Abstract:
Results of magnetic field and temperature dependent neutron diffraction and magnetization measurements on oxy-arsenate Rb$_{2}$Fe$_{2}$O(AsO$_{4}$)$_{2}$ are reported. The crystal structure of this compound contains pseudo-one-dimensional [Fe$_{2}$O$_{6}$]$^\infty$ sawtooth-like chains, formed by corner sharing isosceles triangles of $Fe^{3+}$ ions occupying two nonequivalent crystallographic sites. The chains extend infinitely along the crystallographic $b$-axis and are structurally confined from one another via diamagnetic (AsO$_{4}$)$^{3-}$ units along the $a$-axis, and Rb$^+$ cations along the $c$-axis direction. Neutron diffraction measurements indicate the onset of a long range antiferromagnetic order below approximately 25 K. The magnetic structure consists of ferrimagnetic chains which are antiferromagnetically coupled with each other. Within each chain, one of the two Fe sites carries a moment which lies along the \emph{b}-axis, while the second site bears a canted moment in the opposite direction. Externally applied magnetic field induces a transition to a ferrimagnetic state, in which the coupling between the sawtooth chains becomes ferromagnetic. Magnetization measurements performed on optically-aligned single crystals reveal evidence for an uncompensated magnetization at low magnetic fields that could emerge from to a phase-segregated state with ferrimagnetic inclusions or from antiferromagnetic domain walls. The observed magnetic states and the competition between them is expected to arise from strongly frustrated interactions within the sawtooth chains and relatively weak coupling between them.

Possibility of generation of large-scale
sheared zonal flow and magnetic field by coupled under the typical ionospheric
conditions short-scale planetary low-frequency waves is shown. Propagation of
coupled internal-gravity-Alfven, Rossby-Khantadze, Rossby-Alfven-Khantadze and
collision-less electron skin depth order drift-Alfven waves is revealed and
investigated in detail. To describe the nonlinear interaction of such coupled
waves with sheared zonal flow the corresponding nonlinear equations are
deduced. The instability mechanism is based on the nonlinear parametric triple
interaction of the finite amplitude short-scale planetary waves leading to the
inverse energy cascade toward the longer wavelengths. It is shown that under
such interaction intense sheared magnetic fields can be generated. Appropriate
growth rates are discussed in detail.

Abstract:
This paper describes the wave-front correction system developed for the Sunrise balloon telescope, and provides information about its in-flight performance. For the correction of low-order aberrations, a Correlating Wave-Front Sensor (CWS) was used. It consisted of a six-element Shack-Hartmann wave-front sensor (WFS), a fast tip-tilt mirror for the compensation of image motion, and an active telescope secondary mirror for focus correction. The CWS delivered a stabilized image with a precision of 0.04 arcsec (rms), whenever the coarse pointing was better than 90 arcsec peak-to-peak. The automatic focus adjustment maintained a focus stability of 0.01 waves in the focal plane of the CWS. During the 5.5 day flight, good image quality and stability was achieved during 33 hours, containing 45 sequences that lasted between 10 and 45 minutes.

Abstract:
We apply the approach of the Google matrix, used in computer science and World Wide Web, to description of properties of neuronal networks. The Google matrix ${\bf G}$ is constructed on the basis of neuronal network of a brain model discussed in PNAS {\bf 105}, 3593 (2008). We show that the spectrum of eigenvalues of ${\bf G}$ has a gapless structure with long living relaxation modes. The PageRank of the network becomes delocalized for certain values of the Google damping factor $\alpha$. The properties of other eigenstates are also analyzed. We discuss further parallels and similarities between the World Wide Web and neuronal networks.

Abstract:
We study numerically the behavior of qubit coupled to a quantum dissipative driven oscillator (resonator). Above a critical coupling strength the qubit rotations become synchronized with the oscillator phase. In the synchronized regime, at certain parameters, the qubit exhibits tunneling between two orientations with a macroscopic change of number of photons in the resonator. The life times in these metastable states can be enormously large. The synchronization leads to a drastic change of qubit radiation spectrum with appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev {\it et al.} Nature {\bf 449}, 588 (2007)].

Abstract:
Using method of quantum trajectories we study the behavior of two identical or different superconducting qubits coupled to a quantum dissipative driven resonator. Above a critical coupling strength the qubit rotations become synchronized with the driving field phase and their evolution becomes entangled even if two qubits may significantly differ from one another. Such entangled qubits can radiate entangled photons that opens new opportunities for entangled wireless communication in a microwave range.

Abstract:
Using the methods of quantum trajectories we study numerically the phenomenon of quantum synchronization in a quantum dissipative system with periodic driving. Our results show that at small values of Planck constant $\hbar$ the classical devil's staircase remains robust with respect to quantum fluctuations while at large $\hbar$ values synchronization plateaus are destroyed. Quantum synchronization in our model has close similarities with Shapiro steps in Josephson junctions and it can be also realized in experiments with cold atoms.

Abstract:
We study properties of Wigner crystal in snaked nanochannels and show that they are characterized by conducting sliding phase at low charge densities and insulating pinned phase emerging above a certain critical charge density. The transition between these phases has a devil's staircase structure typical for the Aubry transition in dynamical maps and the Frenkel-Kontorova model. We discuss implications of this phenomenon for charge density waves in quasi-one-dimensional organic conductors and for supercapacitors in nanopore materials.

Abstract:
The influence of nonlinear properties of semiconductor saturable absorbers on ultrashort pulse generation was investigated. It was shown, that linewidth enhancement, quadratic and linear ac Stark effect contribute essentially to the mode locking in cw solid-state lasers, that can increase the pulse stability, decrease pulse duration and reduce the mode locking threshold

Abstract:
A Particle-in-Cell (PIC) numerical simulation of the electron Weibel instability is applied in a frame of Darwin (radiationless) approximation of the self-consistent fields of sparse plasma. As a result, we were able to supplement the classical picture of the instability and, in particular, to obtain the dependency of the basic characteristics (the time of development and the maximum field energy) of the thermal anisotropy parameter, to trace the dynamic restructuring of current filaments accompanying the nonlinear stage of the instability and to trace in detail the evolution of the initial anisotropy of the electron component of plasma.