Optimal policies for Bayesian olfactory search in turbulent flows.

In many practical scenarios, a flying insect must search for the source of an emitted cue which is advected by the atmospheric wind. On the macroscopic scales of interest, turbulence tends to mix the cue into patches of relatively high concentration over a background of very low concentration, so that the insect will detect the cue only intermittently and cannot rely on chemotactic strategies which simply climb the concentration gradient. In this work we cast this search problem in the language of a partially observable Markov decision process and use the Perseus algorithm to compute strategies that are near-optimal with respect to the arrival time. We test the computed strategies on a large two-dimensional grid, present the resulting trajectories and arrival time statistics, and compare these to the corresponding results for several heuristic strategies, including (space-aware) infotaxis, Thompson sampling, and QMDP. We find that the near-optimal policy found by our implementation of Perseus outperforms all heuristics we test by several measures. We use the near-optimal policy to study how the search difficulty depends on the starting location. We also discuss the choice of initial belief and the robustness of the policies to changes in the environment. Finally, we present a detailed and pedagogical discussion about the implementation of the Perseus algorithm, including the benefits-and pitfalls-of employing a reward-shaping function.

Optimizing airborne wind energy with reinforcement learning.

Airborne wind energy is a lightweight technology that allows power extraction from the wind using airborne devices such as kites and gliders, where the airfoil orientation can be dynamically controlled in order to maximize performance. The dynamical complexity of turbulent aerodynamics makes this optimization problem unapproachable by conventional methods such as classical control theory, which rely on accurate and tractable analytical models of the dynamical system at hand. Here we propose to attack this problem through reinforcement learning, a technique that-by repeated trial-and-error interactions with the environment-learns to associate observations with profitable actions without requiring prior knowledge of the system. We show that in a simulated environment reinforcement learning finds an efficient way to control a kite so that it can tow a vehicle for long distances. The algorithm we use is based on a small set of intuitive observations and its physically transparent interpretation allows to describe the approximately optimal strategy as a simple list of manoeuvring instructions.

Finding efficient swimming strategies in a three-dimensional chaotic flow by reinforcement learning.

We apply a reinforcement learning algorithm to show how smart particles can learn approximately optimal strategies to navigate in complex flows. In this paper we consider microswimmers in a paradigmatic three-dimensional case given by a stationary superposition of two Arnold-Beltrami-Childress flows with chaotic advection along streamlines. In such a flow, we study the evolution of point-like particles which can decide in which direction to swim, while keeping the velocity amplitude constant. We show that it is sufficient to endow the swimmers with a very restricted set of actions (six fixed swimming directions in our case) to have enough freedom to find efficient strategies to move upward and escape local fluid traps. The key ingredient is the learning-from-experience structure of the algorithm, which assigns positive or negative rewards depending on whether the taken action is, or is not, profitable for the predetermined goal in the long-term horizon. This is another example supporting the efficiency of the reinforcement learning approach to learn how to accomplish difficult tasks in complex fluid environments.

Prompt gamma imaging of proton pencil beams at clinical dose rate.

In this work, we present experimental results of a prompt gamma camera for real-time proton beam range verification. The detection system features a pixelated Cerium doped lutetium based scintillation crystal, coupled to Silicon PhotoMultiplier arrays, read out by dedicated electronics. The prompt gamma camera uses a knife-edge slit collimator to produce a 1D projection of the beam path in the target on the scintillation detector. We designed the detector to provide high counting statistics and high photo-detection efficiency for prompt gamma rays of several MeV. The slit design favours the counting statistics and could be advantageous in terms of simplicity, reduced cost and limited footprint. We present the description of the realized gamma camera, as well as the results of the characterization of the camera itself in terms of imaging performance. We also present the results of experiments in which a polymethyl methacrylate phantom was irradiated with proton pencil beams in a proton therapy center. A tungsten slit collimator was used and prompt gamma rays were acquired in the 3-6 MeV energy range. The acquisitions were performed with the beam operated at 100 MeV, 160 MeV and 230 MeV, with beam currents at the nozzle exit of several nA. Measured prompt gamma profiles are consistent with the simulations and we reached a precision (2σ) in shift retrieval of 4 mm with 0.5 × 10(8), 1.4 × 10(8) and 3.4 × 10(8) protons at 100, 160 and 230 MeV, respectively. We conclude that the acquisition of prompt gamma profiles for in vivo range verification of proton beam with the developed gamma camera and a slit collimator is feasible in clinical conditions. The compact design of the camera allows its integration in a proton therapy treatment room and further studies will be undertaken to validate the use of this detection system during treatment of real patients.

Repulsion and metabolic switches in the collective behavior of bacterial colonies.

