arXiv subjects

Alain Pumir

Publications and source records attributed to Alain Pumir.

At least 55 records · Page 3Linked to original sources

arXiv2015

Collisional Aggregation due to Turbulence

Collisions between particles suspended in a fluid play an important role in many physical processes. As an example, collisions of microscopic water droplets in clouds are a necessary step in the production of macroscopic raindrops. Collisions of dust grains are also conjectured to be important for planet formation in the gas surrounding young stars, and also to play a role in the dynamics of sand storms. In these processes, collisions are favoured by fast turbulent motions. Here we review recent advances in the understanding of collisional aggregation due to turbulence. We discuss the role of fractal clustering of particles, and caustic singularities of their velocities. We also discuss limitations of the Smoluchowski equation for modelling these processes. These advances lead to a semi-quantitative understanding on the influence of turbulence on collision rates, and point to deficiencies in the current understanding of rainfall and planet formation.

physics.flu-dyn↗

arXiv2015

Irreversibility and small-scale generation in 3D turbulent flows

In three-dimensional turbulent flows energy is supplied at large scales and cascades down to the smallest scales where viscosity dominates. The flux of energy through scales implies the generation of small scales from larger ones, which is the fundamental reason for the irreversibility of the dynamics of turbulent flows. As we showed recently, this irreversibility manifests itself by an asymmetry of the probability distribution of the instantaneous power $p$ of the forces acting on fluid elements. In particular, the third moment of $p$ was found to be negative. Yet, a physical connection between the irreversibility manifested in the distribution of $p$ and the energy flux or small-scale generation in turbulence has not been established. Here, with analytical calculations and support from numerical simulations of fully developed turbulence, we connect the asymmetry in the power distribution, {\it i.e.}, the negative value of $\langle p^3 \rangle$, to the generation of small scales, or more precisely, to the amplification (stretching) of vorticity in turbulent flows. Our result is the first step towards a quantitative understanding of the origin of the irreversibility observed at the level of individual Lagrangian trajectories in turbulent flows.

physics.flu-dyn↗

arXiv2015

Lagrangian view of time irreversibility of fluid turbulence

A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is dissipated, the more so as the turbulent intensity (the Reynolds number) is larger. The resulting energy flux over the range of scales, intermediate between energy injection and dissipation, acts as a source of time irreversibility. As it is now possible to follow accurately fluid particles in a turbulent flow field, both from laboratory experiments and from numerical simulations, a natural question arises: how do we detect time irreversibility from these Lagrangian data? Here we discuss recent results concerning this problem. For Lagrangian statistics involving more than one fluid particle, the distance between fluid particles introduces an intrinsic length scale into the problem. The evolution of quantities dependent on the relative motion between these fluid particles, including the kinetic energy in the relative motion, or the configuration of an initially isotropic structure can be related to the equal-time correlation functions of the velocity field, and is therefore sensitive to the energy flux through scales, hence to the irreversibility of the flow. In contrast, for single-particle Lagrangian statistics, the most often studied velocity structure functions cannot distinguish the "arrow of time." Recent observations from experimental and numerical simulation data, however, show that the change of kinetic energy following the particle motion, is sensitive to time-reversal. We end the survey with a brief discussion of the implication of this line of work.

physics.flu-dyn↗

arXiv2015

Stochastic Cascade Amplification of Fluctuations

We consider a dynamical system which has a stable attractor and which is perturbed by an additive noise. Under some quite typical conditions, the fluctuations from the attractor are intermittent and have a probability distribution with power-law tails. We show that this results from a stochastic cascade of amplification of fluctuations due to transient periods of instability. The exponent of the power-law is interpreted as a negative fractal dimension.

nlin.CD↗

arXiv2014

The role of cellular coupling in the spontaneous generation of electrical activity in uterine tissue

The spontaneous emergence of contraction-inducing electrical activity in the uterus at the beginning of labor remains poorly understood, partly due to the seemingly contradictory observation that isolated uterine cells are not spontaneously active. It is known, however, that the expression of gap junctions increases dramatically in the approach to parturition, which results in a significant increase in inter-cellular electrical coupling. In this paper, we build upon previous studies of the activity of electrically excitable smooth muscle cells (myocytes) and investigate the mechanism through which the coupling of these cells to electrically passive cells results in the generation of spontaneous activity in the uterus. Using a recently developed, realistic model of uterine muscle cell dynamics, we investigate a system consisting of a myocyte coupled to passive cells. We then extend our analysis to a simple two-dimensional lattice model of the tissue, with each myocyte being coupled to its neighbors, as well as to a random number of passive cells. We observe that different dynamical regimes can be observed over a range of gap junction conductances: at low coupling strength, the activity is confined to cell clusters, while the activity for high coupling may spread across the entire tissue. Additionally, we find that the system supports the spontaneous generation of spiral wave activity. Our results are both qualitatively and quantitatively consistent with observations from in vitro experiments. In particular, we demonstrate that an increase in inter-cellular electrical coupling, for realistic parameter values, strongly facilitates the appearance of spontaneous action potentials that may eventually lead to parturition.

