Assessing the Potential Ecotoxicological Risk of Different Organic Amendments Used in Agriculture: Approach Using Acute Toxicity Tests on Plants and Earthworms.

In Europe, spreading organic wastes to fertilize soils is an alternative commonly used instead of chemical fertilizers. Through their contributions of nutrients and organic matter, these wastes promote plant growth and thus agricultural production. However, these organic amendments can also contain mineral and organic pollutants requiring chemical and ecotoxicological analyses to guarantee their harmlessness on soil and its organisms during spreading. The purpose of this study was to assess the potential toxicity of three organic amendments from different sources (sewage sludge, dairy cow manure, dairy cow slurry) by performing chemical analyses and acute toxicity tests on three types of organism: earthworms, plants, soil microbial communities. Chemical analysis revealed a higher content of certain pharmaceuticals, polycyclic aromatic hydrocarbons and metals in sewage sludge in comparison with the two other types of organic wastes. The ecotoxicological assessment showed a dose-dependent effect on soil organisms for the three organic amendments with higher toxic effects during the exposure tests with a soil amended with dairy cow slurry. However, at realistic spreading doses (10 and 20 g kg-1 dry weight of organic amendments) on a representative exposed soil, organic amendment did not show any toxicity in the three organisms studied and had positive effects such as increased earthworm biomass, increased plant root growth and earthworm behavior showing attraction for organic amendment. On the contrary, exposure assays carried out on a limited substrate like sandy soil showed increased toxicity of organic amendments on plant germination and root growth. Overall, the ecotoxicological analysis revealed greater toxicity for soil organisms during the amendment of cow slurry, contrary to the chemical analysis which showed the potential high risk of spreading sewage sludge due to the presence of a higher quantity of pollutants. The analysis of the chemical composition and use of acute toxicity tests is the first essential step for assessing the ecotoxicological risk of spreading organic amendments on soil organisms. In addition to standard tests, the study suggests using a representative soil in acute toxicity tests to avoid overestimating the toxic effects of these organic amendments.

Microscopic interplay of temperature and disorder of a one-dimensional elastic interface.

Elastic interfaces display scale-invariant geometrical fluctuations at sufficiently large lengthscales. Their asymptotic static roughness then follows a power-law behavior, whose associated exponent provides a robust signature of the universality class to which they belong. The associated prefactor has instead a nonuniversal amplitude fixed by the microscopic interplay between thermal fluctuations and disorder, usually hidden below experimental resolution. Here we compute numerically the roughness of a one-dimensional elastic interface subject to both thermal fluctuations and a quenched disorder with a finite correlation length. We evidence the existence of a power-law regime at short lengthscales. We determine the corresponding exponent ζ_{dis} and find compelling numerical evidence that, contrarily to available analytic predictions, one has ζ_{dis}<1. We discuss the consequences on the temperature dependence of the roughness and the connection with the asymptotic random-manifold regime at large lengthscales. We also discuss the implications of our findings for other systems such as the Kardar-Parisi-Zhang equation and the Burgers turbulence.

SIPIBEL observatory: Data on usual pollutants (solids, organic matter, nutrients, ions) and micropollutants (pharmaceuticals, surfactants, metals), biological and ecotoxicity indicators in hospital and urban wastewater, in treated effluent and sludge from wastewater treatment plant, and in surface and groundwater.

The Bellecombe pilot site - SIPIBEL - was created in 2010 in order to study the characterisation, treatability and impacts of hospital effluents in an urban wastewater treatment plant. This pilot site is composed of: i) the Alpes Léman hospital (CHAL), opened in February 2012, ii) the Bellecombe wastewater treatment plant, with two separate treatment lines allowing to fully separate the hospital wastewater and the urban wastewater, and iii) the Arve River as the receiving water body and a tributary of the Rhône River and the Geneva aquifer. The database includes in total 48 439 values measured on 961 samples (raw and treated hospital and urban wastewater, activated sludge in aeration tanks, dried sludge after dewatering, river and groundwater, and a few additional campaigns in aerobic and anaerobic sewers) with 44 455 physico-chemistry values (including 15 pharmaceuticals and 14 related transformation products, biocides compounds, metals, organic micropollutants), 2 193 bioassay values (ecotoxicity), 1 679 microbiology values (including microorganisms and antibioresistance indicators) and 112 hydrobiology values.

Supersymmetries in nonequilibrium Langevin dynamics.

Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It has been known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). These are revealed when the path-integral action is written as a function not only of the physical fields, but also of Grassmann fields representing a Jacobian arising from the noise distribution. SUSYs leave the action invariant upon a transformation of the fields that mixes the physical and the Grassmann ones. We show that contrary to common belief, it is possible to extend the known reversible construction to the case of arbitrary irreversible dynamics, for overdamped Langevin equations with additive white noise-provided their steady state is known. The construction is based on the fact that the Grassmann representation of the functional determinant is not unique, and can be chosen so as to present a generalization of the Parisi-Sourlas SUSY. We show how such SUSYs are related to time-reversal symmetries and allow one to derive modified fluctuation-dissipation relations valid in nonequilibrium. We give as a concrete example the results for the Kardar-Parisi-Zhang equation.

Hysteretic depinning of a particle in a periodic potential: Phase diagram and criticality.

We consider a massive particle driven with a constant force in a periodic potential and subjected to a dissipative friction. As a function of the drive and damping, the phase diagram of this paradigmatic model is well known to present a pinned, a sliding, and a bistable regime separated by three distinct bifurcation lines. In physical terms, the average velocity v of the particle is nonzero only if either (i) the driving force is large enough to remove any stable point, forcing the particle to slide or (ii) there are local minima but the damping is small enough, below a critical damping, for the inertia to allow the particle to cross barriers and follow a limit cycle; this regime is bistable and whether v>0 or v=0 depends on the initial state. In this paper, we focus on the asymptotes of the critical line separating the bistable and the pinned regimes. First, we study its behavior near the "triple point" where the pinned, the bistable, and the sliding dynamical regimes meet. Just below the critical damping we uncover a critical regime, where the line approaches the triple point following a power-law behavior. We show that its exponent is controlled by the normal form of the tilted potential close to its critical force. Second, in the opposite regime of very low damping, we revisit existing results by providing a simple method to determine analytically the exact behavior of the line in the case of a generic potential. The analytical estimates, accurately confirmed numerically, are obtained by exploiting exact soliton solutions describing the orbit in a modified tilted potential which can be mapped to the original tilted washboard potential. Our methods and results are particularly useful for an accurate description of underdamped nonuniform oscillators driven near their triple point.

Statistics of zero crossings in rough interfaces with fractional elasticity.

We study numerically the distribution of zero crossings in one-dimensional elastic interfaces described by an overdamped Langevin dynamics with periodic boundary conditions. We model the elastic forces with a Riesz-Feller fractional Laplacian of order z=1+2ζ, such that the interfaces spontaneously relax, with a dynamical exponent z, to a self-affine geometry with roughness exponent ζ. By continuously increasing from ζ=-1/2 (macroscopically flat interface described by independent Ornstein-Uhlenbeck processes [Phys. Rev. 36, 823 (1930)PHRVAO0031-899X10.1103/PhysRev.36.823]) to ζ=3/2 (super-rough Mullins-Herring interface), three different regimes are identified: (I) -1/2<ζ<0, (II) 0<ζ<1, and (III) 1<ζ<3/2. Starting from a flat initial condition, the mean number of zeros of the discretized interface (I) decays exponentially in time and reaches an extensive value in the system size, or decays as a power-law towards (II) a subextensive or (III) an intensive value. In the steady state, the distribution of intervals between zeros changes from an exponential decay in (I) to a power-law decay P(ℓ)∼ℓ^{-γ} in (II) and (III). While in (II) γ=1-θ with θ=1-ζ the steady-state persistence exponent, in (III) we obtain γ=3-2ζ, different from the exponent γ=1 expected from the prediction θ=0 for infinite super-rough interfaces with ζ>1. The effect on P(ℓ) of short-scale smoothening is also analyzed numerically and analytically. A tight relation between the mean interval, the mean width of the interface, and the density of zeros is also reported. The results drawn from our analysis of rough interfaces subject to particular boundary conditions or constraints, along with discretization effects, are relevant for the practical analysis of zeros in interface imaging experiments or in numerical analysis.

Activity statistics in a colloidal glass former: Experimental evidence for a dynamical transition.

In a dense colloidal suspension at a volume fraction below the glass transition, we follow the trajectories of an assembly of tracers over a large time window. We define a local activity, which quantifies the local tendency of the system to rearrange. We determine the statistics of the time integrated activity, and we argue that it develops a low activity tail that comes together with the onset of glassy-like behavior and heterogeneous dynamics. These rare events may be interpreted as the reflection of an underlying dynamic phase transition.

The SIPIBEL project: treatment of hospital and urban wastewater in a conventional urban wastewater treatment plant.

