Mutual Linearity of Nonequilibrium Network Currents.

For continuous-time Markov chains and open unimolecular chemical reaction networks, we prove that any two stationary currents are linearly related upon perturbations of a single edge's transition rates, arbitrarily far from equilibrium. We extend the result to nonstationary currents in the frequency domain, provide and discuss an explicit expression for the current-current susceptibility in terms of the network topology, and discuss possible generalizations. In practical scenarios, the mutual linearity relation has predictive power and can be used as a tool for inference or model proof testing.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.