Simple derivation of the condition for the transition point from absolute
instability of plane dark solitons to their convective instability is
suggested. It is shown that unstable wave packet expands with velocity equal to
the minimal group velocity of the disturbance waves propagating along a dark
soliton. The growth rate of the length of dark solitons generated by the flow
of Bose-Einstein condensate past an obstacle is estimated. Analytical theory is
confirmed by the results of numerical simulations
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schrödinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.
Formation of oblique solitons by a flow of polariton condensate past an obstacle is considered. The flow is non-uniform due to a finite life-time of polaritons what changes drastically the conditions of formation of oblique solitons compared with the atomic condensate case. The theory shows that the polariton solitons can be generated by a subsonic flow in agreement with the recent experiment [A. Amo et al., Science, 332, 1167]. Geometric form of oblique solitons and other their parameters are calculated analytically and analytical results are confirmed by numerical simulations.
Water contamination of motor oils during storage and use in low-temperature conditions cause formation of deposits. These deposits, which consist of asphaltenes and additives, characterize the colloidal stability of the oils. A decrease in the concentration of additives worsens the performance properties of the motor oils..In 1955, Anglo-American engineers turned their attention to the greasy black sediments in the lubricating systems of internal combustion engines for the first time [1,2]. Five years later, Soviet scientists also showed an interest in these formations [3]. All investigators agreed that the presence of water in the motor oil is the basic cause of the deposits. Such deposits can also be found on the bottom of motor oil storage tanks. The presence of water in oil is determined in laboratory conditions using special equipment in the first case and visually during cleaning of oil tanks in the second case.How does water affect the state of motor oils and what are the consequences?The additives it contains play the paramount role in ensuring the performance of motor oils. The effect of water on the state of motor oils was investigated with a specially developed method using fresh motor oils of guaranteed quality: M-8V (GOST 10541-78) and Turbo-1 M-8D(m) (TU 38.30119110-97).The method of investigation provided for: forced introduction of 0.5, 5, 10, and 15% water in samples of motor oils; careful mixing; resting for 72 h; visual observation for the state of the oils; emission spectral analysis of the top layer of the sample on a MFS-7 unit for recording the content of elements -additive indicators.After introduction of the water, stirring, and holding, the liquids stratified with formation of sediment. The height of the sediment layer was a function of the water content in the mixture and the concentration of additives in the oil. The additives were salts of organic acids and different metals.The change in the content of ash additives can be judged by the change in the concentration of metals in the oil, determined in spectral analysis. The results of spectral analysis of the top layer of the water-contaminated oils are shown in Fig. 1.
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