Triangle percolation in mean field random graphs -- with PDE

We apply a PDE-based method to deduce the critical time and the size of the giant component of the ``triangle percolation'' on the Erd\H{o}s-R\'enyi random graph process investigated by Palla, Der\'enyi and VicsekComment: Summary of the changes made: We have changed a remark about k-clique percolation in the first paragraph. Two new paragraphs are inserted after equation (4.4) with two applications of the equation. We have changed the names of some variables in our formula

The stochastic limit in the analysis of the open BCS model

In this paper we show how the perturbative procedure known as {\em stochastic limit} may be useful in the analysis of the Open BCS model discussed by Buffet and Martin as a spin system interacting with a fermionic reservoir. In particular we show how the same values of the critical temperature and of the order parameters can be found with a significantly simpler approach

Equivalence of Bose-Einstein condensation and symmetry breaking

Based on a classic paper by Ginibre [Commun. Math. Phys. {\bf 8} 26 (1968)] it is shown that whenever Bogoliubov's approximation, that is, the replacement of a_0 and a_0^* by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymptotic equality of ||^2/V and /V in symmetry breaking fields, irrespective of the existence or absence of Bose-Einstein condensation. Because the former was proved by Ginibre to hold for absolutely integrable superstable pair interactions, the latter is equally valid in this case. Apart from Ginibre's work, our proof uses only a simple convexity inequality due to Griffiths.Comment: An error in my summary of previous results (the definition of F') is corrected. The correction is to be done also in the PR

Gaussian field theories, random Cantor sets and multifractality

The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian field theories in terms of random Cantor sets and show how universal multifractal scaling exponents can be calculated. We use this approach to characterize the multifractal critical wave function of Dirac fermions interacting with a random vector potential in two spatial dimensions. We show that the multifractal scaling exponents are self-averaging.Comment: Extensive modifications of previous version; exact results replace numerical calculation

Anomalous fluctuations of the condensate in interacting Bose gases

We find that the fluctuations of the condensate in a weakly interacting Bose gas confined in a box of volume $V$ follow the law $\sim V^{4/3}$. This anomalous behaviour arises from the occurrence of infrared divergencies due to phonon excitations and holds also for strongly correlated Bose superfluids. The analysis is extended to an interacting Bose gas confined in a harmonic trap where the fluctuations are found to exhibit a similar anomaly.Comment: 4 pages, RevTe

THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connfiguration; the random walk acts as the random environment. This model provides a continuum version of a model with some relevance to protein conformation. The thermodynamic limit of the specific free energy is shown to exist and to be self-averaging, i.e. it is equal to a trivial --- explicitly computed --- random variable. An estimate of the asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip

Active oceanic spreading in the northern north Fiji basin : results of the NOFI cruise of R/V l'Atalante (Newstarmer project)

The South Pandora and the Tripartite Ridges are active spreading centers located in the northern part of the North Fiji Basin. These spreading centers were surveyed over a distance of 750 km during the NOFI cruise of R/V L'Atalante (August-September 1994) which was conducted in the frame of the french-japanese Newstarmer cooperation project. SIMRAD EM12-dual full coverage swath bathymetric and imagery data as well as airgun 6-channel seismic, magnetics and gravity profiles were recorded along an off-axis from 170°40'E to 178°E. Dredging and piston coring were also performed along and off-axis. The axial domain of the South Pandora Ridge is divided into 5 first-order segments characterized by contrasted morphologies. The average width of the active domain is 20 km and corresponds either to bathymetric highs or to deep elongated grabens. The bathymetric highs are volcanic constructions, locally faulted and rifted, which can obstruct totally the axial valley. The grabens show the typical morphology of slow spreading axes, with two steep walls flanking a deep axial valley. Elongated lateral ridges may be present on both sides of the grabens. Numerous volcanoes, up to several kilometers in diameter, occur on both flanks of the South Pandora Ridge. The Tripartite Ridge consists of three main segments showing a sigmoid shape. Major changes in the direction of the active zones are observed at the segment discontinuities. These discontinuities show various geometrical patterns which suggest complex transform relay zones. Preliminary analysis of seismic reflection profiles suggest that the Tripartite Ridge is a very young feature which propagates into an older oceanic domain characterized by a significant sedimentary cover. By contrast, a very thin to absent sedimentary cover is observed about 100 km on both flanks of the South Pandora Ridge active axis. The magnetic anomaly profiles give evidence of long and continuous lineations, parallel to the South Pandora Ridge spreading axis. (Résumé d'auteur

A restatement of the natural science evidence base concerning grassland management, grazing livestock and soil carbon storage

Approximately a third of all annual greenhouse gas emissions globally are directly or indirectly associated with the food system, and over a half of these are linked to livestock production. In temperate oceanic regions, such as the UK, most meat and dairy is produced in extensive systems based on pasture. There is much interest in the extent to which such grassland may be able to sequester and store more carbon to partially or completely mitigate other greenhouse gas emissions in the system. However, answering this question is difficult due to context-specificity and a complex and sometimes inconsistent evidence base. This paper describes a project that set out to summarize the natural science evidence base relevant to grassland management, grazing livestock and soil carbon storage potential in as policy-neutral terms as possible. It is based on expert appraisal of a systematically assembled evidence base, followed by a wide stakeholders engagement. A series of evidence statements (in the appendix of this paper) are listed and categorized according to the nature of the underlying information, and an annotated bibliography is provided in the electronic supplementary material