q-bio.TO↗

arXiv2014

Power Fluctuations and Irreversibility in Turbulence

The breaking of detailed balance, the symmetry between forward and backward probability transition between two states, is crucial to understand irreversible systems. In hydrodynamic turbulence, a far-from equilibrium system, we observe a strong manifestation of the breaking of detailed balance by following the evolution of the kinetic energy of individual fluid elements. We found in all the flows that we have investigated that fluid elements decelerate faster than they accelerate, giving rise to negative third moment of energy increments, independently of space dimensionality. The exchange of energy between fluid elements however is fundamentally different in two and three dimensions. While pressure forces do not provide net energy change to slow or fast particles in two dimensions, they tend to transfer energy from {\it slow} to {\it fast} particles in three dimensions, possibly implying a runaway of energy.

physics.flu-dyn↗

arXiv2014

Time-symmetry breaking in turbulence

In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time symmetry. We show here that this irreversibility can be quantified by following the relative motion of several Lagrangian tracers. We find by analytical calculation, numerical analysis and experimental observation that the existence of the energy flux implies that, at short times, two particles separate temporally slower forwards than backwards, and the difference between forward and backward dispersion grows as $t^3$. We also find the geometric deformation of material volumes, surrogated by four points spanning an initially regular tetrahedron, to show sensitivity to the time-reversal with an effect growing linearly in $t$. We associate this with the structure of the strain rate in the flow.

physics.flu-dyn↗

arXiv2014

Collision rate for suspensions at large Stokes numbers - comparing Navier-Stokes and synthetic turbulence

The use of simplified models of turbulent flows provides an appealing possibility to study the collision rate of turbulent suspensions, especially in conditions relevant to astrophysics, which require large time scale separations. To check the validity of such approaches, we used a direct numerical simulation (DNS) velocity field, which satisfies the Navier-Stokes equations (although it neglects the effect of the suspended particles on the flow field), and a kinematic simulation (KS) velocity field, which is a random field designed so that its statistics are in accord with the Kolmogorov theory for fully-developed turbulence. In the limit where the effects of particle inertia (characterised by the Stokes number) are negligible, the collision rates from the two approaches agree. As the Stokes number St increases, however, we show that the DNS collision rate exceeds the KS collision rate by orders of magnitude. We propose an explanation for this phenomenon and explore its consequences. We discuss the collision rate $R$ for particles in high Reynolds number flows at large Stokes number, and present evidence that $R\propto \sqrt{\rm St}$.

physics.flu-dyn↗

arXiv2013

Multiple collisions in turbulent flows

In turbulent suspensions, collision rates determine how rapidly particles coalesce or react with each other. To determine the collision rate, many numerical studies rely on the 'Ghost Collision Approximation' (GCA), which simply records how often pairs of point particles come within a threshold distance. In many applications, the suspended particles stick (or in the case of liquid droplets, coalesce) upon collision, and it is the frequency of first contact which is of interest. If a pair of 'ghost' particles undergoes multiple collisions, the GCA may overestimate the true collision rate. Here, using fully resolved Direct Numerical Simulations of turbulent flows at moderate Reynolds number (R_λ= 130), we investigate the prevalence and properties of multiple collisions. We demonstrate that the GCA leads to a systematic overestimate of the collision rate, which is of the order of 15% when the particle inertia is small, and slowly decreases when inertia increases. We investigate the probability P(N) for a given pair of ghost particles colliding N times. We find P(N)=βα^N for N_>1, where αand βare coefficients which depend upon the particle inertia. This result is used to explain the discrepancy between the GCA and the true collision rates. We also investigate the statistics of the times that ghost particles remain in contact. We show that the probability density function of the contact time is different for the first collision. The difference is explained by the effect of caustics in the phase space of the suspended particles.

physics.flu-dyn↗

arXiv2013

Prevalence of the sling effect for enhancing collision rates in turbulent suspensions

Turbulence facilitates collisions between particles suspended in a turbulent flow. Two effects have been proposed which can enhance the collision rate at high turbulence intensities: 'preferential concentration' (a clustering phenomenon) and the 'sling effect' (arising from the formation of caustic folds in the phase-space of the suspended particles). We have determined numerically the collision rate of small heavy particles as a function of their size and densities. The dependence on particle densities reveals that the enhancement by turbulence of the collision rate of particles with significant inertia is due almost entirely to the sling effect.

physics.flu-dyn↗

arXiv2013

A model for the shapes of advected triangles

Three particles floating on a fluid surface define a triangle. The aim of this paper is to characterise the shape of the triangle, defined by two of its angles, as the three vertices are subject to a complex or turbulent motion. We consider a simple class of models for this process, involving a combination of a random strain of the fluid and Brownian motion of the particles. Following D. G. Kendall, we map the space of triangles to a sphere, whose equator corresponds to degenerate triangles with colinear vertices, with equilaterals at the poles. We map our model to a diffusion process on the surface of the sphere and find an exact solution for the shape distribution. Whereas the action of the random strain tends to make the shape of the triangles infinitely elongated, in the presence of a Brownian diffusion of the vertices, the model has an equilibrium distribution of shapes. We determine here exactly this shape distribution in the simple case where the increments of the strain are diffusive.

