Nonstationary energy localization vs conventional stationary localization in weakly coupled nonlinear oscillators

In this paper we study the effect of nonstationary energy localization in a nonlinear conservative resonant system of two weakly coupled oscillators. This effect is alternative to the well-known stationary energy localization associated with the existence of localized normal modes and resulting from a local topological transformation of the phase portraits of the system. In this work we show that nonstationary energy localization results from a global transformation of the phase portrait. A key to solving the problem is the introduction of the concept of limiting phase trajectories (LPTs) corresponding to maximum possible energy exchange between the oscillators. We present two scenarios of nonstationary energy localization under the condition of 1:1 resonance. It is demonstrated that the conditions of nonstationary localization determine the conditions of efficient targeted energy transfer in a generating dynamical system. A possible extension to multi-particle systems is briefly discussed.     

Statistical mechanics of solid and liquid mixtures of ortho- and para-hydrogen

It is known from experimental measurements that the configurational free energy of solid and liquid mixtures of p-H₂ and o-H₂ is approximately of the form

where is the mole fraction of o-H₂. Assuming that this dependence of F _conf on is due solely to orientational forces a quantum-mechanical calculation of F _conf is developed which is valid for moderately low temperatures. A simplified statistical model is used consisting of a rigid lattice. The theoretical free energy obtained is however much smaller than the experimental one probably on account of the crudeness of the model. Various refinements are discussed.     

Evidence of chaotic dynamics of brain activity during the sleep cycle

Recent progress in nonlinear dynamics provides the means for the characterisation of the behavior of natural systems from time series. The analysis of electroencephalogram data from the human brain during the sleep cycle reveals the existence of chaotic attractors for sleep stages two and four. The onset of sleep is followed by increasing “coherence” towards deterministic dynamics involving a limited set of variables.     

On the theory of fluctuations in continuum systems

The probability of occurrence of fluctuations around nonequilibrium steady states is discussed from a kinetic viewpoint. It is shown that in a large class of continuous media it is possible to extend the thermodynamic theory of fluctuations, provided one uses suitable steady-state parameters rather than equilibrium quantities.     

Mechanisms of target and spiral wave propagation in single cells

Target and spiral wave propagation have been observed in single cells such as myocites. Moreover, in the same cells, transition from target waves to planar waves or from the latter to spiral waves was also observed. Considering an oscillatory medium described by the Ginzburg-Landau equation we suggest that such phenomena could be explained if cell nuclei and cell organelles are considered as obstacles in a small bounded medium. We discuss the role of cell geometry as well as the phenomenon of reentry at the cellular level.     

Rotational effect on the thermodynamic properties of isotopes

It is shown that the differences in the thermodynamic properties of HT and D₂ is due to the fact that, for the same total mass, the distribution of mass between the two atoms is not the same. This fact introduces for the heteronuclear molecules a correlation between translational and rotational degrees of freedom. This is a pure quantal effect. A quantum-mechanical perturbation calculation shows that the energy of the ground state is higher for assemblies of heteronuclear molecules than for assemblies of homonuclear ones. On account of this the equation of state of heteronuclear hydrogen molecules is different from that of homonuclear hydrogen molecules. This permits an understanding, for example, of the higher vapour pressure of HT compared to D₂ and the anomalous behaviour of HD.     

Statistical mechanics of solid and liquid mixtures of ortho- and para-hydrogen: II

Various refinements are added to a previous theoretical calculation of the configurational free energy of condensed mixtures of o- and p-hydrogen, based on an oversimplified statistical model: (a) account is taken of the fact that the forces acting between o- and p-molecules are somewhat different and (b) the rigid lattice model previously used is replaced by an ensemble of Einstein oscillators. A better agreement with experiment is reached.