Oscillating elastic defects: competition and frustration

We consider a dynamical generalization of the Eshelby problem: the strain profile due to an inclusion or "defect" in an isotropic elastic medium. We show that the higher the oscillation frequency of the defect, the more localized is the strain field around the defect. We then demonstrate that the qualitative nature of the interaction between two defects is strongly dependent on separation, frequency and direction, changing from "ferromagnetic" to "antiferromagnetic" like behavior. We generalize to a finite density of defects and show that the interactions in assemblies of defects can be mapped to XY spin-like models, and describe implications for frustration and frequency-driven pattern transitions.Comment: 4 pages, 5 figure

Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems

Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called "exactness of the mean-field theory". It is found out that this expectation is not necessarily true if the microcanonical ensemble is not equivalent to the canonical ensemble in the mean-field model. Moreover, necessary and sufficient conditions for exactness of the mean-field theory are obtained. These conditions are investigated for two concrete models, the \alpha-Potts model with annealed vacancies and the \alpha-Potts model with invisible states.Comment: 23 pages, to appear in J. Stat. Phy

Ensemble Inequivalence in Mean-field Models of Magnetism

Mean-field models, while they can be cast into an {\it extensive} thermodynamic formalism, are inherently {\it non additive}. This is the basic feature which leads to {\it ensemble inequivalence} in these models. In this paper we study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the {\it canonical} and in the {\it microcanonical} ensembles. The microcanonical solution is obtained both by direct state counting and by the application of large deviation theory. The canonical phase diagram has first order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These two features are discussed in a general context and the appropriate Maxwell constructions are introduced. Some preliminary extensions of these results to weakly decaying nonintegrable interactions are presented.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/

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 $0\leq\alpha<1$

Ensemble inequivalence in systems with long-range interactions

Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions. We display a connection between such behaviour and a mean-field like structure of the partition function. Since short-range models cannot display this kind of behaviour, this strongly suggests that such systems are necessarily non-mean field in the sense indicated here. We illustrate our results showing an application to the Blume-Emery-Griffiths model. We further show that a broad class of systems with non-integrable interactions are indeed of mean-field type in the sense specified, so that they are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble.Comment: 12 pages, no figure

Lyapunov exponents as a dynamical indicator of a phase transition

We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first order-like or second order phase transition depending on the ratio of two length scales: this is an excellent model to characterize $\lambda_1$ as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell's theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.Comment: 6 pages, 7 figure

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