Random Field and Random Anisotropy Effects in Defect-Free Three-Dimensional XY Models

Monte Carlo simulations have been used to study a vortex-free XY ferromagnet with a random field or a random anisotropy on simple cubic lattices. In the random field case, which can be related to a charge-density wave pinned by random point defects, it is found that long-range order is destroyed even for weak randomness. In the random anisotropy case, which can be related to a randomly pinned spin-density wave, the long-range order is not destroyed and the correlation length is finite. In both cases there are many local minima of the free energy separated by high entropy barriers. Our results for the random field case are consistent with the existence of a Bragg glass phase of the type discussed by Emig, Bogner and Nattermann.Comment: 10 pages, including 2 figures, extensively revise

2-loop Functional Renormalization Group Theory of the Depinning Transition

We construct the field theory which describes the universal properties of the quasi-static isotropic depinning transition for interfaces and elastic periodic systems at zero temperature, taking properly into account the non-analytic form of the dynamical action. This cures the inability of the 1-loop flow-equations to distinguish between statics and quasi-static depinning, and thus to account for the irreversibility of the latter. We prove two-loop renormalizability, obtain the 2-loop beta-function and show the generation of "irreversible" anomalous terms, originating from the non-analytic nature of the theory, which cause the statics and driven dynamics to differ at 2-loop order. We obtain the roughness exponent zeta and dynamical exponent z to order epsilon^2. This allows to test several previous conjectures made on the basis of the 1-loop result. First it demonstrates that random-field disorder does indeed attract all disorder of shorter range. It also shows that the conjecture zeta=epsilon/3 is incorrect, and allows to compute the violations, as zeta=epsilon/3 (1 + 0.14331 epsilon), epsilon=4-d. This solves a longstanding discrepancy with simulations. For long-range elasticity it yields zeta=epsilon/3 (1 + 0.39735 epsilon), epsilon=2-d (vs. the standard prediction zeta=1/3 for d=1), in reasonable agreement with the most recent simulations. The high value of zeta approximately 0.5 found in experiments both on the contact line depinning of liquid Helium and on slow crack fronts is discussed.Comment: 32 pages, 17 figures, revtex

Field quantization for open optical cavities

We study the quantum properties of the electromagnetic field in optical cavities coupled to an arbitrary number of escape channels. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant $\epsilon({\bf r})$ and cavities defined by mirrors of arbitrary shape. Using the Feshbach projector technique we quantize the field in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system--and--bath Hamiltonian of quantum optics. The field dynamics is investigated using the input--output theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise inflicted by the external field. For wave chaotic resonators the mode dynamics is determined by a non--Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.Comment: 16 pages, added references, corrected typo

Topological Defects, Orientational Order, and Depinning of the Electron Solid in a Random Potential

We report on the results of molecular dynamics simulation (MD) studies of the classical two-dimensional electron crystal in the presence disorder. Our study is motivated by recent experiments on this system in modulation doped semiconductor systems in very strong magnetic fields, where the magnetic length is much smaller than the average interelectron spacing $a_0$, as well as by recent studies of electrons on the surface of helium. We investigate the low temperature state of this system using a simulated annealing method. We find that the low temperature state of the system always has isolated dislocations, even at the weakest disorder levels investigated. We also find evidence for a transition from a hexatic glass to an isotropic glass as the disorder is increased. The former is characterized by quasi-long range orientational order, and the absence of disclination defects in the low temperature state, and the latter by short range orientational order and the presence of these defects. The threshold electric field is also studied as a function of the disorder strength, and is shown to have a characteristic signature of the transition. Finally, the qualitative behavior of the electron flow in the depinned state is shown to change continuously from an elastic flow to a channel-like, plastic flow as the disorder strength is increased.Comment: 31 pages, RevTex 3.0, 15 figures upon request, accepted for publication in Phys. Rev. B., HAF94MD

Dynamic Ordering and Transverse Depinning of a Driven Elastic String in a Disordered Media

We examine the dynamics of an elastic string interacting with quenched disorder driven perpendicular and parallel to the string. We show that the string is the most disordered at the depinning transition but with increasing drive partial ordering is regained. For low drives the noise power is high and we observe a 1/f^2 noise signature crossing over to a white noise character with low power at higher drives. For the parallel driven moving string there is a finite transverse critical depinning force with the depinning transition occuring by the formation of running kinks.Comment: 4 pages, 4 postscript figure

Progressive island colonization and ancient origin of Hawaiian Metrosideros (Myrtaceae)

