On classification of Poisson vertex algebras

We describe a conjectural classification of Poisson vertex algebras of CFT type and of Poisson vertex algebras in one differential variable (= scalar Hamiltonian operators)

Seasonal variations in Greenland Ice Sheet motion : Inland extent and behaviour at higher elevations

Peer reviewedPreprin

Minimum dissipation principle in stationary non equilibrium states

We generalize to non equilibrium states Onsager's minimum dissipation principle. We also interpret this principle and some previous results in terms of optimal control theory. Entropy production plays the role of the cost necessary to drive the system to a prescribed macroscopic configuration

Quantitative analysis of Clausius inequality

In the context of driven diffusive systems, for thermodynamic transformations over a large but finite time window, we derive an expansion of the energy balance. In particular, we characterize the transformations which minimize the energy dissipation and describe the optimal correction to the quasi-static limit. Surprisingly, in the case of transformations between homogeneous equilibrium states of an ideal gas, the optimal transformation is a sequence of inhomogeneous equilibrium states.Comment: arXiv admin note: text overlap with arXiv:1404.646

Large deviation approach to non equilibrium processes in stochastic lattice gases

We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.Comment: Extended version of the lectures given by G. Jona-Lasinio at the 9th Brazilian school of Probability, August 200

On the long range correlations of thermodynamic systems out of equilibrium

Experiments show that macroscopic systems in a stationary nonequilibrium state exhibit long range correlations of the local thermodynamic variables. In previous papers we proposed a Hamilton-Jacobi equation for the nonequilibrium free energy as a basic principle of nonequilibrium thermodynamics. We show here how an equation for the two point correlations can be derived from the Hamilton-Jacobi equation for arbitrary transport coefficients for dynamics with both external fields and boundary reservoirs. In contrast with fluctuating hydrodynamics, this approach can be used to derive equations for correlations of any order. Generically, the solutions of the equation for the correlation functions are non-trivial and show that long range correlations are indeed a common feature of nonequilibrium systems. Finally, we establish a criterion to determine whether the local thermodynamic variables are positively or negatively correlated in terms of properties of the transport coefficients.Comment: 4 page

Macroscopic current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach to density fluctuations developed in previous articles. More precisely, we derive large deviation estimates for the space--time fluctuations of the empirical current which include the previous results. Large time asymptotic estimates for the fluctuations of the time average of the current, recently established by Bodineau and Derrida, can be derived in a more general setting. There are models where we have to modify their estimates and some explicit examples are introduced.Comment: 4 pages, LaTeX, Changed conten

Large deviations of the empirical current in interacting particle systems

We study current fluctuations in lattice gases in the hydrodynamic scaling limit. More precisely, we prove a large deviation principle for the empirical current in the symmetric simple exclusion process with rate functional I. We then estimate the asymptotic probability of a fluctuation of the average current over a large time interval and show that the corresponding rate function can be obtained by solving a variational problem for the functional I. For the symmetric simple exclusion process the minimizer is time independent so that this variational problem can be reduced to a time independent one. On the other hand, for other models the minimizer is time dependent. This phenomenon is naturally interpreted as a dynamical phase transition.Comment: 26 page

Flood-risk assessment and hazard mitigation mesures : case studies and lessons learnt in Italy

The effect of climate change and the growing world population are together increaing both the chance of flooding and the consequences. In Italy , in the wake of the floods that plagued the northen part of the country in the fifties and sixties ,a process was set in motion aimed at developing a new integrated approach to water management, at the catchment level,suitable for coping with water related disasters.In this context,three case-studies of flood risk management and hazard assessment are described

Liquid phase epitaxy and optical investigation of KYb(WO4)2 thin layers

In recent years, Yb3+ has attracted much attention as an activating ion because of its small quantum defect for laser emission from 2F5/2 to 2F7/2 at ~1.03 µm [1], which provides high efficiency and reduced heat generation. Of high practical interest is the thin-disk laser concept [2], which possesses a tremendous advantage over rod lasers because of its axial-cooling approach and consequent weak thermal lensing and good beam quality.\ud A promising material for Yb3+ thin-disk lasers is KYb(WO4)2 (KYbW) [3]. It can be grown from high-temperature solutions [4]. Nevertheless, the growth of high-quality, single-crystalline layers with thickness in the range of the absorption length of ~13 µm at 981 nm has as yet not been reported. A suitable substrate material is KY(WO4)2 (KYW), but the relatively large differences in the thermal expansion coefficients between KYW and KYbW along the [100], [001], and especially [010] directions [5] favor low temperatures for the hetero-epitaxial growth.\ud For the first time, we demonstrate liquid phase epitaxy (LPE) of KYbW layers. The layers were grown at start temperatures as low as 520°C, which is favorable in order to decrease the thermal stresses due to the differences in the thermal expansion coefficients of substrate and layer. Moreover, the choice of [010]-oriented substrates bypasses the large difference in the thermal expansion coefficient along the [010] direction. KY1-xYbx(WO4)2 layers with varying x = 0.03-1.00 were grown by LPE. The chloride solvent consisted of the eutectic composition [6] 24.4 mol.% KCl, 30.4 mol.% NaCl, and 42.2 mol.% CsCl. The growth temperature spanned the range from 580 to 500°C and the cooling rate was 0.67-1.00 Kh-1. Crack-free, transparent KYbW layers were grown on (010) substrates.\ud Spectroscopic investigations have shown that the lifetime of ~250 µs measured in our LPE-grown KYbW layers is dominated by radiative decay and is very similar to that measured in top-seeded-solution-grown bulk samples [4]. Fast energy migration among the Yb3+ ions and energy transfer to small amounts of Tm3+ and Er3+ ions present in the YbCl3 reagent lead to visible upconversion luminescence in the layers under 981-nm excitation.\ud \ud [1] T.Y. Fan, IEEE J. Quantum Electron. 29, 1457 (1993).\ud [2] A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, Appl. Phys. B 58, 365 (1994).\ud [3] P. Klopp, U. Griebner, V. Petrov, X. Mateos, M.A. Bursukova, M.C. Pujol, R. Solé, J. Gavaldà, M. Aguiló, F. Güell, J. Massons, T. Kirilov, F. Díaz, Appl. Phys. B 74, 185 (2002).\ud [4] M.C. Pujol, M.A. Bursukova, F. Güell, X. Mateos, R. Solé, J. Gavaldà, M. Aguiló, J. Massons, F. Díaz, P. Klopp, U. Griebner, V. Petrov, Phys. Rev. B 65, 165121 (2002).\ud [5] M.C. Pujol, X. Mateos, R. Solé, J. Massons, J. Gavaldà, F. Díaz, M. Aguiló, Mater. Sci. Forum 378-381, 710 (2001).\ud [6] D. Ehrentraut, M. Pollnau, S. Kück, Appl. Phys. B 75, 59 (2002)