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For five individuals, a social network was constructed from a series of his or her dreams. Three important network measures were calculated for each network: transitivity, assortativity, and giant component proportion. These were monotonically related; over the five networks as transitivity increased, assortativity increased and giant component proportion decreased. The relations indicate that characters appear in dreams systematically. Systematicity likely arises from the dreamer's memory of people and their relations, which is from the dreamer's cognitive social network. But the dream social network is not a copy of the cognitive social network. Waking life social networks tend to have positive assortativity; that is, people tend to be connected to others with similar connectivity. Instead, in our sample of dream social networks assortativity is more often negative or near 0, as in online social networks. We show that if characters appear via a random walk, negative assortativity can result, particularly if the random walk is biased as suggested by remote associations.

Measurements of trace elements leached from host rocks can indicate the source of flowing groundwater and provide the host rock's fingerprint information that may be useful in understanding the mixing patterns of different groundwaters and flowpaths. In this study, the leaching characteristics of three widely-distributed aquifer host rocks in Southern Nevada were investigated through leaching experiments of 13 trace elements under different experimental conditions (leaching time, pH, grain size, and rock mineralogy). The fraction of leached trace elements from different aquifer host rocks was calculated for examining the water-rock interaction in different conditions. The effect of host rock mineralogy on leachate composition was examined, which could provide useful information about groundwater source. Solute speciation and saturation indices were simulated using geochemical modeling to further explore the redistribution and leaching process of trace elements.

This research was initiated to investigate associations between flour breadmaking traits and mixing and empirical dough rheological properties under thermal stress. Thirty hard spring wheat flour samples were analyzed by a Mixolab standard procedure. Mixolab profiles were divided into six different stages, and torque measurements of individual stages were modeled by nonlinear curve fitting using a compound of two solution searching procedures, multidimensional unconstrained nonlinear minimization and genetic algorithm. Mixing patterns followed exponential equations. Dough torque patterns under heat constraint, specifically dough thermal weakening and pasting profiles, were described by a sigmoid logistic equation as a function of time. Dough stability during heating appeared important for bread loaf volume increase from significant correlations between bread loaf volume and parameters generated from models of a dough thermal weakening stage. Multivariate continuum regression was employed to calib...

Experimental and numerical investigations have been carried out to assess the effect of the vessel geometry (number of baffles) and the shape of the Maxblend impeller (configuration of the bottom paddle and angle of the upper grid) with viscous Newtonian fluids in the laminar and lower turbulent mixing regimes. Two parameters have been explored namely the power consumption of the impeller and the mixing time. Videos of the discoloration process have also been taken to get access to the mixing patterns. A nominal 50-l vessel has been used in the experiments. The number of baffles has been varied from 1 to 4, and the bottom paddle has been modified by making openings to allow flow passage. Finally, the effect of using a straight grid in the upper part of the Maxblend has been studied under the same conditions. It is shown that the number of baffles does not have a significant effect on the power consumption, the mixing evolution, and the mixing time regardless of the flow regime. Making openings in the bottom paddle allows for the destruction of the segregated zones at the bottom of the tank at the expense of a very slight increase in power consumption and mixing time. Finally, the power and mixing time are both increased with a straight grid Maxblend. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd.

This work reviews some evidence for the existence of large-scale structures in turbulent diffusion flames, at low and high Reynolds numbers, for free jets and jets in crossflow over a range of buoyancy conditions. The striking differences between the velocity field and the scalar field will be highlighted and implications for mixing and reaction are explored. The origins of these differences are discussed by analogy to simple large-scale wave motions in the velocity field leading to complex mixing patterns in the scalar field.

