Energy Diffusion in Harmonic System with Conservative Noise

We prove diffusive behaviour of the energy fluctuations in a system of harmonic oscillators with a stochastic perturbation of the dynamics that conserves energy and momentum. The results concern pinned systems in any dimension, or unpinned systems in dimension $d\ge 3$ .     

Convection–diffusion equation with space–time ergodic random flow

We prove the homogenization of convection-diffusion in a time-dependent, ergodic, incompressible random flow which has a bounded stream matrix and a constant mean drift. We also prove two variational formulas for the effective diffusivity. As a consequence, we obtain both upper and lower bounds on the effective diffusivity. Received: 17 December 1996/Revised revision: 9 February 1998     

Ergodicity in infinite Hamiltonian systems with conservative noise

Summary. We study the stationary measures of an infinite Hamiltonian system of interacting particles in ℝ ³ subject to a stochastic local perturbation conserving energy and momentum. We prove that the translation invariant measures that are stationary for the deterministic Hamiltonian dynamics, reversible for the stochastic dynamics, and with finite entropy density, are convex combination of “Gibbs” states. This result implies hydrodynamic behavior for the systems under consideration. Received: 17 December 1994/In revised form: 12 April 1996     

On the Superdiffusive Behavior of Passive Tracer with a Gaussian Drift

In the present article we consider a motion of a passive tracer particle, whose trajectory satisfies the Itô stochastic differential equation d x(t) = V(t, x(t)) dt + d w(t), where w(·) is a Brownian motion, V is a stationary Gaussian random field with incompressible realizations independent of w(·) and >0. We prove the superdiffusive character of the motion under certain conditions on the energy spectrum of the velocity field. The result is shown both for steady (time independent) and time dependent and Markovian velocity fields. In addition, we provide explicit upper and lower bounds for the Hurst exponent of the trajectory. All previous rigorous results concerned explicitely solvable shear flows cases.     

Equilibrium Fluctuations for Interacting Ornstein-Uhlenbeck Particles

 We study the hydrodynamic density fluctuations of an infinite system of interacting particles on ℝ ^d . The particles interact between them through a two body superstable potential, and with a surrounding fluid in equilibrium through a random viscous force of Ornstein-Uhlenbeck type. The stationary initial distribution is the Gibbs measure associated with the potential and with a given temperature and fugacity. We prove that the time-dependent density fluctuation field converges in law, under diffusive scaling of space and time, to the solution of a linear stochastic partial differential equation driven by white noise. Received: 10 July 2001 / Accepted: 9 September 2002 Published online: 8 January 2003 RID="*" ID="*" We thank J. Fritz for fruitful discussions, in particular about the existence of the infinite dynamics. A special thanks to L. Bertini for help in the proof of the spectral gap estimate (cf. Appendix B). Communicated by H. Spohn     

DNA as a solar dosimeter in the ocean.

Stratospheric ozone depletion may result in increased solar UV-B radiation to the ocean's upper layers and may cause deleterious effects on marine organisms. The primary UV-B damage induced in biological systems is to DNA. While physical measurements of solar UV-B penetration into the sea have been made, the effective depth and magnitude of actual DNA damage have not been determined. In the experiments reported here, UV-B-induced photoproducts (cyclobutane pyrimidine dimers) have been quantified in DNA molecules exposed to solar UV at the surface and at various depths in clear, tropical marine waters off Lee Stocking Island (23 degrees 45' N, 76 degrees 0.7' W), Exuma Cays, Bahamas. (14C)thymidine-labeled DNA or unlabeled bacteriophage phi X174 DNA was placed in specially designed quartz tubes at various depths for up to five days. Following exposure, DNA samples were removed to the laboratory where UV-B-induced pyrimidine dimers were quantified using a radiochromatographic assay, and bacteriophage DNA inactivation by solar UV-B was assayed by plaque formation in spheroplasts of Escherichia coli. Pyrimidine dimer induction was linear with time but the accumulation of dimers in DNA with time varied greatly with depth. Attenuation of dimer formation with depth of water was exponential. DNA at 3 m depth had only 17% of the pyrimidine dimers found at the surface. Bacteriophage phi X174 DNA, while reduced 96% in plaque-forming ability by a one day exposure to solar UV at the surface of the water, showed no effect on plaque formation after a similar exposure at 3 m. The data collected at the water's surface showed a "surface-enhanced dose" in that DNA damages at the real surface were greater than at the imaginary surface, which was obtained by extrapolating the data at depth to the surface. These results show the sensitivity of both the biochemical (dimers) and biological (phage plaques) DNA dosimeters. DNA dosimeters offer a sensitive, convenient and relatively inexpensive monitoring system, having both biochemical and biological endpoints for monitoring the biologically effective UV-B flux in the marine environment. Unlike physical dosimeters, DNA dosimeters do not have to be adjusted for biological effectiveness since they are sensitive only to DNA-mediated biologically effective UV-B radiation. Results of pyrimidine dimer induction in DNA by solar UV accurately predicted UV doses to the phage DNA.     

Equilibrium fluctuations of asymmetric simple exclusion processes in dimension d≥3

We consider an asymmetric exclusion process in dimension d≥ 3 under diffusive rescaling starting from the Bernoulli product measure with density 0 < α < 1. We prove that the density fluctuation field Y ^N _t converges to a generalized Ornstein–Uhlenbeck process, which is formally the solution of the stochastic differential equatin dY _t = ?Y _t dt + dB ^∇ _t , where ? is a second order differential operator and B ^∇ _t is a mean zero Gaussian field with known covariances. Received: 31 May 1999 / Revised version: 15 June 2000 / Published online: 24 January 2001     

Thermal Conductivity of the Toda Lattice with Conservative Noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter γ. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length n of the chain according to κ(n)∼n ^α , with 0<α≤1/2. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent α of the divergence depends on γ.     

On Viscosity and Fluctuation-Dissipation in Exclusion Processes

We consider the asymmetric simple exclusion process. We review some results in dimension d≥3 concerning the fluctuation-dissipation theorem and we prove regularity of viscosity coefficients.     

Equilibrium Fluctuations for a System of Harmonic Oscillators with Conservative Noise

We investigate the harmonic chain forced by a multiplicative noise, the evolution is given by an infinite system of stochastic differential equations. Total energy and deformation are preserved, the conservation of momentum is destroyed by the noise. Gaussian product measures are the extremal stationary states of this model. Equilibrium fluctuations of the conserved fields at a diffusive scaling are described by a couple of generalized Ornstein-Uhlenbeck processes. 1991 Mathematics Subject Classification: Primary 60K31, secondary 82C22 Partially supported by Hungarian Science Foundation Grant T37685, the European Science Foundation Project RDSES, and by the ACI-NIM 168 ‘Transport hors équilibre.’