In situ cloud particle tracking experiment.

The collision-coalescence process of inertial particles in turbulence is held responsible for the quick growth of cloud droplets from ∼15 to ∼50 µm in diameter, but it is not well understood. Turbulence has two effects on cloud droplets: (1) it brings them closer together, preferentially concentrating them in certain parts of the flow, and (2) it sporadically creates high accelerations, causing droplets to detach from the underlying flow. These turbulence-cloud droplet interactions are difficult to study numerically or in the laboratory due to the large range of scales involved in atmospheric turbulence, so in situ measurements are needed. Here, we present a Lagrangian particle tracking (LPT) experimental setup situated close to the summit of Mt. Zugspitze at an altitude of 2650 m above the sea level on top of the environmental research station Schneefernerhaus. Clouds naturally occur at this location about a quarter of the time. The LPT experiment probes a volume of ∼40 × 20 × 12 mm3, has a spatial resolution of 5 µm and a temporal resolution of 0.1 ms, and measures accelerations to within 0.1 m s-2. Furthermore, the experiment can slide over a set of rails, driven by a linear motor, to compensate for the mean wind. It can slide up to 7.5 m s-1. By doing so, the average residence time of the particles in the measurement volume increases. The mean wind compensation allows us to study various dynamical quantities, such as the velocity autocorrelation, or the dynamics of clustering. Moreover, it is beneficial for particle tracking, in general, since longer particle tracks allow us to apply better filtering to the tracks and thus increase accuracy. We present the radial distribution function, which quantifies clustering, the longitudinal relative velocity distribution, and the Lagrangian velocity autocorrelation, all computed from cloud droplet trajectories.

Periodic sequence of stabilized wave segments in an excitable medium.

Numerical computations show that a stabilization of a periodic sequence of wave segments propagating through an excitable medium is possible only in a restricted domain within the parameter space. By application of a free-boundary approach, we demonstrate that at the boundary of this domain the parameter H introduced in our Rapid Communication is constant. We show also that the discovered parameter predetermines the propagation velocity and the shape of the wave segments. The predictions of the free-boundary approach are in good quantitative agreement with results from numerical reaction-diffusion simulations performed on the modified FitzHugh-Nagumo model.

Unusual spiral wave dynamics in the Kessler-Levine model of an excitable medium.

The Kessler-Levine model is a two-component reaction-diffusion system that describes spatiotemporal dynamics of the messenger molecules in a cell-to-cell signaling process during the aggregation of social amoeba cells. An excitation wave arising in the model has a phase wave at the wave back, which simply follows the wave front after a fixed time interval with the same propagation velocity. Generally speaking, the medium excitability and the refractoriness are two important factors which determine the spiral wave dynamics in any excitable media. The model allows us to separate these two factors relatively easily since the medium refractoriness can be changed independently of the medium excitability. For rigidly rotating waves, the universal relationship has been established by using a modified free-boundary approach, which assumes that the front and the back of a propagating wave are thin in comparison to the wave plateau. By taking a finite thickness of the domain boundary into consideration, the validity of the proposed excitability measure has been essentially improved. A novel method of numerical simulation to suppress the spiral wave instabilities is introduced. The trajectories of the spiral tip observed for a long refractory period have been investigated under a systematic variation of the medium refractoriness.

Crosstalk of cardiomyocytes and fibroblasts in co-cultures.

Electromechanical function of cardiac muscle depends critically on the crosstalk of myocytes with non-myocytes. Upon cardiac fibrosis, fibroblasts translocate into infarcted necrotic tissue and alter their communication capabilities. In the present in vitro study, we determined a multiple parameter space relevant for fibrotic cardiac tissue development comprising the following essential processes: (i) adhesion to substrates with varying elasticity, (ii) dynamics of contractile function, and (iii) electromechanical connectivity. By combining electric cell-substrate impedance sensing (ECIS) with conventional optical microscopy, we could measure the impact of fibroblast-cardiomyocyte ratio on the aforementioned parameters in a non-invasive fashion. Adhesion to electrodes was quantified via spreading rates derived from impedance changes, period analysis allowed us to measure contraction dynamics and modulations of the barrier resistance served as a measure of connectivity. In summary, we claim that: (i) a preferred window for substrate elasticity around 7 kPa for low fibroblast content exists, which is shifted to stiffer substrates with increasing fibroblast fractions. (ii) Beat frequency decreases nonlinearly with increasing fraction of fibroblasts, while (iii) the intercellular resistance increases with a maximal functional connectivity at 75% fibroblasts. For the first time, cardiac cell-cell junction density-dependent connectivity in co-cultures of cardiomyocytes and fibroblasts was quantified using ECIS.

