Snakes: Oriented families of periodic orbits,their sources,sinks, and continuation

Poincaré observed that for a differential equation $\text{x′ = ?(x, α)}$ depending on a parameter α, each periodic orbit generally lies in a connected family of orbits in (x, α)-space. In order to investigate certain large connected sets (denoted Q) of orbits containing a given orbit, we introduce two indices: an orbit index φ and a “center” index

defined at certain stationary points. We show that genetically there are two types of Hopf bifurcation, those we call “sources” ($\textcolor{red}{}\text{= 1}$) and “sinks” ($\textcolor{red}{}\text{= ?1}$). Generically if the set Q is bounded in (x, α)-space, and if there is an upper bound for periods of the orbits in Q, then Q must have as many source Hopf bifurcations as sink Hopf bifurcations and each source is connected to a sink by an oriented one-parameter “snake” of orbits. A “snake” is a maximal path of orbits that contains no orbits whose orbit index is 0. See Fig. 1.1.     

Fractal basin boundaries generated by basin cells and the geometry of mixing chaotic flows

Experiments and computations indicate that mixing in chaotic flows generates certain coherent spatial structures. If a two-dimensional basin has a basin cell (a trapping region whose boundary consists of pieces of the stable and unstable manifold of some periodic orbit) then the basin consists of a central body (the basin cell) and a finite number of channels attached to it and the basin boundary is fractal. We demonstrate an amazing property for certain global structures: A basin has a basin cell if and only if every diverging curve comes close to every basin boundary point of that basin.     

Electrical properties and spin fluctuations studies of Y(Co1−xNix)2 compounds

Synthesis by arc melting, the structural and the electric properties of Y(Co_1−xNi_x)₂ alloys were studied by X-ray diffraction (XRD) and four probe dc electrical measurements. XRD analysis (300 K) shows that all samples crystallize in a cubic MgCu₂-type structure. The lattice parameters linearly decrease with Ni content. Electrical resistivity for the Y(Co_1−xNi_x)₂ intermetallic series was measured in a temperature range of 15-1100 K. The parameters involved in the dependence of resistivity on temperature were determined. Residual, phonon and spin fluctuations resistivity were separated from electrical resistivity using both the Matthiesen formula and the Bloch-Gruneisen formula. The spin fluctuations resistivity of the Y(Co_1−xNi_x)₂ series are compared to the mean square amplitudes of spin fluctuations previously calculated by the Linear Muffin Tin Orbital-Tight Binding Approach method for these series in the literature. The contribution of spin fluctuations to total resistivity ρ_sf is proportional to T² at low temperatures. The proportionality parameter strongly reduces across the Y(Co_1−xNi_x)₂ series.     

Photoelectronic characterization of n-type silicon wafers using photocarrier radiometry

Photocarrier radiometry (PCR) was used to characterize four n-type silicon wafers with different resistivity values in the 1-20 Ω cm range. Simulations of the PCR signal have been performed to study the influence of the recombination lifetime and front surface recombination velocity on them; besides, the transport parameters (carrier recombination lifetime, diffusion coefficient, and frontal surface recombination) of the wafers were obtained by means of a fitting procedure. The PCR images that are related to the lifetime are presented, and the first photoelectronic images of a porous silicon sample are obtained.