Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg-Landau equation

For spatio-temporal chaos observed in numerical simulations of the complex Ginzburg-Landau equation (CGL) and in experiments on inclined-layer convection (ILC) we report numerical and experimental data on the statistics of defects and of defect loops. These loops consist of defect trajectories in space-time that are connected to each other through the pairwise annihilation or creation of the associated defects. While most such loops are small and contain only a few defects, the loop distribution functions decay only slowly with the quantities associated with the loop size, consistent with power-law behavior. For the CGL, two of the three power-law exponents are found to agree, within our computational precision, with those from previous investigations of a simple lattice model. In certain parameter regimes of the CGL and ILC, our results for the single-defect statistics show significant deviations from the previously reported findings that the defect dynamics are consistent with those of random walkers that are created with fixed probability and annihilated through random collisions.     

Localized transverse bursts in inclined layer convection

We investigate a novel bursting state in inclined layer thermal convection in which convection rolls exhibit intermittent, localized, transverse bursts. With increasing temperature difference, the bursts increase in duration and number while exhibiting a characteristic wave number, magnitude, and size. We propose a mechanism which describes the duration of the observed bursting intervals and compare our results to bursting processes in other systems.     

Statistics of defect motion in spatiotemporal chaos in inclined layer convection

We report experiments on defect-tracking in the state of undulation chaos observed in thermal convection of an inclined fluid layer. We characterize the ensemble of defect trajectories according to their velocities, relative positions, diffusion, and gain and loss rates. In particular, the defects exhibit incidents of rapid transverse motion which result in power law distributions for a number of quantitative measures. We examine connections between this behavior and Levy flights and anomalous diffusion. In addition, we describe time-reversal and system size invariance for defect creation and annihilation rates.     

Hysteresis and competition between disorder and crystallization in sheared and vibrated granular flow

Experiments on spherical particles in a 3D annular shear cell vibrated from below and sheared from above show a hysteretic freezing or melting transition. Under sufficient vibration a crystallized state is observed, which can be melted by sufficient shear. The critical line for this transition coincides with equal kinetic energies for vibration and shear. The force distribution is double peaked in the crystalline state and single peaked with an approximately exponential tail in the disordered state. Continuous relations between pressure and volume (with dP/dV>0) exist for a continuum of partially and/or intermittently melted states over a range of parameters.     

Pattern formation in inclined layer convection

We report experiments on thermally driven convection in an inclined layer of large aspect ratio in a fluid of Prandtl number sigma approximately 1. We observed a number of new nonlinear, mostly spatiotemporally chaotic, states. At small angles of inclination we found longitudinal rolls, subharmonic oscillations, Busse oscillations, undulation chaos, and crawling rolls. At larger angles, in the vicinity of the transition from buoyancy- to shear-driven instability, we observed drifting transverse rolls, localized bursts, and drifting bimodals. For angles past vertical, when heated from above, we found drifting transverse rolls and switching diamond panes.     

Bestimmung von optischen Konstanten an Palladium und Silber aus Energieverlustmessungen im Energiebereich von 2 bis 90 eV

The energy loss functions Im (?1/?) of Silver and Palladium are determined from energy loss experiments with 60 keV electrons. The influence of surface effects and multiple losses is discussed and the values of Im (?1/?) are corrected for them. By means of Kramers-Kronig analysis the optical constants? ₁ and? ₂ are calculated from the energy loss function and found to be in good agreement with data derived from optical experiments by various authors.