A layer of intensive mixing (entrainment interface layer, [EIL]) at the top of marine stratocumulus under a strong inversion has been investigated with 10 cm resolution using an ultrafast thermometer (UFT-F; temperature), a particle volume monitor PVM–100A (liquid water content), and a fast forward scattering spectrometer probe (FFSSP; droplet spectra). Measurements were collected on board the NCAR C-130 aircraft during research flight RF05 of DYCOMS-II field study. The EIL consists of mutual filaments of cloudy and clear air at different stages of stirring, mixing, and homogenization. Borders between these filaments are often very sharp, with the 10 cm resolution of the instruments being insufficient to characterize them properly in many cases. Certain classifications of these filaments and hypotheses about the mechanisms of their formation have been proposed. The common occurrence of filaments of sizes smaller than the resolution of instruments has been indirectly confirmed. This is in agreement with the observed cloud droplet spectra showing variations of droplet number concentration without significant change of the mean droplet diameter and spectrum width. Copyright © 2007 Royal Meteorological Society

Mixing of shear-thinning fluids with yield stress is investigated in a three-dimensional (3-D) flow both in experiments and in simulations. Experiments are conducted in a stirred tank using tracer visualization and velocity measurements. Bulk flow visualization shows the familiar cavern formation around the impeller with stagnant zones surrounding it. Detailed flow visualization inside caverns reveals the main ingredients of chaotic flow: lobe formation, stretching, folding, and self-similar mixing patterns. For multiple impeller systems, however, we find strong compartmentalization characterized by robust segregation between adjacent caverns, hindering mixing performance. Mixing efficiency is enhanced by moving the shaft off-center, which breaks spatial symmetry. The displacement of the shaft from the tank centerline has a beneficial effect on manifold structure: segregated regions are destroyed, separatrices are eliminated, and axial circulation is improved. Numerical simulations are performed by solving the incompressible Reynolds Averaged Navier Stokes equation with a Galerkin Least-Squares finite-element formulation and a macroscopic rheological model. Simulations are able to capture the main features of the flow and are used to investigate stretching statistics and scale behavior. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Anabaena circinalis is common in the lower Murray River, Australia, and may compromise water quality due to the release of toxins. The water is turbid and thermal structure may significantly affect light availability. An in situ experiment was designed to represent complete mixing, diurnal stratification and persistent stratification and test the effect on growth of A. circinalis. To represent the mixing treatments, cells were incubated in diffusion chambers that were adjusted to different positions in the water-column throughout the day. Populations exposed to persistent stratification over six days grew significantly faster than the other treatments at a rate of 0.65 day−1. However, growth of the diurnally stratified populations was slower than (0.28 day−1), or similar to (0.40 day−1) the mixed population (0.40 day−1). Therefore, the growth of the subpopulations exposed to the euphotic zone was insufficient to counteract the slow growth of the majority that were confined to darkness during the stratified period. A relationship between growth rate (G) and average daily light dose (I) was constructed and growth rate at optimal light dose (Gmax), slope of linear section of G–I curve (α), and light dose where lines of Gmax and light-limited portion of G–I curve intersect (Ik) were solved as 0.66 day−1, 0.12 day−1 (mol−1 m−2 day−1)−1 and 5.4 mol m−2 day−1, respectively. Using these parameters, a model was developed to predict possible differences in growth between diurnal and mixed populations under varying conditions of vertical light attenuation, mixed depth and incubation time. Copyright © 2003 John Wiley & Sons, Ltd.

A detailed Lagrangian analysis of partially mixed structures in an SMX static mixer is presented, with emphasis on laminar flows with Reynolds numbers between 1 and 100. The distribution of a small amount of equal-viscosity additive is examined based on computing the trajectories of passive tracer particles through the mixer. Three radial positions (one centerline and two off-center) are chosen for injection and the mixing patterns are compared in order to investigate the effect of injection location on mixing. Mixing measures, such as the decrease in the variation coefficient with axial distance, and the increase in the average rate of stretching, are discussed in order to quantify mixing performance. It is found that mixing rates for the centerline injections are larger than for the off-center injection positions investigated. The presence of self-similarity in the stretching field and the mixing patterns, and the exponential decrease in variation coefficient with increasing axial distance provides evidence for chaotic mixing behavior in this device.

