A left-handed simplicial action for euclidean general relativity

An action for simplicial euclidean general relativity involving only left-handed fields is presented. The simplicial theory is shown to converge to continuum general relativity in the Plebanski formulation as the simplicial complex is refined. This contrasts with the Regge model for which Miller and Brewin have shown that the full field equations are much more restrictive than Einstein's in the continuum limit. The action and field equations of the proposed model are also significantly simpler then those of the Regge model when written directly in terms of their fundamental variables. An entirely analogous hypercubic lattice theory, which approximates Plebanski's form of general relativity is also presented.Comment: Version 3. Adds current home address + slight corrections to references of version 2. Version 2 = substantially clarified form of version 1. 29 pages, 4 figures, Latex, uses psfig.sty to insert postscript figures. psfig.sty included in mailing, also available from this archiv

Topological Lattice Gravity Using Self-Dual Variables

Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of B\w F theory. The extra symmetries not present in gravity that kill the local degrees of freedom in $B\wedge F$ theory are removed. The remaining symmetries preserve the geometrical character of the lattice. Using self-dual variables, the conditions that guarantee the geometricity of the lattice become reality conditions. The local part of the remaining symmetry generators, that respect the geometricity-reality conditions, has the form of Ashtekar's constraints for GR. Only after constraining the initial data to flat lattices and considering the non-local (plus local) part of the constraints does the algebra of the symmetry generators close. A strategy to extend the model for non-flat connections and quantization are discussed.Comment: 22 pages, revtex, no figure

Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force

We find the lateral projection of the Casimir force for a configuration of a sphere above a corrugated plate. This force tends to change the sphere position in the direction of a nearest corrugation maximum. The probability distribution describing different positions of a sphere above a corrugated plate is suggested which is fitted well with experimental data demonstrating the nontrivial boundary dependence of the Casimir force.Comment: 5 pages, 1 figur

The Casimir force and the quantum theory of lossy optical cavities

We present a new derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are in general lossy and characterized by frequency dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the Casimir force. The force is obtained as an integral over the real frequencies, including the contribution of evanescent waves besides that of ordinary waves, and, then, as an integral over imaginary frequencies. The demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the Casimir force.Comment: 18 pages, 6 figures, minor amendment

Electric current circuits in astrophysics

Cosmic magnetic structures have in common that they are anchored in a dynamo, that an external driver converts kinetic energy into internal magnetic energy, that this magnetic energy is transported as Poynting fl ux across the magnetically dominated structure, and that the magnetic energy is released in the form of particle acceleration, heating, bulk motion, MHD waves, and radiation. The investigation of the electric current system is particularly illuminating as to the course of events and the physics involved. We demonstrate this for the radio pulsar wind, the solar flare, and terrestrial magnetic storms

A Cognitive Model of an Epistemic Community: Mapping the Dynamics of Shallow Lake Ecosystems

We used fuzzy cognitive mapping (FCM) to develop a generic shallow lake ecosystem model by augmenting the individual cognitive maps drawn by 8 scientists working in the area of shallow lake ecology. We calculated graph theoretical indices of the individual cognitive maps and the collective cognitive map produced by augmentation. The graph theoretical indices revealed internal cycles showing non-linear dynamics in the shallow lake ecosystem. The ecological processes were organized democratically without a top-down hierarchical structure. The steady state condition of the generic model was a characteristic turbid shallow lake ecosystem since there were no dynamic environmental changes that could cause shifts between a turbid and a clearwater state, and the generic model indicated that only a dynamic disturbance regime could maintain the clearwater state. The model developed herein captured the empirical behavior of shallow lakes, and contained the basic model of the Alternative Stable States Theory. In addition, our model expanded the basic model by quantifying the relative effects of connections and by extending it. In our expanded model we ran 4 simulations: harvesting submerged plants, nutrient reduction, fish removal without nutrient reduction, and biomanipulation. Only biomanipulation, which included fish removal and nutrient reduction, had the potential to shift the turbid state into clearwater state. The structure and relationships in the generic model as well as the outcomes of the management simulations were supported by actual field studies in shallow lake ecosystems. Thus, fuzzy cognitive mapping methodology enabled us to understand the complex structure of shallow lake ecosystems as a whole and obtain a valid generic model based on tacit knowledge of experts in the field.Comment: 24 pages, 5 Figure

What does inflation really predict?

