Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model

We study synchronization in disordered arrays of Josephson junctions. In the first half of the paper, we consider the relation between the coupled resistively- and capacitively shunted junction (RCSJ) equations for such arrays and effective phase models of the Winfree type. We describe a multiple-time scale analysis of the RCSJ equations for a ladder array of junctions \textit{with non-negligible capacitance} in which we arrive at a second order phase model that captures well the synchronization physics of the RCSJ equations for that geometry. In the second half of the paper, motivated by recent work on small world networks, we study the effect on synchronization of random, long-range connections between pairs of junctions. We consider the effects of such shortcuts on ladder arrays, finding that the shortcuts make it easier for the array of junctions in the nonzero voltage state to synchronize. In 2D arrays we find that the additional shortcut junctions are only marginally effective at inducing synchronization of the active junctions. The differences in the effects of shortcut junctions in 1D and 2D can be partly understood in terms of an effective phase model.Comment: 31 pages, 21 figure

Gravity Anomalies and Flexure of the Lithosphere along the Hawaiian-Emperor Seamount Chain

Simple models for the flexure of the lithosphere caused by the load of the Hawaiian-Emperor Seamount Chain have been determined for different values of the effective flexural rigidity of the lithosphere. The gravity effect of the models have been computed and compared to observed free-air gravity anomaly profiles in the vicinity of the seamount chain. The values of the effective flexural rigidity which most satisfactorily explain both the amplitude and wavelength of the observed profiles have been determined. Computations show that if the lithosphere is modelled as a continuous elastic sheet, a single effective flexural rigidity of about 5 × 10²⁹ dyne-cm can explain profiles along the Hawaiian-Emperor Seamount Chain. If the lithosphere is modelled as a discontinuous elastic sheet an effective flexural rigidity of about 2 × 10³⁰ dyne-cm is required. Since the age of the seamount chain increases from about 3 My near Hawaii to about 70 My near the northernmost Emperor seamount these results suggest there is apparently little decrease in the effective flexural rigidity of the lithosphere with increase in the age of loading. This suggests the lithosphere is rigid enough to support the load of the seamount chain for periods of time of at least several tens of millions of years. Thus the subsidence of atolls and guyots along the chain is most likely to be regional in extent and is unlikely to be caused by an inelastic behaviour of the lithosphere beneath individual seamounts

Influence of Introduced Peregrine Falcons on the Distribution of Red Knots within a Spring Staging Site

Predator recovery driven by single-species management approaches may lead to conservation conflicts between recovered predators and prey species of conservation concern. As part of an aggressive recovery plan, the Eastern Peregrine Falcon Recovery Team released (1975–1985) 307 captive-reared peregrine falcons (Falco peregrinus) and successfully established a breeding population within the mid-Atlantic Coastal Plain, a physiographic region with no historic breeding population and a critical spring staging area for migratory shorebirds. We examined the influence of resident falcons on the distribution of foraging red knots during spring migration. We conducted weekly aerial surveys (2006–2009) along the Virginia barrier islands during the spring staging period (25 April– 6 June) to map foraging red knots (Calidris canutus) and evaluated the influence of proximity (0–3, 3–6, \u3e6 km) of beaches to active peregrine falcon nests on knot density (birds/km). Accumulated use of beaches throughout the season by red knots was significantly influenced by proximity of beaches to active falcon nests such that mean density was more than 6 fold higher on beaches that were \u3e6 km compared to beaches that were only 0–3 km from active eyries. Whether or not an eyrie was used in a given year had a significant influence on the use of associated close (0–3 km) beaches. From 6.5 to 64 fold more knots used beaches when associated eyries were not active compared to when they were active depending on the specific site. Historically, red knots and other migratory shorebirds would have enjoyed a peregrine-free zone within this critical staging site. The establishment of a dense breeding population of falcons within the area represents a new hazard for the knot population

Evolution of reference networks with aging

We study the growth of a reference network with aging of sites defined in the following way. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the Barab\'{a}si-Albert's model and (ii) to $\tau^{-\alpha}$, where $\tau$ is the age of the old site. We consider $\alpha$ of any sign although reasonable values are $0 \leq \alpha \leq \infty$. We find both from simulation and analytically that the network shows scaling behavior only in the region $\alpha < 1$. When $\alpha$ increases from $-\infty$ to 0, the exponent $\gamma$ of the distribution of connectivities ($P(k) \propto k^{-\gamma}$ for large $k$) grows from 2 to the value for the network without aging, i.e. to 3 for the Barab\'{a}si-Albert's model. The following increase of $\alpha$ to 1 makes $\gamma$ to grow to $\infty$. For $\alpha>1$ the distribution $P(k)$ is exponentional, and the network has a chain structure.Comment: 4 pages revtex (twocolumn, psfig), 5 figure

Gravity anomalies and flexure of the lithosphere: A three-dimensional study of the Great Meteor Seamount, northeast Atlantic

