Finite-Time Lyapunov Exponents of Deep Neural Networks.

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep feed-forward networks and dynamical systems, where the growth or decay of local perturbations is characterized by finite-time Lyapunov exponents. We show that the maximal exponent forms geometrical structures in input space, akin to coherent structures in dynamical systems. Ridges of large positive exponents divide input space into different regions that the network associates with different classes. These ridges visualize the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities.

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.

Alignment of Nonspherical Active Particles in Chaotic Flows.

We study the orientation statistics of spheroidal, axisymmetric microswimmers, with shapes ranging from disks to rods, swimming in chaotic, moderately turbulent flows. Numerical simulations show that rodlike active particles preferentially align with the flow velocity. To explain the underlying mechanism, we solve a statistical model via the perturbation theory. We show that such an alignment is caused by correlations of fluid velocity and its gradients along particle paths combined with fore-aft symmetry breaking due to both swimming and particle nonsphericity. Remarkably, the discovered alignment is found to be a robust kinematical effect, independent of the underlying flow evolution. We discuss its possible relevance for aquatic ecology.

Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning.

To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel that has a slip velocity with fixed intensity, Vs, but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasioptimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process and are, therefore, not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when Vs is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small.

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.

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.

Preferential Sampling and Small-Scale Clustering of Gyrotactic Microswimmers in Turbulence.

Recent studies show that spherical motile microorganisms in turbulence subject to gravitational torques gather in down-welling regions of the turbulent flow. By analyzing a statistical model we analytically compute how shape affects the dynamics, preferential sampling, and small-scale spatial clustering. We find that oblong organisms may spend more time in up-welling regions of the flow, and that all organisms are biased to regions of positive fluid-velocity gradients in the upward direction. We analyze small-scale spatial clustering and find that oblong particles may either cluster more or less than spherical ones, depending on the strength of the gravitational torques.

Statistical model for collisions and recollisions of inertial particles in mixing flows.

Finding a quantitative description of the rate of collisions between small particles suspended in mixing flows is a long-standing problem. Here we investigate the validity of a parameterisation of the collision rate for identical particles subject to Stokes force, based on results for relative velocities of heavy particles that were recently obtained within a statistical model for the dynamics of turbulent aerosols. This model represents the turbulent velocity fluctuations by Gaussian random functions. We find that the parameterisation gives quantitatively good results in the limit where the "ghost-particle approximation" applies. The collision rate is a sum of two contributions due to "caustics" and to "clustering". Within the statistical model we compare the relative importance of these two collision mechanisms. The caustic formation rate is high when the particle inertia becomes large, and we find that caustics dominate the collision rate as soon as they form frequently. We compare the magnitude of the caustic contribution to the collision rate to the formation rate of caustics.

Tumbling of small axisymmetric particles in random and turbulent flows.

We analyze the tumbling of small nonspherical, axisymmetric particles in random and turbulent flows. We compute the orientational dynamics in terms of a perturbation expansion in the Kubo number, and obtain the tumbling rate in terms of Lagrangian correlation functions. These capture preferential sampling of the fluid gradients, which in turn can give rise to differences in the tumbling rates of disks and rods. We show that this is a weak effect in Gaussian random flows. But in turbulent flows persistent regions of high vorticity cause disks to tumble much faster than rods, as observed in direct numerical simulations [S. Parsa, E. Calzavarini, F. Toschi, and G. A. Voth, Phys. Rev. Lett. 109, 134501 (2012)]. For larger particles (at finite Stokes numbers), rotational and translational inertia affects the tumbling rate and the angle at which particles collide, due to the formation of rotational caustics.

Multiple regimes of diffusion.

We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviors, depending upon the limiting cases which are considered, some of which have been discussed in earlier work. Here, we explore the full space of dimensionless parameters and present an "asymptotic phase diagram" which delineates the limiting regimes.

Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles.

We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component V_{R} for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D_{2}. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011)PLEEE81539-375510.1103/PhysRevE.84.045304; J. Turbul. 15, 34 (2014)1468-524810.1080/14685248.2013.875188] that the scale invariant part of the distribution has two asymptotic regimes: (1) |V_{R}|≪R, where the distribution depends solely on R, and (2) |V_{R}|≫R, where the distribution is a function of |V_{R}| alone. The probability distributions in these two regimes are matched along a straight line: |V_{R}|=z^{*}R. Our simulations confirm that this is indeed correct. We further obtain D_{2} and z^{*} as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St≈0.7 and the latter has only a weak dependence on St.

Relative velocities in bidisperse turbulent suspensions.

We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analyzing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes numbers. This number, St, is a measure of particle inertia which in turn depends on particle size. When the Stokes numbers are similar, the distribution exhibits power-law tails, just as in the case of equal St. The power-law exponent is a nonanalytic function of the mean Stokes number St[over ¯], so that the exponent cannot be calculated in perturbation theory around the advective limit. When the Stokes-number difference is larger, the power law disappears, but the tails of the distribution still dominate the relative-velocity moments, if St[over ¯] is large enough.

Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers.

