Electric Fields in Liquid Water Irradiated with Protons at Ultrahigh Dose Rates.

We study the effects of irradiating water with 3 MeV protons at high doses by observing the motion of charged polystyrene beads outside the proton beam. By single-particle tracking, we measure a radial velocity of the order of microns per second. Combining electrokinetic theory with simulations of the beam-generated reaction products and their outward diffusion, we find that the bead motion is due to electrophoresis in the electric field induced by the mobility contrast of cations and anions. This work sheds light on the perturbation of biological systems by high-dose radiations and paves the way for the manipulation of colloid or macromolecular dispersions by radiation-induced diffusiophoresis.

Simultaneous speciation analysis of Hg and Se in fish by high-performance liquid chromatography and inductively coupled plasma-mass spectrometry following microwave-assisted enzymatic hydrolysis.

This study reports the development and validation of a new analytical method for simultaneous speciation analysis of Se and Hg in fish muscle. For this purpose, four Se species (selenite/Se(IV), selenate/Se(VI), selenomethionine/SeMet, and selenocysteine/SeCys) and two Hg species (inorganic mercury/iHg and methylmercury/MeHg) were extracted simultaneously by microwave-assisted enzymatic hydrolysis and then separated by HPLC in less than 15 min by using a column with both anion and cation exchange mechanisms and a mobile phase consisting of a mixture of methanol 5% (v/v), 45 mM HNO3, 0.015% 2-mercaptoethanol, and 1.5 mM sodium 3-mercapto-1-propanesulfonate. The separated species of Hg and Se were detected online by inductively coupled plasma-mass spectrometry (ICP-MS). The speciation analysis method was validated by means of the accuracy profile approach by carrying out three series of measurements in duplicate on three different days over a time-span of 3 weeks. The limits of quantification (LOQ) are in the range of 0.010-0.013 mg/kg wet weight (ww) for all selenium species, except for Se(IV) (0.15 mg/kg ww), while the coefficient of variation in terms of intermediate reproducibility (CVR) was < 7%. The LOQ for MeHg was 0.006 mg/kg ww, while the CVR was 3%. The method was successfully applied to the analysis of muscle samples from four different fish species: rainbow trout, tuna, swordfish, and dogfish.

Imperfect narrow escape problem.

We consider the kinetics of the imperfect narrow escape problem, i.e., the time it takes for a particle diffusing in a confined medium of generic shape to reach and to be adsorbed by a small, imperfectly reactive patch embedded in the boundary of the domain, in two or three dimensions. Imperfect reactivity is modeled by an intrinsic surface reactivity κ of the patch, giving rise to Robin boundary conditions. We present a formalism to calculate the exact asymptotics of the mean reaction time in the limit of large volume of the confining domain. We obtain exact explicit results in the two limits of large and small reactivities of the reactive patch, and a semianalytical expression in the general case. Our approach reveals an anomalous scaling of the mean reaction time as the inverse square root of the reactivity in the large-reactivity limit, valid for an initial position near the extremity of the reactive patch. We compare our exact results with those obtained within the "constant flux approximation"; we show that this approximation turns out to give exactly the next-to-leading-order term of the small-reactivity limit, and provides a good approximation of the reaction time far from the reactive patch for all reactivities, but not in the vicinity of the boundary of the reactive patch due to the above-mentioned anomalous scaling. These results thus provide a general framework to quantify the mean reaction times for the imperfect narrow escape problem.

Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks.

Persistence, defined as the probability that a signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. Often, persistence decays algebraically with time with non trivial exponents. However, general analytical methods to calculate persistence exponents cannot be applied to the ubiquitous case of non-Markovian systems relaxing transiently after an imposed initial perturbation. Here, we introduce a theoretical framework that enables the non-perturbative determination of persistence exponents of Gaussian non-Markovian processes with non stationary dynamics relaxing to a steady state after an initial perturbation. Two situations are analyzed: either the system is subjected to a temperature quench at initial time, or its past trajectory is assumed to have been observed and thus known. Our theory covers the case of spatial dimension higher than one, opening the way to characterize non-trivial reaction kinetics for complex systems with non-equilibrium initial conditions.

How Stickiness Can Speed Up Diffusion in Confined Systems.

The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian tracers. Here, using a general adsorption desorption model with surface diffusion, we show analytically that making surfaces or obstacles attractive can accelerate dispersion. In particular, we show that this enhancement of diffusion can exist even when the surface diffusion constant is smaller than that in the bulk. Even more remarkably, this enhancement effect occurs when the effective diffusion constant, when restricted to surfaces only, is lower than the effective diffusivity with purely reflecting boundaries. We give analytical formulas for this intriguing effect in periodic arrays of spheres as well as undulating microchannels. Our results are confirmed by numerical calculations and Monte Carlo simulations.

Assessment of the mercury-selenium antagonism in rainbow trout fish.

