arXiv subjects

Emily S. C. Ching

Publications and source records attributed to Emily S. C. Ching.

34 records · Page 2Linked to original sources

arXiv2007

Multifractality and scale invariance in human heartbeat dynamics

Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov et al., Nature {\bf 399}, 461 (1999)]. This multifractal character could be manifested as a dependence on scale or beat number of the probability density functions (PDFs) of the heart rate increments. On the other hand, scale invariance has been recently reported in a detrended analysis of healthy heart rate increments [Kiyono et al., Phys. Rev. Lett. {\bf 93}, 178103 (2004)]. In this paper, we resolve this paradox by clarifying that the scale invariance reported is actually exhibited by the PDFs of the sum of detrended healthy heartbeat intervals taken over different number of beats, and demonstrating that the PDFs of detrended healthy heart rate increments are scale dependent. Our work also establishes that this scale invariance is a general feature of human heartbeat dynamics, which is shared by heart rate fluctuations in both healthy and pathological states.

nlin.CD↗

arXiv2007

Comparison of Theory and Direct Numerical Simulations of Drag Reduction by Rodlike Polymers in Turbulent Channel Flows

Numerical simulations of turbulent channel flows, with or without additives, are limited in the extent of the Reynolds number \Re and Deborah number \De. The comparison of such simulations to theories of drag reduction, which are usually derived for asymptotically high \Re and \De, calls for some care. In this paper we present a study of drag reduction by rodlike polymers in a turbulent channel flow using direct numerical simulation and illustrate how these numerical results should be related to the recently developed theory.

nlin.CD↗

arXiv2006

Turbulent Drag Reduction by Flexible and Rodlike Polymers: Crossover Effects at Small Concentrations

Drag reduction by polymers is bounded between two universal asymptotes, the von-Kármán log-law of the law and the Maximum Drag Reduction (MDR) asymptote. It is theoretically understood why the MDR asymptote is universal, independent of whether the polymers are flexible or rodlike. The cross-over behavior from the Newtonian von-Kármán log-law to the MDR is however not universal, showing different characteristics for flexible and rodlike polymers. In this paper we provide a theory for this cross-over phenomenology.

nlin.CD↗

arXiv2005

Additive Equivalence in Turbulent Drag Reduction by Flexible and Rodlike Polymers

We address the "Additive Equivalence" discovered by Virk and coworkers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar Maximum Drag Reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.

nlin.CD↗

arXiv2004

Drag Reduction in Homogeneous Turbulence by Scale-Dependent Effective Viscosity

The phenomenon of drag reduction by polymer additives had been studied in simulations on the basis of non-Newtonian fluid mechanical models that take into account the field of polymer extension (conformation tensor) and its interaction with the velocity field. Drag reduction was found in both homogeneous and wall bounded turbulent flows. In the latter case it was shown recently that the notion of scale-dependent effective viscosity allows quantitative predictions of the characteristics of drag reduction in close correspondence with experiments. In this paper we demonstrate that also drag reduction in homogeneous turbulence is usefully discussed in terms of a scale-dependent viscosity. In other words, the essence of the phenomena under study can be recaptured by an "equivalent" equation of motion for the velocity field alone, with a judiciously chosen scale-dependent effective viscosity that succinctly summarizes the important aspects of the interaction between the polymer conformation tensor field and the velocity field. We will also clarify here the differences between drag reduction in homogeneous and wall bounded flows.

physics.flu-dyn↗

arXiv2003

Hierarchical Structure in Healthy and Diseased Heart Rate Variability in Humans

It is shown that the heart rate variability (HRV) in healthy and diseased humans possesses a hierarchical structure of the She-Leveque (SL) form. This structure, first found in measurements in turbulent fluid flows, implies further details in the HRV multifractal scaling. The potential of diagnosis is also discussed based on the characteristics derived from the SL hierarchy.

nlin.CD↗

arXiv2003

Extraction of Plumes in Turbulent Thermal Convection

We present a scheme to extract information about plumes, a prominent coherent structure in turbulent thermal convection, from simultaneous local velocity and temperature measurements. Using this scheme, we study the temperature dependence of the plume velocity and understand the results using the equations of motion. We further obtain the average local heat flux in the vertical direction at the cell center. Our result shows that heat is not mainly transported through the central region but instead through the regions near the sidewalls of the convection cell.

nlin.CD↗

arXiv2002

Active and Passive Fields in Turbulent Transport: the Role of Statistically Preserved Structures

We have recently proposed that the statistics of active fields (which affect the velocity field itself) in well-developed turbulence are also dominated by the Statistically Preserved Structures of auxiliary passive fields which are advected by the same velocity field. The Statistically Preserved Structures are eigenmodes of eigenvalue 1 of an appropriate propagator of the decaying (unforced) passive field, or equivalently, the zero modes of a related operator. In this paper we investigate further this surprising finding via two examples, one akin to turbulent convection in which the temperature is the active scalar, and the other akin to magneto-hydrodynamics in which the magnetic field is the active vector. In the first example, all the even correlation functions of the active and passive fields exhibit identical scaling behavior. The second example appears at first sight to be a counter-example: the statistical objects of the active and passive fields have entirely different scaling exponents. We demonstrate nevertheless that the Statistically Preserved Structures of the passive vector dominate again the statistics of the active field, except that due to a dynamical conservation law the amplitude of the leading zero mode cancels exactly. The active vector is then dominated by the sub-leading zero mode of the passive vector. Our work thus suggests that the statistical properties of active fields in turbulence can be understood with the same generality as those of passive fields.

