Nonanomalous heat transport in a one-dimensional composite chain.

Translation-invariant low-dimensional systems are known to exhibit anomalous heat transport. However, there are systems, such as the coupled-rotor chain, where translation invariance is satisfied, yet transport remains diffusive. It has been argued that the restoration of normal diffusion occurs due to the impossibility of defining a global stretch variable with a meaningful dynamics. In this Letter, an alternative mechanism is proposed, namely, that the transition to anomalous heat transport can occur at a scale that, under certain circumstances, may diverge to infinity. To illustrate the mechanism, I consider the case of a composite chain that conserves local energy and momentum as well as global stretch, and at the same time obeys, in the continuum limit, Fourier's law of heat transport. It is shown analytically that for vanishing elasticity the stationary temperature profile of the chain is linear; for finite elasticity, the same property holds in the continuum limit.

Erratum: Description of a stochastic system by a nonadapted stochastic process [Phys. Rev. E 104, 014139 (2021)].

This corrects the article DOI: 10.1103/PhysRevE.104.014139.

Description of a stochastic system by a nonadapted stochastic process.

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling between forward and backward variables, and it is well suited for situations in which initial and final conditions are imposed on different components of the system, and the coupling between those components is weak. The form of the stochastic equations in our approach is determined by requiring that they generate the same statistics obtained in a forward description of the dynamics. Numerical tests are carried out on a few simple two-degrees-of-freedom systems. The merit and the difficulties of the approach are discussed and compared to more traditional strategies based on transition path sampling and simple shooting algorithms.

SAR image wave spectra to retrieve the thickness of grease-pancake sea ice using viscous wave propagation models.

Young sea ice composed of grease and pancake ice (GPI), as well as thin floes, considered to be the most common form of sea ice fringing Antarctica, is now becoming the "new normal" also in the Arctic. A study of the rheological properties of GPI is carried out by comparing the predictions of two viscous wave propagation models: the Keller model and the close-packing (CP) model, with the observed wave attenuation obtained by SAR image techniques. In order to fit observations, it is shown that describing GPI as a viscous medium requires the adoption of an ice viscosity which increases with the ice thickness. The consequences regarding the possibility of ice thickness retrieval from remote sensing data of wave attenuation are discussed. We provide examples of GPI thickness retrievals from a Sentinel-1 C band SAR image taken in the Beaufort Sea on 1 November 2015, and three CosmoSkyMed X band SAR images taken in the Weddell Sea on March 2019. The estimated GPI thicknesses are consistent with concurrent SMOS measurements and available local samplings.

Limit regimes of ice formation in turbulent supercooled water.

A study of ice formation in stationary turbulent conditions is carried out in various limit regimes of crystal growth, supercooling, and ice entrainment at the water surface. Analytical expressions for the temperature, salinity, and ice concentration mean profiles are provided, and the role of fluctuations in ice production is numerically quantified. Lower bounds on the ratio of sensible heat flux to latent heat flux to the atmosphere are derived and their dependence on key parameters such as salt rejection in freezing and ice entrainment in the water column is elucidated.

Pros and cons of swimming in a noisy environment.

The problem of optimal microscopic swimming in a noisy environment is analyzed. A simplified model in which propulsion is generated by the relative motion of three spheres connected by immaterial links has been considered. We show that an optimized noisy microswimmer requires less power for propulsion (on average) than an optimal noiseless counterpart migrating with identical mean velocity and swimming stroke amplitude. We also show that noise can be used to overcome some of the limitations of the scallop theorem and have a swimmer that is able to propel itself with control over just one degree of freedom.

Effect of demographic noise in a phytoplankton-zooplankton model of bloom dynamics.

An extension of the Truscott-Brindley model [Bull. Math. Biol. 56, 981 (1994)] is derived to account for the effect of demographic fluctuations. In the presence of seasonal forcing and sufficiently shallow water conditions, the fluctuations induced by the discreteness of the zooplankton component appear sufficient to cause switching between the bloom and no-bloom cycles predicted at the mean-field level by the model. The destabilization persists in the thermodynamic limit of a water basin infinitely extended in the horizontal direction.

Forcing anomalous scaling on demographic fluctuations.

We discuss the conditions under which a population of anomalously diffusing individuals can be characterized by demographic fluctuations that are anomalously scaling themselves. Two examples are provided in the case of individuals migrating by Gaussian diffusion, and by a sequence of Lévy flights.

Demographic fluctuations in a population of anomalously diffusing individuals.

The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into exam, in the case that anomalous diffusion is produced by means of a continuous time random walk (CTRW). In the case of independently diffusing individuals, the dynamics appears to coincide with that of (dying and reproducing) Brownian walkers. In the strongly social case, the dynamics coincides with that of nonmigrating individuals. In both limits, the growth rate of the fluctuations becomes independent of the Hurst exponent of the CTRW. The social behaviors that arise when transport in a population is induced by a spatial distribution of random traps have been analyzed.

Passive swimming in low-Reynolds-number flows.

The possibility of microscopic swimming by extraction of energy from an external flow is discussed, focusing on the migration of a simple trimer across a linear shear flow. The geometric properties of swimming, together with the possible generalization to the case of a vesicle, are analyzed. The mechanism of energy extraction from the flow appears to be the generalization to a discrete swimmer of the tank-treading regime of a vesicle. The swimmer takes advantage of the external flow by both extracting energy for swimming and "sailing" through it. The migration velocity is found to scale linearly in the stroke amplitude, and not quadratically as in a quiescent fluid. This effect turns out to be connected with the nonapplicability of the scallop theorem in the presence of external flow fields.