This study aims at the assessment of mercury (Hg)-selenium (Se) antagonism in fish. For this purpose, rainbow trout fish (Oncorhynchus mykiss) were exposed to methylmercury (MeHg) under controlled conditions, in the presence or absence of selenomethionine (SeMet) using an in-house prepared diet (enriched with MeHg and SeMet at 0.2 µg/g and 5.0 µg/g, respectively). The total duration of the exposure study was 3 months. Fish was sampled and analysed for total Se (SeT) and total mercury (HgT) content after 1, 2 and 3 months of exposure. Six feeding protocols were compared, depending on the exposure type: (i) no MeHg nor SeMet exposure (control group); (ii) exposure to SeMet solely; (iii) exposure to MeHg solely; (iv) exposure to both MeHg and SeMet; (v) exposure first to MeHg during 1 month and then to SeMet during 2 months and (vi), exposure to SeMet during 1 month and then to MeHg for 2 months. The levels of SeT and HgT in the fish (control and supplemented with MeHg/SeMet) were measured by inductively coupled plasma-mass spectrometry (ICPMS). Steadily (linear) bioaccumulation of MeHg in the fish muscle occurred when the fish were exposed individually to this species during the period. The bioaccumulation of MeHg is diminished when the fish are firstly exposed to SeMet and then to MeHg, hence indicating the MeHg detoxification due to SeMet supplementation.

Effective diffusivity of Brownian particles in a two dimensional square lattice of hard disks.

We revisit the classic problem of the effective diffusion constant of a Brownian particle in a square lattice of reflecting impenetrable hard disks. This diffusion constant is also related to the effective conductivity of non-conducting and infinitely conductive disks in the same geometry. We show how a recently derived Green's function for the periodic lattice can be exploited to derive a series expansion of the diffusion constant in terms of the disk's volume fraction φ. Second, we propose a variant of the Fick-Jacobs approximation to study the large volume fraction limit. This combination of analytical results is shown to describe the behavior of the diffusion constant for all volume fractions.

Survival probability of stochastic processes beyond persistence exponents.

For many stochastic processes, the probability [Formula: see text] of not-having reached a target in unbounded space up to time [Formula: see text] follows a slow algebraic decay at long times, [Formula: see text]. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent [Formula: see text] has been studied at length, the prefactor [Formula: see text], which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for [Formula: see text] for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for [Formula: see text] are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.

Trace element contamination in fish impacted by bauxite red mud disposal in the Cassidaigne canyon (NW French Mediterranean).

From 1966 to 2015, the Gardanne alumina refinery discharged some 20 million tons of bauxite residue (called red mud) into the Cassidaigne Canyon (northwest French Mediterranean) with impacts on local ecosystem functioning. Although these red muds contained high levels of trace elements (TE), in particular titanium (Ti), vanadium (V), aluminum (Al) and arsenic (As), surprisingly, their impacts on fish contamination levels and the risk related to fish consumption have been little studied until now. Here, 11 trace elements (Al, As, Cd, Cr, Co, Cr, Mn, Ni, Pb, Ti and V) were analyzed in muscle and, when possible, liver, from 1308 fish of 26 species from an impacted zone in the vicinity of the Cassidaigne Canyon and a reference zone, unaffected by red mud disposals. Moreover, 66 arsenic speciation analyses were performed. Although the impact of human activities on the levels of fish contamination by trace elements is generally not easy to assess in situ because it is blurred by interaction with biological effects, we highlighted significant contamination of the fish species collected from the Cassidaigne Canyon, especially by the main trace elements attributable to the discharges of the Gardanne alumina refinery, namely Al, V and Ti. Moreover, inorganic toxic As concentrations were higher in the impacted zone. The results of this baseline research also confirmed the concern previously raised regarding Hg in Mediterranean organisms and that trace element contamination levels in fish are generally negatively related to fish length for all TE except Hg.

Conical Interfaces between Two Immiscible Fluids Induced by an Optical Laser Beam.

We demonstrate the existence of conical interface deformations induced by a laser beam that are similar to Taylor cones in the electrical regime. We show that the cone morphology can be manipulated by fluid and laser parameters. A theory is proposed to quantitatively describe these dependences in good agreement with experimental data obtained for different fluid systems with low interfacial tensions. Counterintuitively, the cone angle is proved to be independent of the refractive index contrast at leading order. These results open a new optofluidic route towards optical spraying technology-an analogue of electrospraying-and more generally for the optical shaping of interfaces.

Dispersion in two-dimensional periodic channels with discontinuous profiles.

The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose cross section presents singular points, such as abrupt changes of radius or the presence of thin walls, with openings, delimiting periodic compartments composing the channel. Dispersion in such systems is analyzed using the Fick-Jacobs (FJ) approximation. This approximation assumes a much faster equilibration in the lateral than in the axial direction, along which the dispersion is measured. If the characteristic width a of the channel is much smaller than the period L of the channel, i.e., ε = a/L is small, this assumption is clearly valid for Brownian particles. For discontinuous channels, the FJ approximation is only valid at the lowest order in ε and provides a rough, though on occasions rather accurate, estimate of the effective diffusivity. Here we provide formulas for the effective diffusivity in discontinuous channels that are asymptotically exact at the next-to-leading order in ε. Each discontinuity leads to a reduction of the effective diffusivity. We show that our theory is consistent with the picture of effective trapping rates associated with each discontinuity, for which our theory provides explicit and asymptotically exact formulas. Our analytical predictions are confirmed by numerical analysis. Our results provide a precise quantification of the kinetic entropic barriers associated with profile singularities.

