Abstract: We have performed a comparative experimental study of the bifurcations in circular Couette flow and Rayleigh-Btnard convection, two systems which long served as classical prototypes for experimental and theoretical investigations of hydrodynamic stability.”* In circular Couette flow in its simplest form a fluid is contained between concentric cylinders with the inner cylinder rotating, and in Rayleigh-Bknard convection the fluid is contained between horizontal thermally conducting plates heated from below. The bifurcation parameter for the Couette flow system can be taken as the Reynolds number R , which describes the distance away from equilibrium and is proportional to the angular velocity of the inner cylinder. Similarly, for the Rayleigh-Btrnard problem the distance away from equilibrium is given by a dimensionless number R , the Rayleigh number, which is proportional to the difference between the temperatures of the two horizontal plates. At small R the flow in the Couette cell is purely azimuthal, but when the Reynolds number exceeds a critical value R , the azimuthal circular Couette flow is no longer stable and there is a bifurcation to a flow with a horizontal toroidal vortex pattern superimposed on the azimuthal flow. This bifurcation was predicted and observed by Taylor in 1923 in work that stands as a classic study of hydrodynamic ~ t a b i l i t y . ~ In 191 6 Rayleigh showed, in the pioneering theoretical paper on the convective instability, that above R, the pure conduction state is unstable to horizontal disturbances, and the system bifurcates to a new state consisting of parallel convection As R is increased further both the circular Couette flow and Rayleigh-Btnard systems bifurcate from the time-independent vortex patterns to time-dependent flows. These secondary bifurfactions have been studied theoretically and experimentally for the past few years; however, there has been little detailed quantita-

Abstract: One considers a perturbed ordinary differential system which is then reduced to the non-perturbed corresponding system; i.e. the existence of a global relation between the solutions of the two systems is established. From this it is easy to deduce the difference between two correspondent solutions, and the theorems of existence for particular solutions (periodic, quasiperiodic,…) or integral manifolds, of the initial system.

Abstract: A rocket observation of two pulsating X-ray binaries, 4U0900-40 and 4U1223-62, found no evidence for periodic or quasiperiodic behavior on time scales down to 2 ms. Evidence for complex high-energy spectral features and intrapulse variability is presented for 4U0900-40.

Abstract: Self-images of a number of spatially periodic (e.g., gratings) and quasiperiodic (e.g., halftone picture) objects have been systematically studied. These studies indicate that self-imaging techniques could be useful in optical computing type operations. It is also established that the Rayleigh relation in the context of self-imaging is quantitatively in error.

Abstract: Measurements of the fluctuations in local velocity in fluid motion between a rotating inner cylinder and a fixed outer cylinder are reported for rotation rates up to $67{R}_{c}$, where ${R}_{c}$ is the critical Reynolds number for Taylor instability. The Reynolds number ${R}_{t}$ for which the transition from periodic or quasiperiodic to aperiodic flow occurs depends strongly on aspect ratio ($\ensuremath{\Gamma}=\mathrm{fluid}\mathrm{height}/\mathrm{gap}$): ${R}_{t}\ensuremath{\simeq}22{R}_{c}$ for $\ensuremath{\Gamma}=20$; ${R}_{t}\ensuremath{\simeq}26{R}_{c}$ for $\ensuremath{\Gamma}=80$. For $\ensuremath{\Gamma}\ensuremath{\gtrsim}25$ a sharp periodic component reemerges in the power spectrum for $28{R}_{c}\ensuremath{\lesssim}R\ensuremath{\lesssim}36{R}_{c}$.

Abstract: Nonadiabatic transitions are, strictly, those arising from a breakdown of the Born-Oppenheimer approximation, the term adiabatic being reserved for the limit in which the electronic problem is solved with the nuclei fixed. This corresponds to a situation in which, in classical terms, the electrons would pass through many cycles of their periodic or quasiperiodic(1) motion in a time short compared with that required to achieve a significant perturbation to this motion by changing the nuclear geometry.