In a one-dimensional model for a turbulent aerosol (inertial particles suspended in a random flow) we compute the distributions of particle-velocity gradients and the rate of caustic formation at finite but small Kubo numbers, Ku, for arbitrary Stokes numbers, St. Our results are consistent with those obtained earlier in the limit Ku→0 and St→∞ such that Ku(2)St remains constant. We show how finite-time correlations and nonergodic effects influence the inertial-particle dynamics at finite but small Kubo numbers.

Distribution of relative velocities in turbulent aerosols.

We compute the distribution of relative velocities for a one-dimensional model of heavy particles suspended in a turbulent flow, quantifying the caustic contribution to the moments of relative velocities. The same principles determine the corresponding caustic contribution in d spatial dimensions. The distribution of relative velocities Δv at small separations R acquires the universal form ρ(Δv,R)∼R(d-1)|Δv|(D(2)-2d) for large (but not too large) values of |Δv|. Here D(2) is the phase-space correlation dimension. Our conclusions are in excellent agreement with numerical simulations of particles suspended in a randomly mixing flow in two dimensions, and in quantitative agreement with published data on direct numerical simulations of particles in turbulent flows.

Variable-range projection model for turbulence-driven collisions.

We discuss the relative speeds DeltaV of inertial particles suspended in a highly turbulent gas when the Stokes number, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution P(DeltaV) approximately exp(-C|DeltaV|(4/3)) (for some constant C). Our conclusions are supported by numerical simulations, and by the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesized mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.

In vitro cultivation of rabbit aortic media and the development of the cultures in relation to cellular heterogeneity.

Explants of rabbit aortic media were transferred to tissue culture and the development of the characteristic regions of the cultures was followed. With a new technique the explants were instantly immobilized in the culture flasks, by which the temporal development was strictly defined. The culture developed along the following four major lines: (1) cells migrated from the explant and some cells formed a network of large, attenuated cells, while other, smaller and poorly flattened cells formed clusters attached to the plastic or the network; (2) with continuing growth the network of larger and attenuated cells expanded, grew denser and formed the monolayered component of the culture; (3) multilayered thickenings formed at sites where poorly flattened small cells were numerous either within or at the outer margin of the monolayer or (4) at the margin of the explant where profuse emigration of cells had occurred. Thus, the development of the culture was dependent upon the growth behaviour and expansion of two subpopulation of cells. In the electron microscope the smaller, poorly flattened type of cell with multilayered growth pattern had features of a highly metabolically active cell and had numerous attachment sites of fibronexus type. The attenuated larger cell type growing as monolayers had very abundant microfilaments. The differences may reflect a functional segregation among different cell subpopulations in arterial smooth muscle tissue.

In vitro complex-formation between the molecular chaperone DnaK and staphylococcal protein A derivatives produced in Escherichia coli and its use in the purification of DnaK.

Complex-formation between a truncated staphylococcal Protein A produced in Escherichia coli and a native E coli molecular chaperone, DnaK, can be used for the purification of DnaK by IgG-affinity chromatography. The half-time constant for in vitro formation of the Protein A-DnaK complex is about 14 min. Complex-formation in the presence of ATP is faster, but pre-incubation of DnaK with ATP decreases the final amount of the complex. A second complex with a slower migration on native PAGE is formed when the ratio of DnaK to Protein A is increased. A derivative of Protein A, ZZ, which essentially contains only two modified domains of Protein A, did not bind DnaK. After insertion of a tryptophan-rich peptide close to the C-terminus, the resulting protein, ZZT3, became able to bind DnaK. The binding of these three proteins to DnaK correlates with proteolysis in E coli, indicating a possible role for the binding of DnaK in the control of proteolysis.

Serum protects against azurophil granule dependent down-regulation of complement receptor type 1 (CR1) on human neutrophils.

We have investigated the effect of gradual degranulation on the expression of functional receptors (CR1 and CR3) on human neutrophils. Incubation with increasing concentrations of fMLP (10(-10) - 10(-7) M) translocated CR1 and CR3 to the cell surface in a similar kinetic pattern. When reaching maximal expression of receptors (10(-7) M fMLP), 78 +/- 10% and 87 +/- 9% of the total pool of CR1 and CR3, respectively, were translocated to the cell surface. To drive the mobilization process further, cytochalasin B was introduced to increase the stimulatory effect of fMLP. No further increase in CR1 surface expression was obtained. However, we found a characteristic time course of surface appearance of CR1 and CR3 with a maximal surface expression within 1 minute, followed by a time-related down-regulation of CR1 but not CR3. In addition, the total pool of CR1 in cytochalasin B treated neutrophils was reduced after 15 minutes stimulation with fMLP measured by flow cytometry and immunoblotting, indicating degradation of CR1. The down-regulation of CR1 was concomitant with a translocation of azurophil granules, in terms of upregulation of CD63. Azurophil, but not specific nor secretory, granule fractions caused a down-regulation of CR1 on fMLP activated neutrophils. The presence of human sera and serine protease inhibitor protected CR1 from down-regulation. Together, these findings indicate that intracellular stored proteases, released in the late part of the sequential mobilization process, alters the expression of functional receptors mobilized in the early part of the mobilization process. The findings also focus on the importance of the microenvironment for the net outcome of neutrophil activation in terms of functional receptor expression.