Universal first-passage statistics in aging media.

It has been known for a long time that the kinetics of diffusion-limited reactions can be quantified by the time needed for a diffusing molecule to reach a target: the first-passage time (FPT). So far the general determination of the mean first-passage time to a target in confinement has left aside aging media, such as glassy materials, cellular media, or cold atoms in optical lattices. Here we consider general non-Markovian scale-invariant diffusion processes, which model a broad class of transport processes of molecules in aging media, and demonstrate that all the moments of the FPT obey universal scalings with the confining volume with nontrivial exponents. Our analysis shows that a nonlinear scaling with the volume of the mean FPT, which quantities the mean reaction time, is the hallmark of aging and provides a general tool to quantify its impact on reaction kinetics in confinement.

Boundaries Control Collective Dynamics of Inertial Self-Propelled Robots.

Simple ingredients, such as well-defined interactions and couplings for the velocity and orientation of self-propelled objects, are sufficient to produce complex collective behavior in assemblies of such entities. Here, we use assemblies of rodlike robots made motile through self-vibration. When confined in circular arenas, dilute assemblies of these rods act as a gas. Increasing the surface fraction leads to a collective behavior near the boundaries: polar clusters emerge while, in the bulk, gaslike behavior is retained. The coexistence between a gas and surface clusters is a direct consequence of inertial effects as shown by our simulations. A theoretical model, based on surface mediated transport accounts for this coexistence and illustrates the exact role of the boundaries. Our study paves the way towards the control of collective behavior: By using deformable but free to move arenas, we demonstrate that the surface induced clusters can lead to directed motion, while the topology of the surface states can be controlled by biasing the motility of the particles.

Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius.

Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential.

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F. The system is studied in the region where the force is close to the critical value F_{c} at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F>F_{c}, whereas for F

Mean first-passage times of non-Markovian random walkers in confinement.

The first-passage time, defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role in quantifying the efficiency of processes as varied as diffusion-limited reactions, target search processes or the spread of diseases. Most methods of determining the properties of first-passage time in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects cannot be neglected: that is, the future motion of the random walker does not depend only on its current position, but also on its past trajectory. Examples of non-Markovian dynamics include single-file diffusion in narrow channels, or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics, dense soft colloids or viscoelastic solutions. Here we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean first-passage time of a Gaussian non-Markovian random walker to a target. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the fictitious trajectory that the random walker would follow after the first-passage event takes place, which are shown to govern the first-passage time kinetics. This analysis is applicable to a broad range of stochastic processes, which may be correlated at long times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes, including the case of fractional Brownian motion in one and higher dimensions. These results reveal, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.

Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions.

This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete nonlinear dynamics. It is found that Markovian treatments based on a Wilemski-Fixman approximation significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics. In addition, this analysis provides scaling laws of the mean first cyclization time (MFCT) with the polymer size N and capture radius b, which are identical in both Markovian and non-Markovian approaches. In particular, it is found that the scaling of the MFCT for large N is given by T ∼ N(3/2)ln(N/b(2)), which differs from the case of the Rouse dynamics where T ∼ N(2). The extension to the case of the reaction kinetics of a monomer of a Zimm polymer with an external target in a confined volume is also presented.

Force-Induced Dispersion in Heterogeneous Media.

The effect of a constant applied external force, induced for instance by an electric or gravitational field, on the dispersion of Brownian particles in periodic media with spatially varying diffusivity, and thus mobility, is studied. We show that external forces can greatly enhance dispersion in the direction of the applied force and also modify, to a lesser extent and in some cases nonmonotonically, dispersion perpendicular to the applied force. Our results thus open up the intriguing possibility of modulating the dispersive properties of heterogeneous media by using externally applied force fields. These results are obtained via a Kubo formula that can be applied to any periodic advection diffusion system in any spatial dimension.

Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.

Cyclization kinetics of Gaussian semiflexible polymer chains.

We consider the dynamics and the cyclization kinetics of Gaussian semiflexible chains, in which the interaction potential tends to align successive bonds. We provide asymptotic expressions for the cyclization time, for the eigenvalues and eigenfunctions, and for the mean square displacement at all time and length scales, with explicit dependence on the capture radius, on the positions of the reactive monomers in the chain, and on the finite number of beads. For the cyclization kinetics, we take into account non-Markovian effects by calculating the distribution of reactive conformations of the polymer, which are not taken into account in the classical Wilemski-Fixman theory. Comparison with numerical simulations confirms the accuracy of this non-Markovian theory.