H. Russell Bernard is Associate Professor in the Department o f Sociology and At~thropology at West Virginia University in Morgan town, West Virginia. Peter Killworth is in the Department of Applied Math and Theoretical Physics at the University of Cambridge in Cambridge, England. This work was carried out with support from the Federal Bureau of Prisons through the Research office of the Kennedy Youth Center, Morgantown, West Virginia. Special thanks are due to Loren Karacki and Helene Cavior, Directors of Research at KYC. James Short and Richard Ball gave useful criticism o f earlier drafts. Richard Kuznicki, programming consultant at West Virginia, aided in data processing. The inmates and staff at K Y C are tested to death: to them we owe immense gratitude for patience and aid. Write-up and continuing research are supported by the Office of Naval Research. Neither the Federal Bureau o f Prisons nor the Office of Naval Research is responsible for any statement or conclusions in the paper. This paper does not represent the views of either agency and is solely the work o f the authors. A ncw sociomclric teclinicluc is dcscrihctl which is pe~ier;~lly ruorc powerl'ul than prior methotls for analy

This chapter contains sections titled: Introduction Data Structures and Mesh Generation Brief Background on Finite Elements Mesh Adaptivity/Optimization Discretization Stability Applications Future Outlook Concluding Remarks

The part of the meridional overturning circulation driven by time-varying winds is usually assumed to be an Ekman flux within a mixed layer, and a depth- and laterally independent return flow beneath. For a simple linear frictional ocean model, the return flow is studied for a range of frequencies from several days to decades. It is shown that while the east-west integral of the return flow is usually, but not always, almost independent of depth, the spatial distribution of the return flow varies strongly with both horizontal and vertical position. This can have important consequences for calculations of the northward heat flux. which traditionally assumes a spatially uniform return flow.

Resumen En este artículo comparamos dos métodos para la estimación del tamaño de las redes personales utilizando una muestra representativa de Estados Unidos a nivel nacional. Ambos métodos se basan en la habilidad de las personas encuestadas para estimar el número de personas que conocen en subpoblaciones específicas de EE.UU. (ej.: diabéticos, nativo-americanos) y gente en categorías específicas de relación (ej.: familia inmediata, compañeros de trabajo). Los resultados muestran una remarcable similitud entre el tamaño medio de la red obtenido por ambos métodos (aproximadamente 291). Se obtuvieron resultados similares con una muestra nacional distinta. La tentativa de corroboración de nuestras estimaciones mediante una reproducción exacta de la encuesta entre un segmento de población propenso a tener redes más amplias (el clero), dio como resultado un tamaño medio de la red superior. Una investigación extensiva sobre la existencia de efectos de respuesta mostró algunas preferencias por usar ciertos números a la hora de realizar estimaciones, pero nada que afectase de forma significativa a la estimación de tamaño de la red más allá del 6 por ciento. Nuestra conclusión es que ambos métodos utilizados para la estimación del tamaño de las redes personales proporcionan resultados válidos y fiables del tamaño de la red real, pero quedan algunas cuestiones pendientes sobre la exactitud. Abstract In this paper we compare two methods for estimating the size of personal networks using a nationally representative sample of the United States. Both methods rely on the ability of respondents to estimate the number of people they know in specific subpopulations of the U.S. (e.g., diabetics, Native Americans) and people in particular relation categories (e.g., immediate family, coworkers). The results demonstrate a remarkable similarity between the average network size generated by both methods (approximately 291). Similar results were obtained with a separate national sample. An attempt to corroborate our estimates by replication among a population we suspect has large networks (clergy), yielded a larger average network size. Extensive investigation into the existence of response effects showed some preference for using certain numbers when making estimates, but nothing that would significantly affect the estimate of network size beyond about 6 percent. We conclude that both methods for estimating personal network size yield valid and reliable proxies for actual network size, but questions about accuracy remain.

This paper examines the representation of eddy fluxes by bolus velocities. In particular, it asks the following: 1) Can an arbitrary eddy flux divergence of density be represented accurately by a nondivergent bolus flux that satisfies the condition of no normal flow at boundaries? 2) If not, how close can such a representation come? 3) If such a representation can exist in some circumstances, what is the size of the smallest bolus velocity that fits the data?The author finds, in agreement with earlier authors, that the answer to the first question is no, although under certain conditions, which include a modification to the eddy flux divergence, a bolus representation becomes possible. One such condition is when the eddy flux divergence is required to balance the time-mean flux divergence. The smallest bolus flow is easily found by solving a thickness-weighted Poisson equation on each density level. This problem is solved for the North Pacific using time-mean data from an eddy-permitting model. The minimum bolus flow is found to be very small at depth but larger than is usually assumed near the surface. The magnitude of this minimum flow is of order one-tenth of the mean flow. Similar but larger results are found for a coarse-resolution model.

