Inertia Induces Strong Orientation Fluctuations of Nonspherical Atmospheric Particles.

The orientation of nonspherical particles in the atmosphere, such as volcanic ash and ice crystals, influences their residence times and the radiative properties of the atmosphere. Here, we demonstrate experimentally that the orientation of heavy submillimeter spheroids settling in still air exhibits decaying oscillations, whereas it relaxes monotonically in liquids. Theoretical analysis shows that these oscillations are due to particle inertia, caused by the large particle-fluid mass-density ratio. This effect must be accounted for to model solid particles in the atmosphere.

Lagrangian Supersaturation Fluctuations at the Cloud Edge.

Evaporation of cloud droplets accelerates when turbulence mixes dry air into the cloud, affecting droplet-size distributions in atmospheric clouds, combustion sprays, and jets of exhaled droplets. The challenge is to model local correlations between droplet numbers, sizes, and supersaturation, which determine supersaturation fluctuations along droplet paths (Lagrangian fluctuations). We derived a statistical model that accounts for these correlations. Its predictions are in quantitative agreement with results of direct numerical simulations, and explain the key mechanisms at play.

Stochastic Interpolation of Sparsely Sampled Time Series via Multipoint Fractional Brownian Bridges.

We propose and test a method to interpolate sparsely sampled signals by a stochastic process with a broad range of spatial and/or temporal scales. To this end, we extend the notion of a fractional Brownian bridge, defined as fractional Brownian motion with a given scaling (Hurst) exponent H and with prescribed start and end points, to a bridge process with an arbitrary number of intermediate and nonequidistant points. Determining the optimal value of the Hurst exponent H_{opt}, appropriate to interpolate the sparse signal, is a very important step of our method. We demonstrate the validity of our method on a signal from fluid turbulence in a high Reynolds number flow and discuss the implications of the non-self-similar character of the signal. The method introduced here could be instrumental in several physical problems, including astrophysics, particle tracking, and specific tailoring of surrogate data, as well as in domains of natural and social sciences.

Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence.

The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parametrization of the distribution of ice crystals in clouds, and potentially lead to an improved understanding of radiation reflection or particle aggregation through collisions in clouds.

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.

Energy flux fluctuations in a finite volume of turbulent flow.

The flux of turbulent kinetic energy from large to small spatial scales is measured in a small domain of varying size . The probability distribution function of the flux is obtained using a time-local version of Kolmogorov four-fifths law. The measurements, made at a moderate Reynolds number, show frequent events where the flux is backscattered from small to large scales, their frequency increasing as is decreased. The observations are corroborated by a numerical simulation based on the motion of many particles and on an explicit form of the eddy damping.

Pinning force in active media.

Pinning of vortices by defects plays an important role in various physical (superconductivity, superfluidity, etc.) or biological (propagation in cardiac muscle) situations. Which defects act as pinning centers? We propose a way to study this general problem by using an advection field to quantify the attraction between an obstacle and a vortex. A full solution is obtained for the real Ginzburg-Landau equation (RGLE). Two pinning mechanisms are found in excitable media. Our results suggest strong analogies with the RGLE when the heterogeneity is excitable. Unpinning from an unexcitable obstacle is qualitatively harder, resulting in a stronger pinning force. We discuss the implications of our results to control vortices and propose experiments in a chemical active medium and in cardiac tissue.

A physical approach to remove anatomical reentries: a bidomain study.

Controlling cardiac chaos is often achieved by applying a large damaging electric shock-defibrillation. It removes all waves, without differentiating reentries and normal waves, anatomical and functional reentries. Anatomical reentries can be removed by anti-tachycardia pacing (ATP) as well. But ATP requires the knowledge of the position of the reentry, and an access to it with an invasive stimulating electrode. We show that the physics of electric field distribution between cardiac cells permits one to deliver an electric pulse exactly to the core of an anatomical reentry, without knowing its position and even to locations where access with a stimulating electrode is not possible. The energy needed is two orders of magnitude less than defibrillation energy. The results are insensitive to both a detailed ionic model and to the geometry of the fibers.

Unpinning and removal of a rotating wave in cardiac muscle.

