An instrumented tracer for Lagrangian measurements in Rayleigh-B\'enard convection

We have developed novel instrumentation for making Lagrangian measurements of temperature in diverse fluid flows. A small neutrally buoyant capsule is equipped with on-board electronics which measure temperature and transmit the data via a wireless radio frequency link to a desktop computer. The device has 80 dB dynamic range, resolving milli-Kelvin changes in temperature with up to 100 ms sampling time. The capabilities of these "smart particles" are demonstrated in turbulent thermal convection in water. We measure temperature variations as the particle is advected by the convective motion, and analyse its statistics. Additional use of cameras allow us to track the particle position and to report here the first direct measurement of Lagrangian heat flux transfer in Rayleigh-B{\'e}nard convection. The device shows promise for opening new research in a broad variety of fluid systems.Comment: 14 page

Liquid sodium model of Earth's outer core

Convective motions in Earth's outer core are responsible for the generation of the geomagnetic field. We present liquid sodium convection experiments in a spherical vessel, designed to model the convective state of Earth's outer core. Heat transfer, zonal fluid velocities, and properties of temperature fluctuations were measured for different rotation rates and temperature drops across the convecting sodium. The small scale fluid motion was highly turbulent, despite the fact that less than half of the total heat transfer was due to convection. Retrograde zonal velocities were measured at speeds up to 0.02 times the tangential speed of the outer wall of the vessel. Power spectra of temperature fluctuations indicate a well defined knee characterizing the convective energy input. This frequency is proportional to the ballistic velocity estimate. In the context of Earth's outer core, our observations imply a thermal Rayleigh number Ra=10^22, a convective velocity near 10^-5 m/s, and length and time scales of convective motions of 100 m and 2 days

Force measurements on rising bubbles

The dynamics of millimeter sized air bubbles rising through still water are investigated using precise ultrasound velocity measurements combined with high speed video. From measurements of speed and three dimensional tra jectories we deduce the forces on the bubble which give rise to planar zigzag and spiraling motion

Inhibition causes ceaseless dynamics in networks of excitable nodes

The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability of activation of network neighbors. We show that, although the direct effect of inhibitory nodes is to decrease activity, the collective dynamics becomes self-sustaining. We explain this counterintuitive result by defining and analyzing a "branching function" which may be thought of as an activity-dependent branching ratio. The shape of the branching function implies that for a range of global coupling parameters dynamics are self-sustaining. Within the self-sustaining region of parameter space lies a critical line along which dynamics take the form of avalanches with universal scaling of size and duration, embedded in ceaseless timeseries of activity. Our analyses, confirmed by numerical simulation, suggest that inhibition may play a counterintuitive role in excitable networks.Comment: 11 pages, 6 figure

Polymer and surface roughness effects on the drag crisis for falling spheres

8 pagesWe make time resolved velocity measurements of steel spheres in free fall through liquid using a continuous ultrasound technique. We explore two different ways to induce large changes in drag on the spheres: 1) a small quantity of viscoelastic polymer added to water and 2) altering the surface of the sphere. Low concentration polymer solutions and/or a pattern of grooves in the sphere surface induce an early drag crisis, which may reduce drag by more than 50 percent compared to smooth spheres in pure water. On the other hand, random surface roughness and/or high concentration polymer solutions reduce drag progressively and suppress the drag crisis. We also present a qualititative argument which ties the drag reduction observed in low concentration polymer solutions to the Weissenberg number and normal stress difference

Predicting criticality and dynamic range in complex networks: effects of topology

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a critical regime with maximum dynamic range. We gain deeper insight on the effects of network topology using a nonlinear analysis in terms of additional spectral properties of the adjacency matrix. We find that homogeneous networks can reach a higher dynamic range than those with heterogeneous topology. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.Comment: 4 pages, 3 figure

Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus

We study the effects of network topology on the response of networks of coupled discrete excitable systems to an external stochastic stimulus. We extend recent results that characterize the response in terms of spectral properties of the adjacency matrix by allowing distributions in the transmission delays and in the number of refractory states, and by developing a nonperturbative approximation to the steady state network response. We confirm our theoretical results with numerical simulations. We find that the steady state response amplitude is inversely proportional to the duration of refractoriness, which reduces the maximum attainable dynamic range. We also find that transmission delays alter the time required to reach steady state. Importantly, neither delays nor refractoriness impact the general prediction that criticality and maximum dynamic range occur when the largest eigenvalue of the adjacency matrix is unity