Simple models for the flexure of the lithosphere caused by the load of the Great Meteor seamount have been determined for different assumed values of the effective flexural rigidity of the lithosphere. The models utilize a new method for determining the flexure of the lithosphere caused by a three-dimensional load. The gravity effect of the models has been computed and compared with observed free-air anomalies in the vicinity of the seamount. Computations show that the observed free-air anomalies can be most satisfactorily explained for an assumed effective flexural rigidity of the lithosphere of about 6×10²⁹ dyn cm. This value, which is similar to other values determined for loads of different ages, suggests that the oceanic lithosphere is rigid enough to support applied loads for periods of time of at least several tens of millions of years

Instability of scale-free networks under node-breaking avalanches

The instability introduced in a large scale-free network by the triggering of node-breaking avalanches is analyzed using the fiber-bundle model as conceptual framework. We found, by measuring the size of the giant component, the avalanche size distribution and other quantities, the existence of an abrupt transition. This test of strength for complex networks like Internet is more stringent than others recently considered like the random removal of nodes, analyzed within the framework of percolation theory. Finally, we discuss the possible implications of our results and their relevance in forecasting cascading failures in scale-free networks.Comment: 4 pages, 4 figures, final version to be published in Europhys. Let

Status and distribution of colonial waterbirds in coastal Virginia: 2018 breeding season

Colonial waterbirds are highly visible components of coastal avifaunas that share the unusual characteristic of nesting in dense assemblages. One consequence of having large portions of populations nesting in few locations is that even restricted disturbance may have profound consequences on a population level. Development of conservation strategies for these sensitive species requires current status and distribution information. In the fall of 1992, a consortium of agencies and individuals agreed that a comprehensive monitoring program for the Virginia colonial waterbird community was needed and that assessments should be made on regular (initially every 10 years but reduced to 5 years in 2003) intervals for trend analyses. Systematic surveys have been conducted during the breeding seasons of 1993, 2003, 2008 and 2013. The 2018 survey reported here is the fifth in the time series. These surveys have covered colonial waterbird populations (24 species – Great Blue Herons were not included in 2008 and 2018 due to budgetary constraints) throughout the Coastal Plain province of Virginia. We surveyed 270 waterbird colonies during the breeding season of 2018. Colonies supported an estimated 43,159 breeding pairs of 23 species. Gulls were the most abundant group with more than 19,700 breeding pairs. Terns and waders accounted for 7,129 and 6,386 pairs respectively. Although they have declined dramatically, Laughing Gulls continue to be the most abundant species and were three times more abundant than any other species, accounting for nearly 40% of the total waterbird community. The barrier island/lagoon system of the Eastern Shore was the most important region for the majority of colonial species encountered. In 2018, this region supported 22 of the 23 species evaluated. The Eastern Shore accounted for 50.5% and 46.6% of all breeding pairs and colonies respectively. For 17 of the 23 species, the region supported more than 50% of the known coastal population. The colonial waterbird community as a whole in coastal Virginia has declined dramatically since 1993 (2018 survey did not include Great Blue Herons or all Great Egrets). Population estimates for 15 (68%) of the 22 species assessed declined between 1993 and 2018. Declines varied considerably between species with 14 species declining more than 40% and 9 species declining more than 60%. Cattle Egrets showed the highest loss rate (-96.7%), declining from an estimated 1,459 to only 48 pairs. Little Blue Herons declined by 83% from 374 to only 64 pairs. Seven species increased between 1993 and 2018. Dramatic expansions were documented for White Ibis, Double-crested Cormorant, and Brown Pelican. Over the past 25 years, two major forces appear to be shaping the colonial waterbird community in Virginia. These include 1) regional shifts in population centers that are driving population increases in Virginia and 2) habitat degradation related to sea-level rise. With the exception of Great Egrets, all species that have increased over the past 20 years have experienced ongoing range expansions and are riding a population wave that is progressing through Virginia. This includes Great Black-backed Gull, Double-crested Cormorant, Brown Pelican, and White Ibis. Most of the decline in medium-sized waders is being driven by habitat loss related to erosion of islands. This erosion results from sea-level rise, is ongoing and represents a significant threat to these populations. Several ground-nesting seabirds are likely more directly impacted by the loss of viable habitat and demographic impacts related to frequent flooding. The most notable example is the Laughing Gull that has experienced a catastrophic decline in both population and distribution

Null vectors, 3-point and 4-point functions in conformal field theory

We consider 3-point and 4-point correlation functions in a conformal field theory with a W-algebra symmetry. Whereas in a theory with only Virasoro symmetry the three point functions of descendants fields are uniquely determined by the three point function of the corresponding primary fields this is not the case for a theory with $W_3$ algebra symmetry. The generic 3-point functions of W-descendant fields have a countable degree of arbitrariness. We find, however, that if one of the fields belongs to a representation with null states that this has implications for the 3-point functions. In particular if one of the representations is doubly-degenerate then the 3-point function is determined up to an overall constant. We extend our analysis to 4-point functions and find that if two of the W-primary fields are doubly degenerate then the intermediate channels are limited to a finite set and that the corresponding chiral blocks are determined up to an overall constant. This corresponds to the existence of a linear differential equation for the chiral blocks with two completely degenerate fields as has been found in the work of Bajnok~et~al.Comment: 10 pages, LaTeX 2.09, DAMTP-93-4