Flow-driven waves and phase-locked self-organization in quasi-one-dimensional colonies of Dictyostelium discoideum.

We report experiments on flow-driven waves in a microfluidic channel containing the signaling slime mold Dictyostelium discoideum. The observed cyclic adenosine monophosphate (cAMP) wave trains developed spontaneously in the presence of flow and propagated with the velocity proportional to the imposed flow velocity. The period of the wave trains was independent of the flow velocity. Perturbations of flow-driven waves via external periodic pulses of the signaling agent cAMP induced 1∶1, 2∶1, 3∶1, and 1∶2 frequency responses, reminiscent of Arnold tongues in forced oscillatory systems. We expect our observations to be generic to active media governed by reaction-diffusion-advection dynamics, where spatially bound autocatalytic processes occur under flow conditions.

Variable density turbulence tunnel facility.

The Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany, produces very high turbulence levels at moderate flow velocities, low power consumption, and adjustable kinematic viscosity between 10(-4) m(2)/s and 10(-7) m(2)/s. The Reynolds number can be varied by changing the pressure or flow rate of the gas or by using different non-flammable gases including air. The highest kinematic viscosities, and hence lowest Reynolds numbers, are reached with air or nitrogen at 0.1 bar. To reach the highest Reynolds numbers the tunnel is pressurized to 15 bars with the dense gas sulfur hexafluoride (SF6). Turbulence is generated at the upstream ends of two measurement sections with grids, and the evolution of this turbulence is observed as it moves down the length of the sections. We describe the instrumentation presently in operation, which consists of the tunnel itself, classical grid turbulence generators, and state-of-the-art nano-fabricated hot-wire anemometers provided by Princeton University [M. Vallikivi, M. Hultmark, S. C. C. Bailey, and A. J. Smits, Exp. Fluids 51, 1521 (2011)]. We report measurements of the characteristic scales of the flow and of turbulent spectra up to Taylor Reynolds number R(λ) ≈ 1600, higher than any other grid-turbulence experiment. We also describe instrumentation under development, which includes an active grid and a Lagrangian particle tracking system that moves down the length of the tunnel with the mean flow. In this configuration, the properties of the turbulence are adjustable and its structure is resolvable up to R(λ) ≈ 8000.

Continuous transition between two limits of spiral wave dynamics in an excitable medium.

By application of a free-boundary approach, we prove the existence of a continuous transition and a full spectrum of solutions between the two known limits of spiral wave dynamics. We identify a control parameter whose essential importance was not realized in earlier studies of spatiotemporal pattern selection in excitable media. The predictions of the free-boundary approach are in good quantitative agreement with results from numerical reaction-diffusion simulations performed on the modified Barkley model.

Selection of spiral waves in excitable media with a phase wave at the wave back.

Universal relationships between the medium excitability and the angular velocity and the core radius of rigidly rotating spiral waves in excitable media are derived for situations where the wave front is a trigger wave and the wave back is a phase wave. Two universal limits restricting the region of existence of spiral waves in the parameter space are demonstrated. The predictions of the free-boundary approach are in good quantitative agreement with results from numerical reaction-diffusion simulations performed on the Kessler-Levine model.

Pattern forming system in the presence of different symmetry-breaking mechanisms.

We report experiments on spatially forced inclined layer convection, where the combined effect of the intrinsic symmetry breaking due to a gravity-induced shear flow and spatially periodic 1D forcing is studied. We observed pattern selection processes resulting in stabilization of spatiotemporal chaos and the emergence of novel two-dimensional states. Phase diagrams depicting the different observed states for typical forcing scenarios are presented. Convection in the weakly nonlinear regime is compared with theory, and a good agreement is found.

Universal intermittent properties of particle trajectories in highly turbulent flows.

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

Wave emission from heterogeneities opens a way to controlling chaos in the heart.

The effectiveness of chaos control in large systems increases with the number of control sites. We find that electric field induced wave emission from heterogeneities (WEH) in the heart gives a unique opportunity to have as many control sites as needed. The number of pacing sites grows with the amplitude of the electric field. We demonstrate that WEH has important advantages over methods used in clinics, and opens a new way to manipulate vortices in experiments, and potentially to radically improve the clinical methods of chaos control in the heart.

Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence.

We describe Lagrangian measurements of water droplets in grid generated wind tunnel turbulence at a Taylor Reynolds number of R(lambda)=250 and an average Stokes number (St) of approximately 0.1. The inertial particles are tracked by a high speed camera moving along the side of the tunnel at the mean flow speed. The standardized acceleration probability density functions of the particles have spread exponential tails that are narrower than those of a fluid particles (St approximately 0) and there is a decrease in the acceleration variance with increasing Stokes number. A simple vortex model shows that the inertial particles selectively sample the fluid field and are less likely to experience regions of the fluid undergoing the largest accelerations. Recent direct numerical simulations compare favorably with these first measurements of Lagrangian statistics of inertial particles in highly turbulent flows.

Double dendrite growth in solidification.

We present experiments on the doublon growth morphology in directional solidification. Samples used are succinonitrile with small amounts of poly(ethylene oxide), acetone, or camphor as the solute. Doublons, or symmetry-broken dendrites, are generic diffusion-limited growth structures expected at large undercooling and low anisotropy. Low anisotropy growth is achieved by selecting a grain near the {111} plane leading to either seaweed (dense branching morphology) or doublon growth depending on experimental parameters. We find selection of doublons to be strongly dependent on solute concentration and sample orientation. Doublons are selected at low concentrations (low solutal undercooling) in contrast to the prediction of doublons at large thermal undercooling in pure materials. Doublons also exhibit preferred growth directions and changing the orientation of a specific doublonic grain changes the character and stability of the doublons. We observe transitions between seaweed and doublon growth with changes in concentration and sample orientation.

Dislocation dynamics in Rayleigh-Bénard convection.

Theoretical results on the dynamics of dislocations in Rayleigh-Bénard convection are reported both for a Swift-Hohenberg model and the Oberbeck-Boussinesq equations. For intermediate Prandtl numbers the motion of dislocations is found to be driven by the superposition of two independent contributions: (i) the Peach-Koehler force and (ii) an advection force on the dislocation core by its self-generated mean flow. Their competition allows to explain the experimentally observed bound dislocation pairs.

Dynamics of low anisotropy morphologies in directional solidification.

We report experimental results on quasi-two-dimensional diffusion limited growth in directionally solidified succinonitrile with small amounts of poly(ethylene oxide), acetone, or camphor as a solute. Seaweed growth, or dense branching morphology, is selected by growing grains close to the [111] plane, where the in-plane surface tension is nearly isotropic. The observed growth morphologies are very sensitive to small anisotropies in surface tension caused by misorientations from the [111] plane. Different seaweed morphologies are found, including the degenerate, the stabilized, and the strongly tilted seaweeds. The degenerate seaweeds show a limited fractal scaling range and, with increased undercooling, suggests a transition from "fractal" to "compact" seaweed. Strongly tilted seaweeds demonstrate a significant twofold anisotropy. In addition, seaweed-dendrite transitions are observed in low anisotropy growth.

Alternating tip splitting in directional solidification.

We report experimental results on the tip splitting dynamics of seaweed growth in directional solidification of succinonitrile alloys. Despite the random appearance of the growth, a tip splitting morphology was observed in which the tip alternately splits to the left and to the right. The tip splitting frequency f was found to be related to the growth velocity V as a power law f~V1.5. This finding is consistent with the predictions of a tip splitting model that is also presented. Small anisotropies are shown to lead to different kinds of seaweed morphologies.

Fluid particle accelerations in fully developed turbulence.

The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport, processes in stirred chemical reactors and combustion systems, and in the industrial production of nanoparticles. The concept of particle trajectories has been used successfully to describe mixing and transport in turbulence, but issues of fundamental importance remain unresolved. One such issue is the Heisenberg-Yaglom prediction of fluid particle accelerations, based on the 1941 scaling theory of Kolmogorov. Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that, within experimental errors, Kolmogorov scaling of the acceleration variance is attained at high Reynolds numbers. Our data indicate that the acceleration is an extremely intermittent variable--particles are observed with accelerations of up to 1,500 times the acceleration of gravity (equivalent to 40 times the root mean square acceleration). We find that the acceleration data reflect the anisotropy of the large-scale flow at all Reynolds numbers studied.

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.