Bacteria inoculated on surfaces create colonies that spread out, forming patterns shaped by their mutual interactions. Here, by a combination of experiments and modeling, we address two striking phenomena observed when colonies spread out circularly, without dendritic instabilities. First, the velocity of spreading is generically found to decrease as levels of nutrients initially deposited on the surface increase. We demonstrate that the slowdown is due to phenomena of differentiation, leading to the coexistence of bacteria in different states of motility and we model their dynamics. Second, colonies spreading out from different inocula on the same surface are observed to merge or repel (halting at a finite distance), depending on experimental conditions. We identify the parameters that determine the fate of merging versus repulsion, and predict the profile of arrest in the cases of repulsion.

Two-dimensional elastic turbulence.

We report numerical evidence of elastic turbulence phenomenology in a two-dimensional periodic Kolmogorov flow. By direct numerical simulations of the Oldroyd-B viscoelastic model at very small Reynolds numbers, we find that above the elastic instability threshold the flow develops an elastic turbulent regime. We observe that both the turbulent drag and the Lyapunov exponent increase with the Weissenberg number, indicating the presence of a disordered, turbulentlike mixing flow. The energy spectrum develops a power-law scaling range with an exponent close to the experimental and theoretical expectations.

Inverse turbulent cascades and conformally invariant curves.

We offer a new example of conformal invariance (local scale invariance) far from equilibrium-the inverse cascade of surface quasigeostrophic (SQG) turbulence. We show that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner evolution or SLEkappa). The diffusivity is close to kappa=4, that is, isotemperature curves belong to the same universality class as domain walls in the O(2) spin model. Several statistics of temperature clusters and isolines are shown to agree with the theoretical expectations for such a spin system at criticality. We also show that the direct cascade in two-dimensional Navier-Stokes turbulence is not conformal invariant. The emerging picture is that conformal invariance may be expected for inverse turbulent cascades of strongly interacting systems.

Dynamical slowdown of polymers in laminar and random flows.

The influence of an external flow on the relaxation dynamics of a single polymer is investigated theoretically and numerically. We show that a pronounced dynamical slowdown occurs in the vicinity of the coil-stretch transition, especially when the dependence on polymer conformation of the drag is accounted for. For the elongational flow, relaxation times are exceedingly larger than the Zimm relaxation time, resulting in the observation of conformation hysteresis. For random smooth flows, hysteresis is not present. Yet, relaxation dynamics is significantly slowed down because of the large variety of accessible polymer configurations. The implications of these results for the modeling of dilute polymer solutions in turbulent flows are addressed.

Multifractal statistics of Lagrangian velocity and acceleration in turbulence.

The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present results for Lagrangian velocity structure functions, the acceleration probability density function, and the acceleration variance conditioned on the instantaneous velocity. These are compared with predictions of the multifractal formalism, and its merits and limitations are discussed.

Intermittency in two-dimensional Ekman-Navier-Stokes turbulence.

We study the statistics of the vorticity field in two-dimensional Navier-Stokes turbulence with linear Ekman friction. We show that the small-scale vorticity fluctuations are intermittent, as conjectured by Bernard [Europhys. Lett. 50, 333 (2000)] and Nam et al. [Phys. Rev. Lett. 84, 5134 (2000)]. The small-scale statistics of vorticity fluctuations coincide with that of a passive scalar with finite lifetime transported by the velocity field itself.

Front propagation in laminar flows.

The problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius type are considered under the assumption of no feedback of the concentration on the velocity. Numerical simulations of advection-reaction-diffusion equations have been performed by an algorithm based on discrete-time maps. The results show a generic enhancement of the speed of front propagation by the underlying flow. For small molecular diffusivity, the front speed V(f) depends on the typical flow velocity U as a power law with an exponent depending on the topological properties of the flow, and on the ratio of reactive and advective time scales. For open-streamline flows we find always V(f) approximately U, whereas for cellular flows we observe V(f) approximately U(1/4) for fast advection and V(f) approximately U(3/4) for slow advection.

Statistical conservation laws in turbulent transport.

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. With very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas.

Statistical geometry in scalar turbulence.

A general link between geometry and intermittency in passive scalar turbulence is established. The anomalous part of the scalar correlation functions is shown to be dominated by special functions of particle configurations. Their major property is that those functions calculated along the particle trajectories remain statistically constant in time. Those conservation laws qualitatively imply the persistence of scalar particles in strongly clustered geometries.