nlin.CD↗

arXiv2013

Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

We describe the structure and dynamics of turbulence by the scale-dependent perceived velocity gradient tensor as supported by following four tracers, i.e. fluid particles, that initially form a regular tetrahedron. We report results from experiments in a von Kármán swirling water flow and from numerical simulations of the incompressible Navier-Stokes equation. We analyze the statistics and the dynamics of the perceived rate of strain tensor and vorticity for initially regular tetrahedron of size $r_0$ from the dissipative to the integral scale. Just as for the true velocity gradient, at any instant, the perceived vorticity is also preferentially aligned with the intermediate eigenvector of the perceived rate of strain. However, in the perceived rate of strain eigenframe fixed at a given time $t=0$, the perceived vorticity evolves in time such as to align with the strongest eigendirection at $t=0$. This also applies to the true velocity gradient. The experimental data at the higher Reynolds number suggests the existence of a self-similar regime in the inertial range. In particular, the dynamics of alignment of the perceived vorticity and strain can be rescaled by $t_0$, the turbulence time scale of the flow when the scale $r_0$ is in the inertial range. For smaller Reynolds numbers we found the dynamics to be scale dependent.

physics.flu-dyn↗

arXiv2012

Large variability in dynamical transitions in biological systems with quenched disorder

Coherent oscillatory activity can arise spontaneously as a result of increased coupling in a system of excitable and passive cells, each being quiescent in isolation. This can potentially explain the appearance of spontaneous rhythmic contractions in the pregnant uterus close to term. We investigate the transition to periodic activity using a model system comprising a lattice of excitable cells, each being coupled to a variable number of passive cells whose distribution defines a quenched realization (replica) of spatial disorder. Close to the transition between quiescent state and sustained oscillations in the system we observe large fluctuations between different replicas induced by variations in the local density of passive cells around an excitable cell. We demonstrate that the disorder-induced fluctuations can be described in terms of a simple scaling relation which involves the strength of coupling between excitable cells, the mean passive cell density, as well as the logarithm of the system size. Our results can be interpreted as suggesting that larger organs will have greater variability in the onset of persistent activity.

cond-mat.dis-nn↗

arXiv2012

Self-organized transition to coherent activity in disordered media

Synchronized oscillations are of critical functional importance in many biological systems. We show that such oscillations can arise without centralized coordination in a disordered system of electrically coupled excitable and passive cells. Increasing the coupling strength results in waves that lead to coherent periodic activity, exhibiting cluster, local and global synchronization under different conditions. Our results may explain the self-organized transition in a pregnant uterus from transient, localized activity initially to system-wide coherent excitations just before delivery.

nlin.AO↗

arXiv2011

Spherical Ornstein-Uhlenbeck processes

The paper considers random motion of a point on the surface of a sphere, in the case where the angular velocity is determined by an Ornstein-Uhlenbeck process. The solution is fully characterized by only one dimensionless number, the persistence angle, which is the typical angle of rotation of the object during the correlation time of the angular velocity. We first show that the two-dimensional case is exactly solvable. When the persistence angle is large, a series for the correlation function has the surprising property that its sum varies much more slowly than any of its individual terms. In three dimensions we obtain asymptotic forms for the correlation function, in the limits where the persistence angle is very small and very large. The latter case exhibits a complicated transient, followed by a much slower exponential decay. The decay rate is determined by the solution of a radial Schrodinger equation in which the angular momentum quantum number takes an irrational value, namely j=(sqrt{17}-1)/2. Possible applications of the model to objects tumbling in a turbulent environment are discussed.

physics.flu-dyn↗

arXiv2010

Rotational intermittency and turbulence induced lift experienced by large particles in a turbulent flow

The motion of a large, neutrally buoyant, particle, freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a manifestation of intermittency. The orientation of the angular velocity with respect to the trajectory, as well as the translational acceleration conditioned on the spinning velocity provide evidence of a lift force acting on the particle.

physics.flu-dyn↗

arXiv2010

Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow

We study the 6-dimensional dynamics -- position and orientation -- of a large sphere advected by a turbulent flow. The movement of the sphere is recorded with 2 high-speed cameras. Its orientation is tracked using a novel, efficient algorithm; it is based on the identification of possible orientation `candidates' at each time step, with the dynamics later obtained from maximization of a likelihood function. Analysis of the resulting linear and angular velocities and accelerations reveal a surprising intermittency for an object whose size lies in the integral range, close to the integral scale of the underlying turbulent flow.

physics.flu-dyn↗

arXiv2010

Wave-train induced unpinning of weakly anchored vortices in excitable media

A free vortex in excitable media can be displaced and removed by a wave-train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.

physics.bio-ph↗