Preferential concentration versus clustering in inertial particle transport by random velocity fields.

The concept of preferential concentration in the transport of inertial particles by random velocity fields is extended to account for the possibility of zero correlation time and compressibility of the velocity field. It is shown that, in the case of an uncorrelated in time random velocity field, preferential concentration takes the form of a condition on the field history leading to the current particle positions. This generalized form of preferential concentration appears to be a necessary condition for clustering in the uncorrelated in time case. The standard interpretation of preferential concentration is recovered considering local time averages of the velocity field. In the compressible case, preferential concentration occurs in regions of negative divergence of the field. In the incompressible case, it occurs in regions of simultaneously high strain and negative field skewness.

Clustering and collision of inertial particles in random velocity fields.

The influence of clustering on the collision rate of inertial particles in a smooth random velocity field, mimicking the smaller scales of a turbulent flow, is analyzed. For small values of the ratio between the relaxation time of the particle velocity and the characteristic time of the field, the effect of clusters is to make more energetic collisions less likely. The result is independent of the flow dimensionality and is due only to the origin of collisions in the process of caustic formation.

Return times for stochastic processes with power-law scaling.

An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried out. The calculation is based on an epsilon expansion in the correlation exponent: C(t)=/t/-1+epsilon. The fixed point of the theory is associated with stretched exponential scaling of the distribution; analytical expressions have been provided in the preasymptotic regime. Also, the permanence time distribution appears to be characterized by stretched exponential scaling. The conditions for application of the theory to non-Gaussian processes have been analyzed and the relations with the issue of return times in the case of multifractal measures have been discussed.

Concentration fluctuations of large Stokes number particles in a one-dimensional random velocity field.

We analyze the behavior of an ensemble of inertial particles in a one-dimensional smooth Gaussian velocity field, in the limit of large inertia, but considering a finite correlation time for the random field. The amplitude of the concentration fluctuations is characterized by slow decay at large inertia and a much larger correlation length than that of the random field. The fluctuation structure in velocity space is very different from predictions from short-time correlated random velocity fields, with only few particle pairs crossing at sufficiently small relative velocity to produce correlations. Concentration fluctuations are associated with depletion of the relative velocity variance of colliding particles.

Orientation dynamics of weakly Brownian particles in periodic viscous flows.

Evolution equations for the orientation distribution of axisymmetric particles in periodic flows are derived in the regime of small but nonzero Brownian rotations. The equations are based on a multiple time scale approach that allows fast computation of the relaxation processes leading to statistical equilibrium. The approach has been applied to the calculation of the effective viscosity of a thin disk suspension in an oscillating strain flow.

Relations between Lagrangian models and synthetic random velocity fields.

The authors propose an alternative interpretation of Markovian transport models based on the well-mixed condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space-time increments. This interpretation allows direct association of the drift and noise terms entering the model, with the geometry of the turbulent fluctuations. In particular, the well-known nonuniqueness problem in the well-mixed approach is solved in terms of the antisymmetric part of the velocity correlations; its relation with the presence of nonzero mean helicity and other geometrical properties of the flow is elucidated. The well-mixed condition appears to be a special case of the relation between conditional velocity increments of the random field and the one-point Eulerian velocity distribution, allowing generalization of the approach to the transport of nontracer quantities. Application to solid particle transport leads to a model satisfying, in the homogeneous isotropic turbulence case, all the conditions on the behavior of the correlation times for the fluid velocity sampled by the particles. In particular, correlation times in the gravity and in the inertia dominated case, respectively, longer and shorter than in the passive tracer case; in the gravity dominated case, correlation times longer for velocity components along gravity, than for the perpendicular ones. The model produces, in channel flow geometry, particle deposition rates in agreement with experiments.

Particle transport in a random velocity field with Lagrangian statistics.

The transport properties of a random velocity field with Kolmogorov spectrum and time correlations defined along Lagrangian trajectories are analyzed. The analysis is carried out in the limit of short correlation times, as a perturbation theory in the ratio, scale by scale, of the eddy decay and turnover time. Various quantities such as the Batchelor constant and the dimensionless constants entering the expression for particle relative and self-diffusion are given in terms of this ratio and of the Kolmogorov constant. Particular attention is paid to particles with finite inertia. The self-diffusion properties of a particle with Stokes time longer than the Kolmogorov time are determined, verifying on an analytical example the dimensional results of Olla [Phys. Fluids 14, 4266 (2002)]. Expressions for the fluid velocity Lagrangian correlations and correlation times along a solid particle trajectory are provided in several parameter regimes, including the infinite Stokes time limit corresponding to Eulerian correlations. The concentration fluctuation spectrum and the nonergodic properties of a suspension of heavy particles in a turbulent flow, in the same regime, are analyzed. The concentration spectrum is predicted to obey, above the scale of eddies with lifetime equal to the Stokes time, a power law with universal -4/3 exponent, and to be otherwise independent of the nature of the turbulent flow. A preference of the solid particle to lie in less energetic regions of the flow is observed.