nlin.CD↗

arXiv2001

Extended Self-Similarity and Hierarchical Structure in Turbulence

It is shown that the two remarkable properties of turbulence, the Extended Self-Similarity (ESS) [R. Benzi {\it et al.}, Phy. Rev. E {\bf 48}, R29, (1993)] and the She-Leveque Hierarchical Structure (SLHS) [Z.S. She and E. Leveque, Phy. Rev. Lett. {\bf 72}, 336, (1994)] are related to each other. In particular, we have shown that a generalized hierarchical structure together with the most intense structures being shock-like give rise to ESS. Our analysis thus suggests that the ESS measured in turbulent flows is an indication of the shock-like intense structures. Results of analysis of velocity measurements in a pipe-flow turbulence support our conjecture.

nlin.CD↗

arXiv2001

Dependence of heat transport on the strength and shear rate of prescribed circulating flows

We study numerically the dependence of heat transport on the maximum velocity and shear rate of physical circulating flows, which are prescribed to have the key characteristics of the large-scale mean flow observed in turbulent convection. When the side-boundary thermal layer is thinner than the viscous boundary layer, the Nusselt number (Nu), which measures the heat transport, scales with the normalized shear rate to an exponent 1/3. On the other hand, when the side-boundary thermal layer is thicker, the dependence of Nu on the Peclet number, which measures the maximum velocity, or the normalized shear rate when the viscous boundary layer thickness is fixed, is generally not a power law. Scaling behavior is obtained only in an asymptotic regime. The relevance of our results to the problem of heat transport in turbulent convection is also discussed.

nlin.CD↗

arXiv2001

Statistically Preserved Structures and Anomalous Scaling in Turbulent Active Scalar Advection

The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity field. While the odd-order correlation functions of the active and passive fields differ, we propose that the even-order correlation functions are the same to leading order (up to a trivial multiplicative factor). The leading correlation functions are statistically preserved structures of the passive scalar decaying problem, and therefore universality of the scaling exponents of the even-order correlations of the active scalar is demonstrated.

nlin.CD↗

arXiv2001

Conditional statistics of temperature fluctuations in turbulent convection

We find that the conditional statistics of temperature difference at fixed values of the locally averaged temperature dissipation rate in turbulent convection become Gaussian in the regime where the mixing dynamics is expected to be driven by buoyancy. Hence, intermittency of the temperature fluctuations in this buoyancy-driven regime can be solely attributed to the variation of the locally averaged temperature dissipation rate. We further obtain the functional behavior of these conditional temperature structure functions. This functional form demonstrates explicitly the failure of dimensional agruments and enhances the understanding of the temperature structure functions.

cond-mat.stat-mech↗

arXiv1998

Energy dependence of mass distributions in fragmentation

We study fragmentation numerically using a simple model in which an object is taken to be a set of particles that interact pairwisely via a Lennard-Jones potential while the effect of the fragmentation-induced forces is represented by some initial velocities assigned to the particles. The motion of the particles, which is given by Newton's laws, is followed by molecular dynamics calculations. As time evolves, the particles form clusters which are identified as fragments. The steady-state cumulative distribution of the fragment masses is studied and found to have an effective power-law region. The power-law exponent increases with the energy given to the particles by the fragmentation-induced forces. This result is confirmed by experiments.

cond-mat↗

arXiv1996

On Conditional Statistics in Scalar Turbulence: Theory vs. Experiment

We consider turbulent advection of a scalar field $T(\B.r)$, passive or active, and focus on the statistics of gradient fields conditioned on scalar differences $ΔT(R)$ across a scale $R$. In particular we focus on two conditional averages $\langle\nabla^2 T\big|ΔT(R)\rangle$ and $\langle|\nabla T|^2\big|ΔT(R) \rangle$. We find exact relations between these averages, and with the help of the fusion rules we propose a general representation for these objects in terms of the probability density function $P(ΔT,R)$ of $ΔT(R)$. These results offer a new way to analyze experimental data that is presented in this paper. The main question that we ask is whether the conditional average $\langle\nabla^2 T\big| ΔT(R)\rangle$ is linear in $ΔT$. We show that there exists a dimensionless parameter which governs the deviation from linearity. The data analysis indicates that this parameter is very small for passive scalar advection, and is generally a decreasing function of the Rayleigh number for the convection data.

chao-dyn↗

arXiv1996

Fusion Rules and Conditional Statistics in Turbulent Advection

Fusion rules in turbulence address the asymptotic properties of many-point correlation functions when some of the coordinates are very close to each other. Here we put to experimental test some non-trivial consequences of the fusion rules for scalar correlations in turbulence. To this aim we examine passive turbulent advection as well as convective turbulence. Adding one assumption to the fusion rules one obtains a prediction for universal conditional statistics of gradient fields. We examine the conditional average of the scalar dissipation field $\left<\nabla^2 T(\B.r)|T(\B.r+\B.R)-T(\B.r)\right>$ for $R$ in the inertial range, and find that it is linear in $T(\B.r+\B.R)-T(\B.r)$ with a fully determined proportionality constant. The implications of these findings for the general scaling theory of scalar turbulence are discussed.

chao-dyn↗

arXiv1994

Stability Limit for Mode-I Fracture

In order to study the stability of mode-I fracture, we consider a crack moving along the centerline of a very wide strip and compute its steady-state response to a small, spatially periodic shear stress. We find that, in the presence of this perturbation, the crack remains very nearly straight up to a critical speed $v_c$ of about $0.8\,v_R$, where $v_R$ is the Rayleigh speed. Deviations from straight-line propagation are suppressed by a factor proportional to $W^{-1/2}$, where $W$ is the width of the strip. At $v_c$, however, this suppression disappears and the steady-state crack follows the wavy curve along which the shear stress vanishes in the unbroken strip. We interpret this behavior as a loss of stability and discuss its implications for a more complete dynamical theory of fracture propagation.

chao-dyn↗