Hospital wastewater (HWW) receives increasing attention because of its specific composition and higher concentrations of some micropollutants. Better knowledge of HWW is needed in order to improve management strategies and to ensure the preservation of wastewater treatment efficiency and freshwater ecosystems. This context pushed forward the development of a pilot study site named Site Pilote de Bellecombe (SIPIBEL), which collects and treats HWW separately from urban wastewater, applying the same conventional treatment process. This particular configuration offers the opportunity for various scientific investigations. It enables to compare hospital and urban wastewater, the efficiency of the two parallel treatment lines, and the composition of the resulting hospital and urban treated effluents, as well as the evaluation of their effects on the environment. The study site takes into account environmental, economic, and social issues and promotes scientific and technical multidisciplinary actions. ᅟ.

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time.

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which-as shown on the contact process-provides a significant improvement of the large deviation function estimators compared to the standard one.

Kardar-Parisi-Zhang equation with short-range correlated noise: Emergent symmetries and nonuniversal observables.

We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the Kardar-Parisi-Zhang (KPZ) dynamics with a noise featuring smooth spatial correlations of characteristic range ξ. We employ nonperturbative functional renormalization group methods to resolve the properties of the system at all scales. We show that the physics of the standard (uncorrelated) KPZ equation emerges on large scales independently of ξ. Moreover, the renormalization group flow is followed from the initial condition to the fixed point, that is, from the microscopic dynamics to the large-distance properties. This provides access to the small-scale features (and their dependence on the details of the noise correlations) as well as to the universal large-scale physics. In particular, we compute the kinetic energy spectrum of the stationary state as well as its nonuniversal amplitude. The latter is experimentally accessible by measurements at large scales and retains a signature of the microscopic noise correlations. Our results are compared to previous analytical and numerical results from independent approaches. They are in agreement with direct numerical simulations for the kinetic energy spectrum as well as with the prediction, obtained with the replica trick by Gaussian variational method, of a crossover in ξ of the nonuniversal amplitude of this spectrum.

Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model.

We analyze large deviations of the time-averaged activity in the one-dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multicanonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process.

The Giardinà-Kurchan-Peliti algorithm is a numerical procedure that uses population dynamics in order to calculate large deviation functions associated to the distribution of time-averaged observables. To study the numerical errors of this algorithm, we explicitly devise a stochastic birth-death process that describes the time evolution of the population probability. From this formulation, we derive that systematic errors of the algorithm decrease proportionally to the inverse of the population size. Based on this observation, we propose a simple interpolation technique for the better estimation of large deviation functions. The approach we present is detailed explicitly in a two-state model.

Dynamical Symmetry Breaking and Phase Transitions in Driven Diffusive Systems.

We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of equilibrium are derived. These transitions manifest themselves as singularities in the large deviation function, resulting in enhanced current fluctuations. Microscopic models which implement each of the scenarios are presented, with possible experimental realizations. Depending on the model, the singularity is associated either with a particle-hole symmetry breaking, which leads to a continuous transition, or in the absence of the symmetry with a first-order phase transition. An exact Landau theory which captures the different singular behaviors is derived.

Population-dynamics method with a multicanonical feedback control.

We discuss the Giardinà-Kurchan-Peliti population dynamics method for evaluating large deviations of time-averaged quantities in Markov processes [Phys. Rev. Lett. 96, 120603 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.120603]. This method exhibits systematic errors which can be large in some circumstances, particularly for systems with weak noise, with many degrees of freedom, or close to dynamical phase transitions. We show how these errors can be mitigated by introducing control forces within the algorithm. These forces are determined by an iteration-and-feedback scheme, inspired by multicanonical methods in equilibrium sampling. We demonstrate substantially improved results in a simple model, and we discuss potential applications to more complex systems.

Distribution of zeros in the rough geometry of fluctuating interfaces.

We study numerically the correlations and the distribution of intervals between successive zeros in the fluctuating geometry of stochastic interfaces, described by the Edwards-Wilkinson equation. For equilibrium states we find that the distribution of interval lengths satisfies a truncated Sparre-Andersen theorem. We show that boundary-dependent finite-size effects induce nontrivial correlations, implying that the independent interval property is not exactly satisfied in finite systems. For out-of-equilibrium nonstationary states we derive the scaling law describing the temporal evolution of the density of zeros starting from an uncorrelated initial condition. As a by-product we derive a general criterion of the von Neumann's type to understand how discretization affects the stability of the numerical integration of stochastic interfaces. We consider both diffusive and spatially fractional dynamics. Our results provide an alternative experimental method for extracting universal information of fluctuating interfaces such as domain walls in thin ferromagnets or ferroelectrics, based exclusively on the detection of crossing points.