H. Russell Bernard is Associate Professor in the Department of Sociology and Anthropology at West Virginia University in Morgan town, West Virginia. Peter Killworth is in the Department of Applied Math and Theoretical Physics at the University of Cambridge in Cambridge, England. This work was carried out with support from the Federal Bureau o f Prisons through the Research office of the Kennedy Youth Center, Morgantown. West Virginia. Special thanks are due to Loren Karachi and Helene Cavior, Directors of Research at KYC. James Short and Richard Ball gave useful criticism of earlier drafts. Richard Kuznicki, programming consultant at West Virginia, aided in data processing. The inmates and staff at KYC are tested to death: to them we owe immense gratitude for patience and aid. Write-up and continuing research are supported by the Office of Naval Research. Neither the Federal Bureau of Prisons nor the Office of Naval Research is responsible for any statement or conclusions in the paper. This paper does not represent the views of either agency and is solely the work of the authors. A new sociometric technique is described which is generally more powerful than prior methods for analyzing the structure of bounded human groups less than about 150 in size. The method is applied to a female cottage of 4 1 inmates and 1 1 staff members (counselors and officers). Data from this application are presented and analyzed regarding the dynamics of subgroup formation. Some general findings are considered, including: (1) a numerical definition of the word "clique"; (2) the role of weak links in a social structure; and (3) the number of persons and "spheres of life" used by any individual in a complex society to order his social relationships.

Previous literature has suggested that multiple peaks in sea level anomalies (SLA) detected by two-dimensional Fourier Transform (2D-FT) analysis are spectral components of multiple propagating signals, which may correspond to different baroclinic Rossby wave modes. We test this hypothesis in the South Pacific Ocean by applying a 2D-FT analysis to the long Rossby wave signal determined from filtered TOPEX/Poseidon and European Remote Sensing-1/2 satellite altimeter derived SLA. The first four baroclinic mode dispersion curves for the classical linear wave theory and the Killworth and Blundell extended theory are used to determine the spectral signature and energy contributions of each mode. South of 17°S, the first two extended theory modes explain up to 60% more of the variance in the observed power spectral energy than their classical linear theory counterparts. We find that Rossby wave modes 2–3 contribute to the total Rossby wave energy in the SLA data. The second mode contributes significantly over most of the basin. The third mode is also evident in some localized regions of the South Pacific but may be ignored at the large scale. Examination of a selection of case study sites suggests that bathymetric effects may dominate at longer wavelengths or permit higher order mode solutions, but mean flow tends to be the more influential factor in the extended theory. We discuss the regional variations in frequency and wave number characteristics of the extended theory modes across the South Pacific basin.

Many ocean and climate models are incapable of resolving ocean eddies, which are generated on the Rossby radius scale (similar to 50 km) in all ocean basins. However, there is an emerging body of evidence supporting the idea that eddies may have several important effects which cannot be simply parameterised. In particular, eddies may play a role in generating low frequency (decadal) variability in the dynamics of mid-latitude ocean circulation. In this manuscript two specific examples - double gyre circulation and wind-driven channel flow - are used to analyse the dynamical mechanisms of low frequency variability in the ocean.

The local response of an ocean with slowly varying mean flow, stratification, and topography to two sources of disturbance is examined, concentrating on whether the resulting surface elevations are observable. The first is the ocean response to surface forcing (Ekman pumping or buoyancy forcing). For typical amplitudes of random forcing, while much of the ocean response is small (surface elevations less than 1 mm), there are sufficient near resonances (or pseudoresonances involving a critical layer) to produce elevations of 1 cm or more in much of the ocean. The second source is baroclinic instability. The fastest linear growth rate, as well as those for specific wavelengths, is computed globally. Almost all of the ocean is baroclinically unstable, and the most unstable waves are found to possess a small wavelength (often less than 10 km) with a disturbance concentrated near the surface: e-folding times O(20 days) are frequently found. However, the phase speed for the disturbances is almost everywhere slower westward than free planetary waves with mean flow and topography. Since the free waves propagate at speeds similar to observations, instability may be a good source of variability but is probably not responsible directly for observed wave propagation.

