Assessing the Performance of Sampling Designs for Measuring the Abundance of Understory Plants

Accurate estimation of responses of understory plants to disturbance is essential for understanding the efficacy of management activities. However, the ability to assess changes in the abundance of plants may be hampered by inappropriate sampling methodologies. Conventional methods for sampling understory plants may be precise for common species but may fail to adequately characterize abundance of less common species. We tested conventional (modified Whittaker plots and Daubenmire and point–line intercept transects) and novel (strip adaptive cluster sampling [SACS]) approaches to sampling understory plants to determine their efficacy for quantifying abundance on control and thinned-and-burned treatment units in Pinus ponderosa forests in western Montana, USA. For species grouped by growth-form and for common species, all three conventional designs were capable of estimating cover with a 50% relative margin of error with reasonable sample sizes (3–36 replicates for growth-form groups; 8–14 replicates for common species); however, increasing precision to 25% relative margin of error required sample sizes that may be infeasible (11–143 replicates for growth-form groups; 28–54 replicates for common species). All three conventional designs required enormous sample sizes to estimate cover of nonnative species as a group (29–60 replicates) and of individual less common species (62–118 replicates), even with a 50% relative margin of error. SACS was the only design that efficiently sampled less common species, requiring only 6–11% as many replicates relative to conventional designs. Conventional designs may not be effective for estimating abundance of the majority of forest understory plants, which are typically patchily distributed with low abundance, or of newly establishing nonnative plants. Novel methods such as SACS should be considered in investigations when cover of these species is of concern

Phase diagram of an impurity in the spin-1/2 chain: two channel Kondo effect versus Curie law

We consider a magnetic s=1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain $J_1$ and the coupling between the two sites $J_2$. By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to a non-trivial phase diagram. Depending on the detailed choice of the two (frustrating) coupling strengths, the stable phases correspond either to a decoupled spin with Curie law behavior or to a non-Fermi liquid fixed point with a logarithmically diverging impurity susceptibility as in the two channel Kondo effect. Our results resolve a controversy about the renormalization flow.Comment: 5 pages in revtex format including 4 embedded figures (using epsf). The latest version in PDF format is available from http://fy.chalmers.se/~eggert/papers/phase-diagram.pd

Vortex pinning by a columnar defect in planar superconductors with point disorder

We study the effect of a single columnar pin on a $(1+1)$ dimensional array of vortex lines in planar type II superconductors in the presence of point disorder. In large samples, the pinning is most effective right at the temperature of the vortex glass transition. In particular, there is a pronounced maximum in the number of vortices which are prevented from tilting by the columnar defect in a weak transverse magnetic field. Using renormalization group techniques we show that the columnar pin is irrelevant at long length scales both above and below the transition, but due to very different mechanisms. This behavior differs from the disorder-free case, where the pin is relevant in the low temperature phase. Solutions of the renormalization equations in the different regimes allow a discussion of the crossover between the pure and disordered cases. We also compute density oscillations around the columnar pin and the response of these oscillations to a weak transverse magnetic field.Comment: 12 pages, 5 figures, minor typos corrected, a new reference adde

Haldane gap in the quasi one-dimensional nonlinear σ\sigma-model

This work studies the appearance of a Haldane gap in quasi one-dimensional antiferromagnets in the long wavelength limit, via the nonlinear $\sigma$-model. The mapping from the three-dimensional, integer spin Heisenberg model to the nonlinear $\sigma$-model is explained, taking into account two antiferromagnetic couplings: one along the chain axis ($J$) and one along the perpendicular planes ($J_\bot$) of a cubic lattice. An implicit equation for the Haldane gap is derived, as a function of temperature and coupling ratio $J_\bot/J$. Solutions to these equations show the existence of a critical coupling ratio beyond which a gap exists only above a transition temperature $T_N$. The cut-off dependence of these results is discussed.Comment: 14 pages (RevTeX 3.0), 3 PostScript figures appended (printing instructions included

Exponentially Small Supersymmetry Breaking from Extra Dimensions

The supersymmetric ``shining'' of free massive chiral superfields in extra dimensions from a distant source brane can trigger exponentially small supersymmetry breaking on our brane of order e^{-2 pi R}, where R is the radius of the extra dimensions. This supersymmetry breaking can be transmitted to the superpartners in a number of ways, for instance by gravity or via the standard model gauge interactions. The radius R can easily be stabilized at a size O(10) larger that the fundamental scale. The models are extremely simple, relying only on free, classical bulk dynamics to solve the hierarchy problem.Comment: RevTex, 1 figure. Comment on mu problem adde

Cosmological Implications of Dynamical Supersymmetry Breaking

We provide a taxonomy of dynamical supersymmetry breaking theories, and discuss the cosmological implications of the various types of models. Models in which supersymmetry breaking is produced by chiral superfields which only have interactions of gravitational strength (\eg\ string theory moduli) are inconsistent with standard big bang nucleosynthesis unless the gravitino mass is greater than \CO(3) \times 10^4 GeV. This problem cannot be solved by inflation. Models in which supersymmetry is dynamically broken by renormalizable interactions in flat space have no such cosmological problems. Supersymmetry can be broken either in a hidden or the visible sector. However hidden sector models suffer from several naturalness problems and have difficulties in producing an acceptably large gluino mass.Comment: 24 pages (uses harvmac) UCSD/PTH 93-26, RU-3

A New Dark Matter Candidate: Non-thermal Sterile Neutrinos

We propose a new and unique dark matter candidate: $\sim 100$ eV to $\sim 10$ keV sterile neutrinos produced via lepton number-driven resonant MSW (Mikheyev-Smirnov-Wolfenstein) conversion of active neutrinos. The requisite lepton number asymmetries in any of the active neutrino flavors range from 10$^{-3}$ to 10$^{-1}$ of the photon number - well within primordial nucleosynthesis bounds. The unique feature here is that the adiabaticity condition of the resonance strongly favors the production of lower energy sterile neutrinos. The resulting non-thermal (cold) energy spectrum can cause these sterile neutrinos to revert to non-relativistic kinematics at an early epoch, so that free-streaming lengths at or below the dwarf galaxy scale are possible. Therefore, the main problem associated with light neutrino dark matter candidates can be circumvented in our model.Comment: Latex 11 pages + 1 figur

The Exact Critical Bubble Free Energy and the Effectiveness of Effective Potential Approximations

To calculate the temperature at which a first-order cosmological phase transition occurs, one must calculate $F_c(T)$, the free energy of a critical bubble configuration. $F_c(T)$ is often approximated by the classical energy plus an integral over the bubble of the effective potential; one must choose a method for calculating the effective potential when $V''<0$. We test different effective potential approximations at one loop. The agreement is best if one pulls a factor of $\mu^4/T^4$ into the decay rate prefactor [where $\mu^2 = V''(\phi_f)$], and takes the real part of the effective potential in the region $V''<0$. We perform a similar analysis on the 1-dimensional kink.Comment: 11 pages plus 3 figures in jyTeX; CALT-68-188