Combining mechanism and drift in community ecology: a novel statistical mechanics approach

A key challenge for models of community ecology is to combine deterministic mechanism and stochastic drift in a systematic, transparent and tractable manner. Another challenge is to explain and unify different ecological patterns, hitherto modelled in isolation, within a single modelling framework. Here, we show that statistical mechanics provides an effective way to meet both challenges. We apply the statistical principle of maximum entropy (MaxEnt) to a simple resource-based, non-neutral model of a plant community. In contrast to previous ecological applications of MaxEnt, our use of MaxEnt emphasises its theoretical basis in the combinatorics of sampling frequencies, an approach that clarifies its ecological interpretation. In this approach, mechanism and drift are identified, respectively, with ecological resource constraints and entropy maximization. We obtain realistic predictions for species abundance distributions as well as contrasting stability-diversity relationships at community and population levels. The model also predicts critical behaviour that may provide a basis for understanding desertification and other ecological tipping points. Our results complement and extend previous ecological applications of MaxEnt to new areas of community ecology, and further illustrate MaxEnt as a powerful yet simple modelling tool for combining mechanism and drift in a way that unifies disparate ecological patterns

Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas

The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a $k$-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases.Comment: 4 pages typeset, including 2 figures. Paper accepted for publication in Phys. Rev. Letter

A comparison of incompressible limits for resistive plasmas

The constraint of incompressibility is often used to simplify the magnetohydrodynamic (MHD) description of linearized plasma dynamics because it does not affect the ideal MHD marginal stability point. In this paper two methods for introducing incompressibility are compared in a cylindrical plasma model: In the first method, the limit $\gamma \to \infty$ is taken, where $\gamma$ is the ratio of specific heats; in the second, an anisotropic mass tensor $\mathbf{\rho}$ is used, with the component parallel to the magnetic field taken to vanish, $\rho_{\parallel} \to 0$. Use of resistive MHD reveals the nature of these two limits because the Alfv\'en and slow magnetosonic continua of ideal MHD are converted to point spectra and moved into the complex plane. Both limits profoundly change the slow-magnetosonic spectrum, but only the second limit faithfully reproduces the resistive Alfv\'en spectrum and its wavemodes. In ideal MHD, the slow magnetosonic continuum degenerates to the Alfv\'en continuum in the first method, while it is moved to infinity by the second. The degeneracy in the first is broken by finite resistivity. For numerical and semi-analytical study of these models, we choose plasma equilibria which cast light on puzzling aspects of results found in earlier literature.Comment: 14 pages, 10 figure

Leakage and spillover effects of forest management on carbon storage: theoretical insights from a simple model.

Leakage (spillover) refers to the unintended negative (positive) consequences of forest carbon (C) management in one area on C storage elsewhere. For example, the local C storage benefit of less intensive harvesting in one area may be offset, partly or completely, by intensified harvesting elsewhere in order to meet global timber demand. We present the results of a theoretical study aimed at identifying the key factors determining leakage and spillover, as a prerequisite for more realistic numerical studies.We use a simple model of C storage in managed forest ecosystems and their wood products to derive approximate analytical expressions for the leakage induced by decreasing the harvesting frequency of existing forest, and the spillover induced by establishing new plantations, assuming a fixed total wood production from local and remote (non-local) forests combined.We find that leakage and spillover depend crucially on the growth rates, wood product lifetimes and woody litter decomposition rates of local and remote forests. In particular, our results reveal critical thresholds for leakage and spillover, beyond which effects of forest management on remote C storage exceed local effects. Order of magnitude estimates of leakage indicate its potential importance at global scales

Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.Comment: Latex (Revtex) source + 13 small postscript figures. Revised versio

Anderson localization of ballooning modes, quantum chaos and the stability of compact quasiaxially symmetric stellarators

The radially local magnetohydrodynamic(MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), is examined just above the ballooning beta limit with a method that can lead to estimates of global stability. Here MHDstability is analyzed through the calculation and examination of the ballooning modeeigenvalue isosurfaces in the 3-space (s,α,θk); s is the edge normalized toroidal flux, α is the field linevariable, and θk is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, and gives rise to new types of nonsymmetric eigenvalue isosurfaces in both the stable and unstable spectrum. For eigenvalues far above the marginal point, isosurfaces are topologically spherical, indicative of strong “quantum chaos.” The complexity of QAS marginal isosurfaces suggests that finite Larmor radius stabilization estimates will be difficult and that fully three-dimensional, high-nMHD computations are required to predict the beta limit.Research supported by U.S. DOE Contract No. DEAC02-76CH0373. John Canik held a U.S. DOE National Undergraduate Fellowship at Princeton Plasma Physics Laboratory, during the summer of 2000

Predictive use of the Maximum Entropy Production principle for Past and Present Climates

In this paper, we show how the MEP hypothesis may be used to build simple climate models without representing explicitly the energy transport by the atmosphere. The purpose is twofold. First, we assess the performance of the MEP hypothesis by comparing a simple model with minimal input data to a complex, state-of-the-art General Circulation Model. Next, we show how to improve the realism of MEP climate models by including climate feedbacks, focusing on the case of the water-vapour feedback. We also discuss the dependence of the entropy production rate and predicted surface temperature on the resolution of the model

Detailed balance has a counterpart in non-equilibrium steady states

When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is theoretically well founded. Hypothesising ergodicity constrains the transition rates in driven steady states to respect relations analogous to, but different from the equilibrium principle of detailed balance. The constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables. This prevents over-description of the non-equilibrium reservoir, and implies that not all stochastic equations of motion are equally valid. The resulting recipe for transition rates has many features in common with equilibrium statistical mechanics.Comment: Replaced with minor revisions to introduction and conclusions. Accepted for publication in Journal of Physics

Lattice-gas model for alkali-metal fullerides: face-centered-cubic structure

A lattice-gas model is suggested for describing the ordering phenomena in alkali-metal fullerides of face-centered-cubic structure assuming the electric charge of alkali ions residing in either octahedral or tetrahedral interstitial sites is completely screened by the first-neighbor C_60 molecules. This approximation allows us to derive an effective ion-ion interaction. The van der Waals interaction between the ion and C_60 molecule is characterized by introducing an additional energy at the tetrahedral sites. This model is investigated by using a three-sublattice mean-field approximation and a simple cluster-variation method. The analysis shows a large variety of phase diagrams when changing the site energy parameter.Comment: 10 twocolumn pages (REVTEX) including 12 PS figure