Static fluctuations of a thick one-dimensional interface in the 1+1 directed polymer formulation: numerical study.

We study numerically the geometrical and free-energy fluctuations of a static one-dimensional (1D) interface with a short-range elasticity, submitted to a quenched random-bond Gaussian disorder of finite correlation length ξ>0 and at finite temperature T. Using the exact mapping from the static 1D interface to the 1+1 directed polymer (DP) growing in a continuous space, we focus our analysis on the disorder free energy of the DP end point, a quantity which is strictly zero in the absence of disorder and whose sample-to-sample fluctuations at a fixed growing time t inherit the statistical translation invariance of the microscopic disorder explored by the DP. Constructing a new numerical scheme for the integration of the Kardar-Parisi-Zhang evolution equation obeyed by the free energy, we address numerically the time and temperature dependence of the disorder free-energy fluctuations at fixed finite ξ. We examine, on one hand, the amplitude D[over ̃](t) and effective correlation length ξ[over ̃](t) of the free-energy fluctuations and, on the other hand, the imprint of the specific microscopic disorder correlator on the large-time shape of the free-energy two-point correlator. We observe numerically the crossover to a low-temperature regime below a finite characteristic temperature T(c)(ξ), as previously predicted by Gaussian variational method computations and scaling arguments and extensively investigated analytically in [Phys. Rev. E 87, 042406 (2013)]. Finally, we address numerically the time and temperature dependence of the roughness B(t), which quantifies the DP end point transverse fluctuations, and we show how the amplitude D[over ̃](∞)(T,ξ) controls the different regimes experienced by B(t)-in agreement with the analytical predictions of a DP toy model approach.

Static fluctuations of a thick one-dimensional interface in the 1+1 directed polymer formulation.

Experimental realizations of a one-dimensional (1D) interface always exhibit a finite microscopic width ξ>0; its influence is erased by thermal fluctuations at sufficiently high temperatures, but turns out to be a crucial ingredient for the description of the interface fluctuations below a characteristic temperature T(c)(ξ). Exploiting the exact mapping between the static 1D interface and a 1+1 directed polymer (DP) growing in a continuous space, we study analytically both the free-energy and geometrical fluctuations of a DP, at finite temperature T, with a short-range elasticity and submitted to a quenched random-bond Gaussian disorder of finite correlation length ξ. We derive the exact time-evolution equations of the disorder free energy F[over ¯](t,y), which encodes the microscopic disorder integrated by the DP up to a growing time t and an endpoint position y, its derivative η(t,y), and their respective two-point correlators C[over ¯](t,y) and R[over ¯](t,y). We compute the exact solution of its linearized evolution R[over ¯](lin)(t,y) and we combine its qualitative behavior and the asymptotic properties known for an uncorrelated disorder (ξ=0) to justify the construction of a "toy model" leading to a simple description of the DP properties. This model is characterized by Gaussian Brownian-type free-energy fluctuations, correlated at small |y|

Finite-temperature and finite-time scaling of the directed polymer free energy with respect to its geometrical fluctuations.

We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length ξ and at finite temperature. We address the correspondence between the geometrical transverse fluctuations of the directed polymer, described by its roughness, and the fluctuations of its free energy, characterized by its two-point correlator. Analytical arguments are provided in favor of a generic scaling law between those quantities, at finite time, nonvanishing ξ, and explicit temperature dependence. Numerical results are in good agreement both for simulations on the discrete directed polymer and on a continuous directed polymer (with short-range correlated disorder). Applications to recent experiments on liquid crystals are discussed.

Unifying approach for fluctuation theorems from joint probability distributions.

Any decomposition of the total trajectory entropy production for Markovian systems has a joint probability distribution satisfying a generalized detailed fluctuation theorem, when all the contributing terms are odd with respect to time reversal. The expression of the result does not bring into play dual probability distributions, hence easing potential applications. We show that several fluctuation theorems for perturbed nonequilibrium steady states are unified and arise as particular cases of this general result. In particular, we show that the joint probability distribution of the system and reservoir trajectory entropies satisfy a detailed fluctuation theorem valid for all times.

Mapping nonequilibrium onto equilibrium: the macroscopic fluctuations of simple transport models.

We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the symmetric simple exclusion process. We show that a nonlocal transformation of densities and currents maps the large deviations of the model into those of an open, isolated chain satisfying detailed balance, where rare fluctuations are the time reversals of relaxations. We argue that the existence of such a mapping is the immediate reason why it is possible for this model to obtain an explicit solution for the large-deviation function of densities through elementary changes of variables. This approach can be generalized to the other models previously treated with the macroscopic fluctuation theory.