If the inflaton potential has multiple minima, as may be expected in, e.g., the string theory "landscape", inflation predicts a probability distribution for the cosmological parameters describing spatial curvature (Omega_tot), dark energy (rho_Lambda, w, etc.), the primordial density fluctuations (Omega_tot, dark energy (rho_Lambda, w, etc.). We compute this multivariate probability distribution for various classes of single-field slow-roll models, exploring its dependence on the characteristic inflationary energy scales, the shape of the potential V and and the choice of measure underlying the calculation. We find that unless the characteristic scale Delta-phi on which V varies happens to be near the Planck scale, the only aspect of V that matters observationally is the statistical distribution of its peaks and troughs. For all energy scales and plausible measures considered, we obtain the predictions Omega_tot ~ 1+-0.00001, w=-1 and rho_Lambda in the observed ballpark but uncomfortably high. The high energy limit predicts n_s ~ 0.96, dn_s/dlnk ~ -0.0006, r ~ 0.15 and n_t ~ -0.02, consistent with observational data and indistinguishable from eternal phi^2-inflation. The low-energy limit predicts 5 parameters but prefers larger Q and redder n_s than observed. We discuss the coolness problem, the smoothness problem and the pothole paradox, which severely limit the viable class of models and measures. Our findings bode well for detecting an inflationary gravitational wave signature with future CMB polarization experiments, with the arguably best-motivated single-field models favoring the detectable level r ~ 0.03. (Abridged)Comment: Replaced to match accepted JCAP version. Improved discussion, references. 42 pages, 17 fig

Marine macroalgae as food for earthworms: Growth and selection experiments across ecotypes

Historically, subsistence farmers around the Atlantic coast of NW Europe utilised marine algae as a fertiliser in agroecosystems, a practice that continued in small areas and is now considered to have real potential for re-establishing sustainable food production systems on marginal soils. Earthworms form a significant component of soil fauna and their ecosystem services are well documented. Therefore, palatability of marine organic amendments to faunal detritivores of terrestrial systems is of interest. This work aimed to assess the potential for growth of Aporrectodea caliginosa, Lumbricus rubellus and Aporrectodea longa fed with two common macroalgae (seaweeds), Laminaria digitata and Fucus serratus. In addition, choice chambers were constructed to permit earthworm selection of these macroalgae with more conventional organic materials, horse manure (HM) and birch leaves (BL). Over a period of two months, earthworm species showed significantly greater mass gain with conventional food (p<0.05). Laminaria outperformed Fucus, which in turn was superior to soil alone. Similarly, when given a choice, a significant preference (p<0.001) was shown for the more nitrogen-rich HM and BL over the seaweeds. No removal was recorded for A. caliginosa when offered seaweeds only. By contrast, L. rubellus and A. longa showed significant preferences (p<0.001) for Laminaria over Fucus and fresh material over degraded. These results underline an interest to profit from natural resources (seaweeds) to maintain or improve soil biological quality in marginal coastal areas

Sediment properties as important predictors of carbon storage in zostera marina meadows: a comparison of four European areas

Seagrass ecosystems are important natural carbon sinks but their efficiency varies greatly depending on species composition and environmental conditions. What causes this variation is not fully known and could have important implications for management and protection of the seagrass habitat to continue to act as a natural carbon sink. Here, we assessed sedimentary organic carbon in Zostera marina meadows (and adjacent unvegetated sediment) in four distinct areas of Europe (Gullmar Fjord on the Swedish Skagerrak coast, Asko in the Baltic Sea, Sozopol in the Black Sea and Ria Formosa in southern Portugal) down to similar to 35 cm depth. We also tested how sedimentary organic carbon in Z. marina meadows relates to different sediment characteristics, a range of seagrass-associated variables and water depth. The seagrass carbon storage varied greatly among areas, with an average organic carbon content ranging from 2.79 +/- 0.50% in the Gullmar Fjord to 0.17 +/- 0.02% in the area of Sozopol. We found that a high proportion of fine grain size, high porosity and low density of the sediment is strongly related to high carbon content in Z. marina sediment. We suggest that sediment properties should be included as an important factor when evaluating high priority areas in management of Z. marina generated carbon sinks