We examine methods for reducing respondent burden in evaluating alter–alter ties on a set of network structural measures. The data consist of two sets, each containing 45 alters from respondent free lists: the first contains 447 personal networks, and the second 554. Respondents evaluated the communication between 990 alter pairs. The methods were (1) dropping alters from the end of the free-list, (2) randomly dropping alters, (3) randomly dropping links, and (4) predicting ties based on transitivity. For some measures network structure is captured with samples of less than 20 alters; other measures are less consistent. Researchers should be aware of the need to sample a minimum number of alters to capture structural variation.

An eddy-permitting numerical ocean model is used to investigate the variability of the meridional overturning circulation (MOC). Both wind stress and fluctuations of the seawater density contribute to MOC changes on subannual and seasonal time scales, whereas the interannual variability mainly reflects changes in the density field. Even on subannual and seasonal time scales, a significant fraction of the total MOC variability is due to changes of the density field in the upper 1000 m of the ocean. These changes reflect perturbations of the isopycnal structure that travel westward as Rossby waves. Because of a temporally changing phase difference between the eastern and western boundaries, the Rossby waves affect the MOC by modifying the basinwide east-west density gradient. Both the numerical model used in this study and calculations based on Rossby wave theory suggest that this effect can account for an MOC variability of several Sverdrups (Sv 106 m(3) s(-1)). These results have implications for the interpretation of variability signals inferred from hydrographic sections and might contribute to the understanding of the results obtained from the Rapid Climate Change (RAPID) monitoring array deployed at 26 degrees N in the North Atlantic Ocean.

This article estimates the variation in personal network size, using respondent data containing two systematic sources of error. The data are the proportion of respondents who, on average, claim to know zero, one, and two people in various subpopulations, such as “people who are widows under the age of 65” or “people who are diabetics.” The two kinds of error—transmission error (respondents are unaware that someone in their network is in a subpopulation) and barrier error (something causes a respondent to know more or less than would be expected, in a subpopulation)—are hard to quantify. The authors show how to estimate the shape of the probability density function (pdf) of the number of people known to a random individual by assuming that respondents give what they assume to be accurate responses based on incorrect knowledge. It is then possible to estimate the relative effective sizes of subpopulations and produce an internally consistent theory. These effective sizes permit an evaluation of the shape of the pdf, which, remarkably, agrees with earlier estimates.

A midlatitude coupled ocean-atmosphere model is used to investigate interactions between the atmosphere and the wind-driven ocean circulation. This model uses idealized geometry, yet rich and complicated dynamic flow regimes arise in the ocean due to the explicit simulation of geostrophic turbulence. An interdecadal mode of intrinsic ocean variability is found, and this mode projects onto existing atmospheric modes of variability, thereby controlling the time scale of the atmospheric modes. It is also shown that ocean circulation controls the time scale of the SST response to wind forcing, and that coupled feedback mechanisms thus modify variability of the atmospheric circulation. It is concluded that ocean-atmosphere coupling in the midlatitudes is unlikely to produce new modes of variability but may control the temporal behavior of modes that exist in uncoupled Systems.

We analyse 10,920 shortest path connections between 105 members of an interviewing bureau, together with the equivalent conceptual, or ‘small world’ routes, which use individuals’ selections of intermediaries. This permits the first study of the impact of accuracy within small world chains. The mean small world path length (3.23) is 40% longer than the mean of the actual shortest paths (2.30), showing that mistakes are prevalent. A Markov model with a probability of simply guessing an intermediary of 0.52 gives an excellent fit to the observations, suggesting that people make the wrong small world choice more than half the time.

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The feasibility of using the network scale-up method to estimate heroin use is described. A random sample was asked “How many people do you personally know” who use heroin, and how many in other subpopulations – robbery, assault, burglary, auto-theft victims, binge drinkers, and marijuana users – whose size is more accurately known. A model estimated the overall number of persons each respondent knew and the size of each subpopulation. Estimates of the subpopulation are compared with known subpopulation sizes to assess the plausibility of the model. Data came from the 1999 survey evaluating the “Fighting Back” substance prevention program. Fourteen sites with clear political boundaries were used (n = 5892). Heroin use varied from city to city. Rates estimated for heroin use correlated .832 with the level of respondents' sense of “crime in their neighborhood.” The average ratio between the known populations and the estimates is .943. Members of each subpopulation, especially drug users, tended to know more people within their own subpopulation.

The oceans relinquish O(1PW) of heat into the atmosphere at high latitudes, the lion's share of which originates in localised ‘hotspots’ of violent convective mixing, but despite their small horizontal scale—O(10–100km)—these features may penetrate deeply into the thermocline and are vital in maintaining the Atlantic Meridional Overturning Circulation (MOC). Accurate modelling of the MOC, therefore, requires a large‐scale numerical model with very fine resolution.