Algebraic damping in the one-dimensional Vlasov equation

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos correcte

Large deviation techniques applied to systems with long-range interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibri um effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the alpha-Ising model in one-dimension with $0\leq\alpha<1$

Improved optical phenotyping of the grape berry surface using light-separation and automated RGB image analysis

Grape resilience towards Botrytis cinerea (B. cinerea) infections (Botrytis bunch rot) is an important concern of breeders and growers. Beside grape bunch architecture, berry surface characteristics like berry bloom (epicuticular wax) as well as thickness and permeability of the berry cuticle represent further promising physical barriers to increase resilience towards Botrytis bunch rot. In previous studies, two efficient sensor-based phenotyping methods were developed to evaluate both berry surface traits fast and objectively: (1) light-separated RGB (red-green-blue) image analysis to determine the distribution of epicuticular wax on the berry surface; and (2) electrical impedance characteristics of the grape berry cuticle based on point measurements. The present proof-of-concept study aiming at the evaluation of light-separated RGB images for both phenotyping applications, phenotyping wax distribution pattern and berry cuticle impedance values. Within the selected grapevine varieties like 'Riesling', 'Sauvignon Blanc' or 'Calardis Blanc' five contributions were achieved: (1) Both phenotyping approaches were fused into one prototypic unified phenotyping method achieving a wax detection accuracy of 98.6 % and a prediction of electrical impedance with an accuracy of 95 %. (2) Both traits are derived using only light-separated images of the grapevine berries. (3) The improved method allows the detection and quantification of additional surface traits of the grape berry surface such as lenticels (punctual lignification) and the berry stem that are also known as being able to affect the grape susceptibility towards Botrytis. (4) The improved image analysis tools are further integrated into a comprehensive workbench allowing end-users, like breeders to combine phenotyping experiments with transparent data management offering valuable services like visualizations, indexing, etc. (5) Annotation work is supported by a sophisticated annotation tool of the image analysis workbench. The usage of light-separated images enables fast and non-invasive phenotyping of different optical berry surface characteristics, which saves time-consuming labor and additionally allows the reuse of the berry samples for subsequent investigations, e.g. Botrytis infection studies

Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions

We investigate the ensemble inequivalence of the spherical spin glass model with nonlinear interactions of polynomial order $p$. This model is solved exactly for arbitrary $p$ and is shown to have first-order phase transitions between the paramagnetic and spin glass or ferromagnetic phases for $p \geq 5$. In the parameter region around the first-order transitions, the solutions give different results depending on the ensemble used for the analysis. In particular, we observe that the microcanonical specific heat can be negative and the phase may not be uniquely determined by the temperature.Comment: 15 pages, 10 figure

On the inequivalence of statistical ensembles

We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient condition for this inequivalence to survive at the thermodynamical limit is worked out. If energy consists in a kinetic and a potential part, the microcanonical ensemble does not converge towards the canonical ensemble when the partial heat capacities per particle fulfill the relation $c_{k}^{-1}+c_{p}^{-1}<0$.Comment: 4 pages, 4 figure

The cavity method for large deviations

A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to compute exponentially small probabilities (rate functions) over different classes of random graphs. It is illustrated with two combinatorial optimization problems, the vertex-cover and coloring problems, for which the presence of replica symmetry breaking phases is taken into account. Applications include the analysis of models on adaptive graph structures.Comment: 18 pages, 7 figure

The working group on the analysis and management of accidents (WGAMA): A historical review of major contributions

The Working Group on the Analysis and Management of Accidents (WGAMA) was created on December 31st, 1999 to assess and strengthen the technical basis needed for the prevention, mitigation and management of potential accidents in NPP and to facilitate international convergence on safety issues and accident management analyses and strategies. WGAMA addresses reactor coolant system thermal-hydraulics, in-vessel behaviour of degraded cores and in-vessel protection, containment behaviour and containment protection, and fission product (FP) release, transport, deposition and retention, for both current and advanced reactors. As a result, WGAMA contributions in thermal-hydraulics, computational fluid-dynamics (CFD) and severe accidents along the first two decades of the 21st century have been outstanding and are summarized in this paper. Beyond any doubt, the Fukushima-Daiichi accident heavily impacted WGAMA activities and the substantial outcomes produced in the accident aftermath are neatly identified in the paper. Beyond specific events, most importantly, around 50 technical reports have become reference material in the different fields covered by the group and they are gathered altogether in the reference section of the paper; a common outstanding feature in most of these reports is the recommendations included for further research, some of which have eventually given rise to some of the projects conducted or underway within the OECD framework. Far from declining, ongoing WGAMA activities are numerous and a number of them is already planned to be launched in the near future; a short mention to them is also included in this paper

Canonical Solution of Classical Magnetic Models with Long-Range Couplings

We study the canonical solution of a family of classical $n-vector$ spin models on a generic $d$-dimensional lattice; the couplings between two spins decay as the inverse of their distance raised to the power $\alpha$, with $\alpha<d$. The control of the thermodynamic limit requires the introduction of a rescaling factor in the potential energy, which makes the model extensive but not additive. A detailed analysis of the asymptotic spectral properties of the matrix of couplings was necessary to justify the saddle point method applied to the integration of functions depending on a diverging number of variables. The properties of a class of functions related to the modified Bessel functions had to be investigated. For given $n$, and for any $\alpha$, $d$ and lattice geometry, the solution is equivalent to that of the $\alpha=0$ model, where the dimensionality $d$ and the geometry of the lattice are irrelevant.Comment: Submitted for publication in Journal of Statistical Physic