On n-quantum vortices in superconductors

Taking into account terms of a higher order than those usually included in the expansion of free energy close to $\kappa = 1/\sqrt 2$ in the Ginzburg-Landau theory can lead either to the transition from the mixed to the intermediate state, as is commonly supposed, or to a chain of sequential transitions from one-to n-quantum vortices (n=2, 3, ...).     

Mutual synchronization of molecular oscillators

Radiophysics and Quantum Electronics -     

Mark Grigor'evich Krein

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, p. 576, April, 1990.     

Fracture and friction: Stick-slip motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first-order phase transitions we discuss a soft selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as functions of the driving velocity. The relevance of our results to recent experiments is discussed.     

Correlation between the mass-spectrometric behavior and chromatographic mobility of epimeric 4-alkyl-1,2-dimethyl-trans-perhydroquinolol N-oxides

The dependence between the Chromatographic mobility, the character of the disintegration under electron impact, and the configuration at C(₄) was found for epimeric N-oxides of 1,2-dimethyl-4-ethyl-,-4-vinyl-, and -4-ethynylperhydro-4-quinolols. It Is proposed that this dependence be used to determine the configuration at C(₄) in 1,4-dialkyl-trans-perhydro-4-quinolols, from which two epimeric N-oxides can be obtained.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 74–76, January, 1973.     

Parametric instability of gravity waves on the surface of deep water

We propose to investigate the characteristics of the parametric generation of gravity waves on the surface of a body of deep water. The threshold conditions for the onset of generation are determined, and the results are compared with the experimental data. The singularities of the excitation of parametric oscillations in a resonator are noted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 182–185, May–June, 1972.The authors are grateful to V. N. Pshenichnikov for assisting with the experiments.