Terminal control in flat systems

The article considers the application of dynamical feedback control to a special class of nonlinear dynamical systems — so-called flat systems. Flat system, linearizing output, and Lie-Backlund isomorphism are among the concepts reviewed. A man-machine algorithm is proposed for solving the terminal control problem for an arbitrary flat system with known linearizing outputs. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 3, pp. 191–200, 2003.     

Phase behaviour of the discotic mesogen 5,10,15,20-tetrakis (4-n-dodecylphenyl)porphyrin under pressure

The phase behaviour of the discotic mesogen 5,10,15,20-tetrakis(4-n -dodecylphenyl)porphyrin (C12TPP) was investigated under hydrostatic pressures up to 300MPa by high pressure DTA and wide angle X-ray diffraction methods. The typical enantiotropic phase transitions of C12TPP, low- to high-temperature crystal (Cr2-Cr1), Cr1-discotic lamellar phase (DL), and DL-isotropic liquid (I) are observed at pressures up to 10MPa. Application of hydrostatic pressure to the sample generates a pressure-induced crystal polymorph (Cr3) between the Cr2 and Cr1 phases, and the phase transitions Cr2-Cr3-Cr1-DL-I occur reversibly in the pressure region between 10 and 180MPa. On heating at higher pressures above 180MPa, the fourth crystal polymorph (Cr4) is formed between the Cr2 and Cr3 phases at lower temperatures, and at the same time the fifth crystal polymorph (Cr5) appears abruptly between the Cr1 and DL phases at high temperatures. The Cr2-Cr4-Cr3-C1-(Cr5)-DL-I transition processes were observed at 180 200MPa. Further increasing the pressure above 270MPa induces entirely different thermal behaviour: only two peaks for the pressure-induced transition between the sixth and fifth polymorphs (Cr6-Cr5) and the Cr5-I transitions are detected at low and high temperatures on heating, while both the DTA and WAXD experiments on cooling show the formation of the DL phase as a monotropic phase between the I and Cr5 phases, indicating the I DL Cr5 Cr6 process. The thermal behaviour was ambiguous and complex in the pressure region between 200 and 260MPa because the peaks for the intermediate crystal transitions were too small to detect with confidence. The two different sequences of the Cr2-Cr4-Cr3-Cr1-DL-I and Cr6-Cr5-(DL)-I processes seems to occur competitively. The T vs. P phase diagram of a sample cooled at 300MPa was studied to determine the triple point of the DL phase and to investigate the phase stability of the pressure-induced crystal polymorphs. The Cr6-Cr5-I transition process was observed on heating at 200 and 300MPa, while the Cr6-Cr5-DL-I process was detected at lower pressures below 100MPa. Since the Cr5-DL transition temperature changes linearly with a slope dT/dP 40 degrees C/100 MPa, while the DL-I transition temperature changes slightly (dT/dP 5.5 degrees C/100MPa), the DL phase forms a triangle in the T vs. P diagram. The triple point of the DL phase was found to be 240.8MPa and 168.8 C. The Cr6 polymorph reorganized to the stable Cr2 form under atmospheric pressure on annealing at room temperature overnight.     

Introduction of substituents into the benzene nucleus of indole

A method for the synthesis of indolinopyrazines has been proposed. The possibility has been shown of dehydrogenating the indolinopyrazines to the corresponding indole derivatives.For part IX, see [1].     

Hopping Transport and Stochastic Dynamics of Electrons in Plasma Layers

We investigate the stochastic dynamics and the hopping transfer of electrons embedded into two‐dimensional atomic layers. First we formulate the quantum statistics of general atom ‐ electron systems based on the tight‐binding approximation and express ‐ following linear response transport theory ‐ the quantum‐mechanical time correlation functions and the conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the atom motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. In the last part we derive Pauli equations for the stochastic electron dynamics including nonlinear excitations of the atomic subsystem. We carry out Monte Carlo simulations and show that mean square displacements of electrons and transport properties are in a moderate to high temperature regime strongly influenced by by soliton‐type excitations and demonstrate the existence of percolation effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Properties of nano-scale soliton-like excitations in two-dimensional lattice layers

Nano-scale soliton-like supersonic, intrinsic localized excitations in two-dimensional atomic anharmonic lattice layers are here considered. We study the propagation, the velocity and other soliton-like features at head-on collisions of such lattice excitations created by using suitable initial mechanical and thermal conditions. Noteworthy is that narrow, highly-energetic solitons moving along one lattice row are very robust, accompanied by weak anti-phase oscillations in the lateral direction.     

Localized nonlinear, soliton-like waves in two-dimensional anharmonic lattices

We discuss here nano-scale size localized wave excitations, which are intrinsic localized traveling modes in two-dimensional anharmonic crystal lattice systems. In particular, using different initial conditions of coordinates and momenta we search for the longest lasting excitations in triangular lattices. As most stable and longest lasting unaltered appear quasi-one-dimensional Toda-like solitons running in rectilinear chains along the main crystallographic axes of such lattices. Furthermore, by following the trace of high energetic excitations like in “bubble chamber” methodology (or in scanning tunneling microscopy) we show how such localized nonlinear waves appearing spontaneously in heated systems can be detected and followed in space-time.     

Field induced chirality in the helix structure of Dy/Y multilayer films and experimental evidence for Dzyaloshinskii-Moriya interaction on the interfaces

Polarized neutron scattering experiments have demonstrated that Dy/Y multilayer structures possess a coherent spin helix with a preferable chirality induced by the magnetic field. The average chirality, being proportional to the difference in the left- and right-handed helix population numbers, is measured as a polarization-dependent asymmetric part of the magnetic neutron scattering. The magnetic field applied in the plane of the sample upon cooling below T(N) is able to repopulate the otherwise equal population numbers for the left- and right-handed helixes. The experimental results strongly indicate that the chirality is caused by Dzyaloshinskii-Moriya interaction due to the lack of the symmetry inversion on the interfaces.