Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles

We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. We then present complete equivalence and nonequivalence results at the level of equilibrium macrostates for the two ensembles.Comment: 57 page

The Large Deviation Principle for Coarse-Grained Processes

The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in statistical mechanics by exploiting the long-range nature of the interaction function defining such models. In particular, the large deviation principle is used in a companion paper to derive the variational principles that characterize equilibrium macrostates in statistical models of two-dimensional and quasi-geostrophic turbulence. Such macrostates correspond to large-scale, long-lived flow structures, the description of which is the goal of the statistical equilibrium theory of turbulence. The large deviation bounds for the coarse-grained process under consideration are shown to hold with respect to the strong $L^2$ topology, while the associated rate function is proved to have compact level sets with respect to the weak topology. This compactness property is nevertheless sufficient to establish the existence of equilibrium macrostates for both the microcanonical and canonical ensembles.Comment: 19 page

Ergot: a perennial issue?

Non-Peer Reviewe

Herbaceous Community Structure and Function in the Kluane Region

Our research on the herbaceous understory vegetation in the Kluane region, Yukon, has focused on the structure and function of natural forest understory and grassland communities. The research has involved two long-term projects. The first investigated fertilizer addition and mammalian herbivore exclosure in understory vegetation over a 20-year period and showed that nutrient availability, and not herbivory, controlled herbaceous biomass. Fertilization increased the amount and nutrient content of vegetation, but 13 species were lost, whereas natural levels of mammalian herbivory rarely affected this vegetation or its diversity. The second study investigated how removing plant functional groups from a grassland influences its functioning. Over a seven-year period, we determined that the identity of the functional group was important in determining ecosystem properties and that graminoids were more influential than expected from their proportional biomass. In both of these studies, short-term responses were transient and not indicative of longer-term responses of these communities. This finding reinforces the need for long-term experiments, especially in northern ecosystems. The long-term plots from both projects will continue to be valuable, and they may detect shifts in the plant community due to climate change or unique events in the area.Notre recherche sur la végétation herbacée de sous-bois dans la région de Kluane, au Yukon, a porté plus précisément sur la structure et la fonction des communautés de forêt naturelle de sous-bois et d’herbages. Cette recherche était composée de deux projets à long terme. Le premier projet consistait à étudier l’ajout de fertilisant et l’exclos de mammifères herbivores dans la végétation de sous-bois sur une période de 20 ans, ce qui a permis de montrer que la disponibilité de nutriments, et non pas l’herbivorisme, contrôlait la biomasse herbacée. La fertilisation a ainsi eu pour effet d’accroître la quantité de végétation ainsi que sa teneur en nutriments, mais 13 espèces ont été perdues, tandis que les taux naturels d’herbivorisme chez les mammifères ont eu peu d’incidences sur cette végétation ou sa diversité. Le deuxième projet consistait à étudier comment le retrait de groupes végétaux fonctionnels dans les herbages influence leur fonctionnement. Pendant une période de sept ans, nous avons déterminé que l’identité du groupe fonctionnel jouait un rôle important dans la détermination des propriétés de l’écosystème et que les graminoïdes exerçaient une plus grande influence que prévu à partir de leur biomasse proportionnelle. Pour ces deux projets, les réactions à court terme étaient transitoires et non indicatives des réactions à plus long terme au sein de ces communautés. Cette constatation renforce la nécessité de faire des expériences de longue échéance, surtout dans les écosystèmes nordiques. Les résultats à long terme de ces deux projets continueront de revêtir de l’importance et pourraient permettre de déceler des variations sur le plan de la communauté végétale, variations attribuables à des changements climatiques ou à des événements uniques susceptibles de se produire dans la région

Generalized canonical ensembles and ensemble equivalence

This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the canonical ensemble with an exponential factor involving a continuous function $g$ of the Hamiltonian $H$. We provide here a simplified introduction to our previous work, focusing now on a number of physical rather than mathematical aspects of the generalized canonical ensemble. The main result discussed is that, for suitable choices of $g$, the generalized canonical ensemble reproduces, in the thermodynamic limit, all the microcanonical equilibrium properties of the many-body system represented by $H$ even if this system has a nonconcave microcanonical entropy function. This is something that in general the standard ($g=0$) canonical ensemble cannot achieve. Thus a virtue of the generalized canonical ensemble is that it can be made equivalent to the microcanonical ensemble in cases where the canonical ensemble cannot. The case of quadratic $g$-functions is discussed in detail; it leads to the so-called Gaussian ensemble.Comment: 8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title changed, references updated, new paragraph added, minor differences with published versio

A Quantitative Comparison of Opacities Calculated Using the Distorted- Wave and R\boldsymbol{R}-Matrix Methods

The present debate on the reliability of astrophysical opacities has reached a new climax with the recent measurements of Fe opacities on the Z-machine at the Sandia National Laboratory \citep{Bailey2015}. To understand the differences between theoretical results, on the one hand, and experiments on the other, as well as the differences among the various theoretical results, detailed comparisons are needed. Many ingredients are involved in the calculation of opacities; deconstructing the whole process and comparing the differences at each step are necessary to quantify their importance and impact on the final results. We present here such a comparison using the two main approaches to calculate the required atomic data, the $R$-Matrix and distorted-wave methods, as well as sets of configurations and coupling schemes to quantify the effects on the opacities for the $Fe\ XVII$ and $Ni\ XIV$ ions.Comment: 10 pages, 2 figure

Quantitative partitioning of regional and local processes shaping regional diversity patterns

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73256/1/j.1461-0248.2005.00855.x.pd

On variational principles for coherent vortex structures

Different approaches are discussed of variational principles characterizing coherent vortex structures in two-dimensional flows. Turbulent flows seem to form ordered structures in the large scales of the motion and the self-organization principle predicts asymptotic states realizing an extremal value of the energy or a minimum of enstrophy. On the other hand the small scales take care of the increase of entropy, and asymptotic results can be obtained by applying the theory of equilibrium statistical mechanics