Knowledge of the evolutionary history of plants that are ecologically dominant in modern ecosystems is critical to understanding the historical development of those ecosystems. Metrosideros is a plant genus found in many ecological and altitudinal zones throughout the Pacific. In the Hawaiian Islands, Metrosideros polymorpha is an ecologically dominant species and is also highly polymorphic in both growth form and ecology. Using 10 non-coding chloroplast regions, we investigated haplotype diversity in the five currently recognized Hawaiian Metrosideros species and an established out-group, Metrosideros collina, from French Polynesia. Multiple haplotype groups were found, but these did not match morphological delimitations. Alternative morphologies sharing the same haplotype, as well as similar morphologies occurring within several distinct island clades, could be the result of developmental plasticity, parallel evolution or chloroplast capture. The geographical structure of the data is consistent with a pattern of age progressive island colonizations and suggests de novo intra-island diversification. If single colonization events resulted in a similar array of morphologies on each island, this would represent parallel radiations within a single, highly polymorphic species. However, we were unable to resolve whether the pattern is instead explained by ancient introgression and incomplete lineage sorting resulting in repeated chloroplast capture. Using several calibration methods, we estimate the colonization of the Hawaiian Islands to be potentially as old as 3.9 (−6.3) Myr with an ancestral position for Kaua'i in the colonization and evolution of Metrosideros in the Hawaiian Islands. This would represent a more ancient arrival of Metrosideros to this region than previous studies have suggested

Spatial turnover of multiple ecosystem functions is more associated with plant than soil microbial β-diversity

Biodiversity—both above- and belowground—influences multiple functions in terrestrial ecosystems. Yet, it is unclear whether differences in above- and belowground species composition (β-diversity) are associated with differences in multiple ecosystem functions (e.g., spatial turnover in ecosystem function). Here, we partitioned the contributions of above- and belowground β-diversity and abiotic factors (geographic distance, differences in environments) on the spatial turnover of multiple grassland ecosystem functions. We compiled a dataset of plant and soil microbial communities and six indicators of grassland ecosystem functions (i.e., plant aboveground live biomass, plant nitrogen [N], plant phosphorus [P], root biomass, soil total N, and soil extractable P) from 18 grassland sites on four continents contributing to the Nutrient Network experiment. We used Mantel tests and structural equation models to disentangle the relationship between above- and belowground β-diversity and spatial turnover in grassland ecosystem functions. We found that the effects of abiotic factors on the spatial turnover of ecosystem functions were largely indirect through their influences on above- and belowground β-diversity, and that spatial turnover of ecosystem function was more strongly associated with plant β-diversity than with soil microbial β-diversity. These results indicate that changes in above- and belowground species composition are one mechanism that interacts with environmental change to determine variability in multiple ecosystem functions across spatial scales. As grasslands face global threats from shrub encroachment, conversion to agriculture, or are lost to development, the functions and services they provide will more strongly converge with increased aboveground community homogenization than with soil microbial community homogenization

A roadmap for island biology: 50 fundamental questions after 50 years of The Theory of Island Biogeography

Aims: The 50th anniversary of the publication of the seminal book, The Theory of Island Biogeography, by Robert H. MacArthur and Edward O. Wilson, is a timely moment to review and identify key research foci that could advance island biology. Here, we take a collaborative horizon-scanning approach to identify 50 fundamental questions for the continued development of the field. Location: Worldwide. Methods: We adapted a well-established methodology of horizon scanning to identify priority research questions in island biology, and initiated it during the Island Biology 2016 conference held in the Azores. A multidisciplinary working group prepared an initial pool of 187 questions. A series of online surveys was then used to refine a list of the 50 top priority questions. The final shortlist was restricted to questions with a broad conceptual scope, and which should be answerable through achievable research approaches. Results: Questions were structured around four broad and partially overlapping island topics, including: (Macro)Ecology and Biogeography, (Macro)Evolution, Community Ecology, and Conservation and Management. These topics were then subdivided according to the following subject areas: global diversity patterns (five questions in total); island ontogeny and past climate change (4); island rules and syndromes (3); island biogeography theory (4); immigration–speciation–extinction dynamics (5); speciation and diversification (4); dispersal and colonization (3); community assembly (6); biotic interactions (2); global change (5); conservation and management policies (5); and invasive alien species (4). Main conclusions: Collectively, this cross-disciplinary set of topics covering the 50 fundamental questions has the potential to stimulate and guide future research in island biology. By covering fields ranging from biogeography, community ecology and evolution to global change, this horizon scan may help to foster the formation of interdisciplinary research networks, enhancing joint efforts to better understand the past, present and future of island biotas. © 2017 John Wiley & Sons Lt

Comment on "Worldwide evidence of a unimodal relationship between productivity and plant species richness"

Fraser et al. (Reports, 17 July 2015, p. 302) report a unimodal relationship between productivity and species richness at regional and global scales, which they contrast with the results of Adler et al. (Reports, 23 September 2011, p. 1750). However, both data sets, when analyzed correctly, show clearly and consistently that productivity is a poor predictor of local species richness