Incomplete approach to homoclinicity in a model with bent-slow manifold geometry

The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical behaviour, including period bubbling and period adding or Farey sequences. The complex bifurcation sequences, characterized by Mixed Mode Oscillations, exhibit partial features of Shilnikov and Gavrilov-Shilnikov scenario. Utilizing the fact that the model has disparate time scales of dynamics, we explain the origin of the relaxation oscillations using the geometrical structure of the bent-slow manifold. Based on a local analysis, we calculate the maximum number of small amplitude oscillations, $s$, in the periodic orbit of $L^s$ type, for a given value of the control parameter. This further leads to a scaling relation for the small amplitude oscillations. The incomplete approach to homoclinicity is shown to be a result of the finite rate of `softening' of the eigen values of the saddle focus fixed point. The latter is a consequence of the physically relevant constraint of the system which translates into the occurrence of back-to-back Hopf bifurcation.Comment: 14 Figures(Postscript); To Appear in Physica D : Nonlinear Phenomen

Level statistics for nearly integrable systems

We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble. We obtain analytical expressions for the level spacing distribution and level number variance for such a system. These expressions are successfully applied to the analysis of the resonance spectrum in a nearly integrable microwave billiard.Comment: 10 pages, 4 figure

Demulsification techniques of water-in-oil and oil-in-water emulsions in petroleum industry

The difficulties associated with transportation and refining of crude oil emulsions and produced water discharge limitations are among the conspicuous clues that have led the oilfield researchers to probe into practical demulsification methods for many decades. Inconsistent research outcomes observed in the literature for a particular demulsification method of a typical emulsion (i.e., water-in-oil or oil-in-water) arise not only from the varied influential parameters associated (such as salinity, temperature, pH, dispersed phase content, emulsifier/demulsifier concentration, and droplet size) but also from the diverse types of emulsion constituents (namely oil, surfactant, salt, alkali, polymer, fine solids, and/or other chemicals/impurities). Being the main component in formation of stabilizing interfacial film surrounding the dispersed phase droplets, surfactant is the most predominant contributor to emulsion stability, extent of which depends on its nature (being ionic or nonionic, and its degree of hydrophilicity/lipophilicity), concentration, and interaction with other surface-active agents in the emulsion as well as on the salinity, temperature, and pH of the system. In this paper, it is endeavored to overview some of the most commonly exploited demulsification techniques (i.e., chemical, biological, membrane, electrical, and microwave irradiation) of both oilfield and synthetic emulsions, taking into account the emulsion-stabilizing and -destabilizing effects with regard to the dominant parameters plus the emulsion composition. Further, the variations occurring in interfacial properties of emulsions by demulsification process are discussed. Finally, the mechanism(s) involved in emulsions resolution achieved by each method is elucidated. Clearly, the most efficient demulsification approach is the one able to attain desirable separation efficiency while complying with the environmental regulations and imposing the least economic burden on the petroleum industry