Rotating waves in cardiac muscle may be pinned to a heterogeneity, as it happens in superconductors or in superfluids. We show that the physics of electric field distribution between cardiac cells permits one to deliver an electric pulse exactly to the core of a pinned wave, without knowing its position, and even to locations where a direct access is not possible. Thus, unpinning or removal of rotating waves can be achieved. The energy needed is 2 orders of magnitude less than defibrillation energy. This opens a way to new manipulations with pinned vortices both in experiments and in cardiac clinics.

Kinematic simulation of turbulent dispersion of triangles.

As three particles are advected by a turbulent flow, they separate from each other and develop nontrivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of three Lagrangian particles advected, in two dimensions, by kinematic simulation (KS). KS is a Lagrangian model of turbulent diffusion that makes no use of any delta correlation in time at any level. With this approach, situations with a very large range of inertial scales and varying persistence of spatial flow structure can be studied. We first demonstrate that the model flow reproduces recent experimental results at low Reynolds numbers. The statistical properties of the shape distribution at a much higher Reynolds number is then considered. The numerical results support the existence of nontrivial shape statistics, with a high probability of having elongated triangles. Even at the highest available inertial range of scales, corresponding to a ratio between large and small scale L/eta=17,000, a perfect self-similar regime is not found. The effects of the parameters of the synthetic flow, such as the exponent of the spectrum and the effect of the sweeping affect our results, are also discussed. Special attention is given to the effects of persistence of spatial flow structure.

Evolution of triangles in a two-dimensional turbulent flow.

As a turbulent flow advects a swarm of Lagrangian markers, the mutual separation between particles grows, and the shape of the swarm gets distorted. By following three points in an experimental turbulent two-dimensional flow with a k(-5/3) spectrum, we investigate the geometry of triangles, in a statistical sense. Two well-characterized shape distributions are identified. At long times when the average size of the triangles is larger than the integral scale, the distribution of shapes is Gaussian. When the size of the triangle is in the inertial range and grows as t(3/2) (Richardson's law), a plausibly self-similar, non-Gaussian probability distribution is observed, where very elongated triangles have a much larger probability than in the Gaussian regime. These results are discussed, and, in the latter case, compared with the predictions of a stochastic model recently introduced [A. Pumir et al., Phys. Rev. Lett. 85, 5324 (2000)].

Statistics of Fourier modes in a turbulent flow.

Fourier series are often used to discuss the properties of a homogeneous turbulent field. We investigate the statistics of Fourier modes of the turbulent velocity field and of a passive scalar. The statistics of individual Fourier modes is known to be Gaussian when the size of the system L is much larger that the integral (correlation) size l(0). The case where the integral size is of the order of the system size L approximately l(0), is studied by direct numerical simulations in the range 20 < or approximately = Rlambda < or approximately = 80. At a given Rlambda, we find that the probabilities of large fluctuations become larger when the wave number increases, in qualitative agreement with the notion of intermittency. As the Reynolds number increases, however, the probability density functions become closer to Gaussian, in sharp contrast with the behavior of velocity increments. We also show that in a simple model of cascade, the Fourier series decomposition is not appropriate to capture intermittency effects. Last, we discuss other issues related to our results.

Geometry of Lagrangian dispersion in turbulence.

Turbulent flows disperse Lagrangian particles resulting in the growth of pairwise separations and, for sets of three or more particles, in a nontrivial dynamics of their configuration. The shape of such clusters is controlled by the competition between coherent straining of the cluster and the independent random motion of the particles due to small scale velocity fluctuations. We introduce a statistical description of the geometry of the Lagrangian clusters and predict a self-similar distribution of shapes, which should be observable in the inertial range of scales in high Reynolds numbers flows.

Unpinning of a rotating wave in cardiac muscle by an electric field.

The possibility of terminating cardiac arrhythmias with electric fields of moderate intensity is a challenging problem from a fundamental point of view and an important issue for clinical applications. In an effort to understand how anatomical re-entries are affected by electric fields, we found that a weak shock, with an amplitude of an order of magnitude less than the defibrillating shock, may unpin the vortices rotating around the defects (obstacles). The unpinning results from a depolarization of the tissue near the obstacle, induced by an external electric field within a distance of order lambda approximately 1 mm. Unpinning was observed both in the FitzHugh model of excitable tissue, and in a specific Beeler-Reuter model of cardiac tissue. This theoretical observation suggests that anatomical re-entries can be transformed into functional re-entries, an effect that can be tested in experiments with cardiac muscle.