Large scale instabilities in two-dimensional magnetohydrodynamics

The stability of a sheared magnetic field is analyzed in two-dimensional magnetohydrodynamics with resistive and viscous dissipation. Using a multiple-scale analysis, it is shown that at large enough Reynolds numbers the basic state describing a motionless fluid and a layered magnetic field, becomes unstable with respect to large scale perturbations. The exact expressions for eddy-viscosity and eddy-resistivity are derived in the nearby of the critical point where the instability sets in. In this marginally unstable case the nonlinear phase of perturbation growth obeys to a Cahn-Hilliard-like dynamics characterized by coalescence of magnetic islands leading to a final new equilibrium state. High resolution numerical simulations confirm quantitatively the predictions of multiscale analysis.

Universality and saturation of intermittency in passive scalar turbulence

The statistical properties of a scalar field advected by the nonintermittent Navier-Stokes flow arising from a two-dimensional inverse energy cascade are investigated. The universality properties of the scalar field are probed by comparing the results obtained with two types of injection mechanisms. Scaling properties are shown to be universal, even though anisotropies injected at large scales persist down to the smallest scales and local isotropy is not fully restored. Scalar statistics is strongly intermittent and scaling exponents saturate to a constant for sufficiently high orders. This is observed also for the advection by a velocity field rapidly changing in time, pointing to the genericity of the phenomenon.

Inverse energy cascade in two-dimensional turbulence: deviations from gaussian behavior

High-resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussian behavior of velocity differences statistics are quantitatively investigated. The level of statistical convergence is pushed enough to permit reliable measurement of the asymmetries in the probability distribution functions of longitudinal increments and odd-order moments, which bring the signature of the inverse energy flux. No measurable intermittency corrections could be found in their scaling laws. The seventh order skewness increases by almost two orders of magnitude with respect to the third, thus becoming of order unity.

Nonasymptotic properties of transport and mixing.

We study relative dispersion of passive scalar in nonideal cases, i.e., in situations in which asymptotic techniques cannot be applied; typically when the characteristic length scale of the Eulerian velocity field is not much smaller than the domain size. Of course, in such a situation usual asymptotic quantities (the diffusion coefficients) do not give any relevant information about the transport mechanisms. On the other hand, we shall show that the Finite Size Lyapunov Exponent, originally introduced for the predictability problem, appears to be rather powerful in approaching the nonasymptotic transport properties. This technique is applied in a series of numerical experiments in simple flows with chaotic behaviors, in experimental data analysis of drifter and to study relative dispersion in fully developed turbulence. (c) 2000 American Institute of Physics.

Passive scalar intermittency in compressible flow.

A compressible generalization of the Kraichnan model [Phys. Rev. Lett. 72, 1016 (1994)] of passive scalar advection is considered. The dynamical role of compressibility on the intermittency of the scalar statistics is investigated for the direct cascade regime. Simple physical arguments suggest that an enhanced intermittency should appear for increasing compressibility, due to the slowing down of Lagrangian trajectory separations. This is confirmed by a numerical study of the dependence of intermittency exponents on the degree of compressibility, by a Lagrangian method for calculating simultaneous N-point tracer correlations.

Pair dispersion in synthetic fully developed turbulence.

The Lagrangian statistics of relative dispersion in fully developed turbulence is numerically investigated. A scaling range spanning many decades is achieved by generating a two-dimensional velocity field by means of a stochastic process with prescribed statistics and of a dynamical model (shell model) with fluctuating characteristic times. When the velocity field obeys Kolmogorov similarity, the Lagrangian statistics is self similar and agrees with Richardson's predictions [Proc. R. Soc. London Ser. A 110, 709 (1926)]. For intermittent velocity fields the scaling laws for the Lagrangian statistics are found to depend on the Eulerian intermittency in agreement with the multifractal description. As a consequence of the Kolmogorov law the Richardson law for the variance of pair separation is, however, not affected by intermittency corrections. Moreover, Lagrangian exponents do not depend on the particular Eulerian dynamics. A method of data analysis, based on fixed scale statistics rather than usual fixed time statistics, is shown to give much wider scaling range, and should be preferred for the analysis of experimental data.

[the experience of the knowledge in Newton's and Goethe's works]. / L'expérience du connaître dans les ouvrages de Newton et de Goethe.

The origin of the knowledge, explained through the perception of the colours saw, during many years, the contrast between the two theories asserted by the objectivists and subjectivists. the authors have emblematically brought the two schools back to two excellent personages: Newton (1704) and Goethe (1810), the former physicist, the latter naturalist. Newton was an upholder of the corpuscolar theory of the light and of the objective process. Goethe, on the contrary, tried to assert the ondulatory theory of the light. Authors' work centers on the exegesis of the significant passages of the two personages' fundamental works together with the reflections of the philosophers of the science, who were contemporary with Newton and Goethe and posteriors to them.