A frequency-domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential-algebraic equations

A general numerical technique is proposed for the assessment of the stability of periodic solutions and the determination of bifurcations for limit cycles in autonomous nonlinear systems represented by ordinary differential equations in the differential-algebraic form. The method is based on the harmonic balance technique, and exploits the same Jacobian matrix of the nonlinear system used in the Newton iterative numerical solution of the harmonic balance equations for the determination of the periodic steady-state. To demonstrate the approach, it is applied to the determination of the bifurcation curves in the parameters' space of Chua's circuit with cubic nonlinearity, and to study the dynamics of the limit cycle of a Colpitts oscillato

Baxter T-Q Equation for Shape Invariant Potentials. The Finite-Gap Potentials Case

The Darboux transformation applied recurrently on a Schroedinger operator generates what is called a {\em dressing chain}, or from a different point of view, a set of supersymmetric shape invariant potentials. The finite-gap potential theory is a special case of the chain. For the finite-gap case, the equations of the chain can be expressed as a time evolution of a Hamiltonian system. We apply Sklyanin's method of separation of variables to the chain. We show that the classical equation of the separation of variables is the Baxter T-Q relation after quantization.Comment: 25 pages, no figures Extended section 10, one reference added. Version accepted for publication in Jurnal of Mathematical Physic

Plasma rotation measurement in small tokamaks using an optical spectrometer and a single photomultiplier as detector

The method for plasma rotation measurement in the tokamak TCABR is reported in this article. During a discharge, an optical spectrometer is used to scan sequentially spectral lines of plasma impurities and spectral lines of a calibration lamp. Knowing the scanning velocity of the diffraction grating of the spectrometer with adequate precision, the Doppler shifts of impurity lines are determined. The photomultiplier output voltage signals are recorded with adequate sampling rate. With this method the residual poloidal and toroidal plasma rotation velocities were determined, assuming that they are the same as those of the impurity ions. The results show reasonable agreement with the neoclassical theory and with results from similar tokamaks

Platelet Ice Under Arctic Pack Ice in Winter

The formation of platelet ice is well known to occur under Antarctic sea ice, where subice platelet layers form from supercooled ice shelf water. In the Arctic, however, platelet ice formation has not been extensively observed, and its formation and morphology currently remain enigmatic. Here, we present the first comprehensive, long‐term in situ observations of a decimeter thick subice platelet layer under free‐drifting pack ice of the Central Arctic in winter. Observations carried out with a remotely operated underwater vehicle (ROV) during the midwinter leg of the MOSAiC drift expedition provide clear evidence of the growth of platelet ice layers from supercooled water present in the ocean mixed layer. This platelet formation takes place under all ice types present during the surveys. Oceanographic data from autonomous observing platforms lead us to the conclusion that platelet ice formation is a widespread but yet overlooked feature of Arctic winter sea ice growth

Oxidation and hydrogenation of benzo[g]isoquinolines

The oxidation of methyl-substituted (in the pyridine and benzene rings) benzo[g]isoquinolines to substituted 2-azaanthraquinones was realized. It was established that the pyridine ring is partially reduced to give 1,2,3,4-tetrahydrobenzo[g]isoquinolines in the hydrogenation of benzo[g]isoquinolines in the presence of rhenium heptasulfide. © 1979 Plenum Publishing Corporation

Oxidation and hydrogenation of benzo[g]isoquinolines

The oxidation of methyl-substituted (in the pyridine and benzene rings) benzo[g]isoquinolines to substituted 2-azaanthraquinones was realized. It was established that the pyridine ring is partially reduced to give 1,2,3,4-tetrahydrobenzo[g]isoquinolines in the hydrogenation of benzo[g]isoquinolines in the presence of rhenium heptasulfide. © 1979 Plenum Publishing Corporation