Planar isotropy of passive scalar turbulent mixing with a mean perpendicular gradient.

A recently proposed evolution equation [Vaienti et al., Physica D 85, 405 (1994)] for the probability density functions (PDF's) of turbulent passive scalar increments obtained under the assumptions of fully three-dimensional homogeneity and isotropy is submitted to validation using direct numerical simulation (DNS) results of the mixing of a passive scalar with a nonzero mean gradient by a homogeneous and isotropic turbulent velocity field. It is shown that this approach leads to a quantitatively correct balance between the different terms of the equation, in a plane perpendicular to the mean gradient, at small scales and at large Péclet number. A weaker assumption of homogeneity and isotropy restricted to the plane normal to the mean gradient is then considered to derive an equation describing the evolution of the PDF's as a function of the spatial scale and the scalar increments. A very good agreement between the theory and the DNS data is obtained at all scales. As a particular case of the theory, we derive a generalized form for the well-known Yaglom equation (the isotropic relation between the second-order moments for temperature increments and the third-order velocity-temperature mixed moments). This approach allows us to determine quantitatively how the integral scale properties influence the properties of mixing throughout the whole range of scales. In the simple configuration considered here, the PDF's of the scalar increments perpendicular to the mean gradient can be theoretically described once the sources of inhomogeneity and anisotropy at large scales are correctly taken into account.

Deexcitation of cardiac cells.

Excitation and deexcitation are fundamental phenomena in the electrophysiology of excitable cells. Both of them can be induced by stimulating a cell with intracellularly injected currents. With extracellular stimulation, deexcitation was never observed; only cell excitation was found. Why? A generic model with two variables (FitzHugh) predicts that an extracellular stimulus can both excite the cell and terminate the action potential (AP). Our experiments with single mouse myocytes have shown that short (2-5 ms) extracellular pulses never terminated the AP. This result agrees with our numerical experiments with the Beeler-Reuter model. To analyze the problem, we exploit the separation of time scales to derive simplified models with fewer equations. Our analysis has shown that the very specific form of the current-voltage (I-V) characteristics of the time-independent potassium current (almost no dependence on voltage for positive membrane potentials) is responsible here. When the shape of the I-V characteristics of potassium currents was modified to resemble that in ischemic tissues, or when the external potassium concentration (K0) is increased, the AP was terminated by extracellular pulses. These results may be important for understanding the mechanisms of defibrillation.

Models of defibrillation of cardiac tissue.

Heterogeneities, such as gap junctions, defects in periodical cellular lattices, intercellular clefts and fiber curvature allow one to understand the effect of an electric field in cardiac tissue. They induce membrane potential variations even in the bulk of the myocardium, with a characteristic sawtooth shape. The sawtooth potential, induced by heterogeneities at large scales (tissue strands) can be more easily observed, and lead to stronger effects than the one induced at the cellular level. In the generic model of propagation in cardiac tissue (FitzHugh), 4 mechanisms of defibrillation were found, two mechanisms based on excitation (E(A),E(M)), and two-on de-excitation (D(A),D(M)). The lowest electric field is required by an E(M) mechanism. In the Beeler-Reuter ionic model, mechanism D(M) is impossible. We critically review the experimental basis of the theory and propose new experiments. (c) 1998 American Institute of Physics.

Two biophysical mechanisms of defibrillation of cardiac tissue.

We have studied the mechanisms whereby a strong electric shock terminates chaotic wave propagation in cardiac tissue (defibrillation). In a generic model of cellular excitable tissue with two variables, we have found two mechanisms: one based on excitation (E), and another based on de-excitation (D) of cells by the small scale periodic component of transmembrane potential induced by the shock. Symmetry properties of the current-voltage characteristics describing the dynamics of the fast ionic currents, along with the strength of the electric field determine which of these mechanisms operates. A prediction of this work to be tested experimentally is that upon increasing the electric field one mechanism may switch to another, resulting in the following unusual sequence of events: defibrillation is first possible by mechanism E at moderate fields, then impossible, and finally possible by mechanism D, at higher fields.