Grégoire Nicolis

On Symmetry‐Breaking Instabilities in Dissipative Systems

The theory of hydrodynamic instability has always been an important part of fluid dynamics [see, e.g., Chandrasekhar, in Hydrodynamic and Hydromagnetic Stability (Clarendon Press, Oxford, England, 1961) and Non‐Equilibrium Thermodynamics, Variation Techniques, and Stability, R. J. Donnelly, R. Herman, and I. Prigogine, Eds. (University of Chicago Press, Chicago, Ill., 1966)]. Such instabilities involve both convective processes (such as mechanical flow) and dissipative processes (such as viscous dissipation). We investigate the possibility of an instability in purely dissipative systems involving chemical reactions and transport processes such as diffusion, but no hydrodynamic motion. We demonstrate that for well‐defined values of the constraints such as the chemical affinities of the over‐all reactions and the constants involved, such systems can indeed become unstable. Such an instability is investigated following an example of autocatalytic reactions first proposed by Turing. The major feature of this ...

On the Theory of Excitons in Liquids. II. A Classical Model of Polarization Waves in a Simple Liquid

Recent studies of the localized excited states of condensed matter have been almost exclusively concerned with the properties of crystalline solids. In this paper we construct an analysis of the exciton states of a particular disordered system, namely a simple liquid. We present a model which is an extension of the model previously used by Fano and which allows the construction of a general theory of polarization waves in which the structure of the liquid appears explicitly. Some particular cases of the general form of the dispersion relation of polarization waves are worked out in detail both in the longitudinal and transverse cases. Finally, the possible mechanisms of damping of the exciton waves are briefly discussed.

Theory of Excitons in Liquids. IV. A Simplified Treatment of the Shift and Damping of Polarization Waves

A simplified theory of the scattering of polarization waves in a liquid arising from the thermal motion of the atoms is presented. The treatment departs somewhat from the general lines of the formal exciton theory in disordered systems set up in the previous papers of this series. Most important, some additional approximations designed to simplify the analysis are introduced. The frequency‐dependent lifetime of the transitions is calculated using second‐order perturbation theory. From this, an expression is deduced for the damping coefficient of excitation waves, both in the case of an impurity atom in a host liquid and in the case of a pure liquid. In both calculations, the thermal motion of the atoms is represented as a small step diffusion or by using a linear‐trajectory approximation. A rough numerical estimation of the level broadening produces the expected orders of magnitude for the lifetimes of states in Ar. Finally, an alternative approach to the exciton problems is discussed in much the same spi...

Optical model calculation of the electronic states of mixed disordered systems

This paper reports a study of the normal modes of simple disordered systems using a dispersion oscillator model with dipolar coupling for the unperturbed electronic states. An equation is derived for the normal‐mode frequencies and for the excitation amplitudes of the system. This equation displays the local structure of the fluid in an explicit way. The nature of the resonance and localized impurity modes is discussed in the particular case of an isotopically disordered uniform system. Finally, the contribution of the thermal motion of the atoms to the damping of the normal modes is discussed. The significance of the results and the relationship to other formal studies of disordered systems is briefly considered.