the quasiparticle damping in a self-consistent way. This approach gives the complete and compact description of quasiparticles and show the flexibility and richness of the generalized spin-fermion model concept.Comment: 37 pages, Late

Relativistic effects in the solar EOS

We study the sensitivity of the sound speed to relativistic corrections of the equation of state (EOS) in the standard solar model by means of a helioseismic forward analysis. We use the latest GOLF/SOHO data for $\ell = 0,1,2,3$ modes to confirm that the inclusion of the relativistic corrections to the adiabatic exponent $\Gamma_1$ computed from both OPAL and MHD EOS leads to a more reliable theoretical modelling of the innermost layers of the Sun.Comment: 3 pages, 3 figures, aa.cls, to appear on Astronomy and Astrophysic

Spin-oscillator model for DNA/RNA unzipping by mechanical force

We model unzipping of DNA/RNA molecules subject to an external force by a spin-oscillator system. The system comprises a macroscopic degree of freedom, represented by a one-dimensional oscillator, and internal degrees of freedom, represented by Glauber spins with nearest-neighbor interaction and a coupling constant proportional to the oscillator position. At a critical value $F_c$ of an applied external force $F$, the oscillator rest position (order parameter) changes abruptly and the system undergoes a first-order phase transition. When the external force is cycled at different rates, the extension given by the oscillator position exhibits a hysteresis cycle at high loading rates whereas it moves reversibly over the equilibrium force-extension curve at very low loading rates. Under constant force, the logarithm of the residence time at the stable and metastable oscillator rest position is proportional to $(F-F_c)$ as in an Arrhenius law.Comment: 9 pages, 6 figures, submitted to PR

Modelling variability of solar activity cycles

Context. Solar activity cycles vary in amplitude and duration. The variations can be at least partly explained by fluctuations in dynamo parameters. Aims. We want to restrict uncertainty in fluctuating dynamo parameters and find out which properties of the fluctuations control the amplitudes of the magnetic field and energy in variable dynamo cycles. Methods. A flux-transport model for the solar dynamo with fluctuations of the Babcock-Leighton type $\alpha$-effect was applied to generate statistics of magnetic cycles for our purposes. The statistics were compared with data on solar cycle periods to restrict the correlation time of dynamo fluctuations. Results. A characteristic time of fluctuations in the $\alpha$-effect is estimated to be close to the solar rotation period. The fluctuations produce asymmetry between the times of rise and descent of dynamo cycles, the rise time being on average shorter. The affect of the fluctuations on cycle amplitudes depends on the phase of the cycle in which the fluctuations occur. Negative fluctuations (decrease in $\alpha$) in the rise phase delay decay of poloidal field and increase the cycle amplitude in toroidal field and magnetic energy. Negative fluctuation in the decline phase reduces the polar field at the end of a cycle and the amplitude of the next cycle. The low amplitude of the 24th solar cycle compared to the preceding 23rd cycle can be explained by this effect. Positive fluctuations in the descent phase enhance the magnetic energy of the next cycle by increasing the seed poloidal field for the next cycle. The statistics of the computed energies of the cycles suggest that superflares of $\ge 10^{34}$ erg are not possible on the Sun.Comment: 8 pages, 11 figures, A&A (accepted