Mixing patterns of a passive dye were investigated experimentally in an unwound screw channel flow with periodic barriers that serve to induce a chaotic flow. Continuous cross-sectional and longitudinal mixing patterns were observed as a function of the barrier fraction and were interpreted in terms of dynamical systems theory, along with 3-D numerical simulations. Observations include: periodically invariant cross-sectional mixing patterns due to the resonance bands; pile-up of dye streaks caused by stretching and folding of manifolds near hyperbolic points; unmixed zones due to KAM tori; longitudinal deformation patterns with exit time distributions; and effects of the barrier fraction on the size of unmixed islands, the thickness of the band of dye streaks, and the distribution of exit times

Summary Scale-free networks are often used to model a wide range of real-world networks, such as social, technological, and biological networks. Understanding the structure of scale-free networks evolves into a big data problem for business, management, and protein function prediction. In the past decade, there has been a surge of interest in exploring the properties of scale-free networks. Two interesting properties have attracted much attention: the assortative mixing and community structure. However, these two properties have been studied separately in either theoretical models or real-world networks. In this paper, we show that the structural features of communities are highly related with the assortative mixing in scale-free networks. According to the value of assortativity coefficient, scale-free networks can be categorized into assortative, disassortative, and neutral networks, respectively. We systematically analyze the community structure in these three types of scale-free networks through six metrics: node embeddedness, link density, hub dominance, community compactness, the distribution of community sizes, and the presence of hierarchical communities. We find that the three types of scale-free networks exhibit significant differences in these six metrics of community structures. First, assortative networks present high embeddedness, meaning that many links lying within communities but few links lying between communities. This leads to the high link density of communities. Second, disassortative networks exhibit great hubs in communities, which results in the high compactness of communities that nodes can reach each other via short paths. Third, in neutral networks, a big portion of links act as community bridges, so they display sparse and less compact communities. In addition, we find that (dis)assortative networks show hierarchical community structure with power-law-distributed community sizes, while neutral networks present no hierarchy. Understanding the structure of communities from the angle of assortative mixing patterns of nodes can provide insights into the network structure and guide us in modeling information propagation in different categories of scale-free networks. Copyright © 2016 John Wiley & Sons, Ltd.

The relationship between concentration c and discharge Q in a stream is one of the aspects of hydrochemical catchment response that has been used widely as a diagnostic. In particular, loops in the c-Q curve, commonly referred to as hysteresis loops, are used to infer particular mixing patterns. At the South Fork of Brokenback Run (SFBR) in the Shenandoah National Park, Virginia, we have evidence that stream dynamics reflect a system composed of an ephemeral subsurface stormflow zone perched above a perennial water table. The relationship between dissolved silica and stream discharge exhibits hysteresis in the clockwise (CW) direction. Modelling this relationship in the context of three-component mixing with constant-concentration end members failed to reproduce the observed c-Q pattern. In this paper we examine the possibility that temporal variation in soil-water concentrations of silica can explain how CW hysteresis loops in the c-Q curve can arise. In particular, we examine the role of the ratio of a hydrological time scale to a chemical time scale in determining the nature of hysteresis loops. The CW loops that we observe in SFBR can be explained by time variability in soil-water concentrations only if the chemical (leaching) time constant is less than (or only slightly greater than) the hydrological time constant. The near equality of these time constants is consistent with reports from hydrological measurements and leaching experiments.

A method of treating data acquired with the planar laser-induced fluorescence technique has been developed to visualize the topology of two-dimensional concentration fields and to describe the dyna ...

An 8-plane 16-sensor ring electrical resistance tomography (ERT) system was designed and installed within a 1.5-m-dia. plant-scale stirred uessel. Results are reported for the unsteady dynamic macromixing of miscible liquids following a pulse addition of brine tracer. Acquired data, afier reconstruction, is conveniently represented as a stack of 2-D tomograms and 3-D solid body isosurjaces, thereby providing an equiualent of medical whole-body scanning for a chemical process unit. The results demonstrate the ability of ERT to distinguish the different mixing patterns from two types of impeller in 3-D and to monitor plant-scale miscible liquid mixing processes aperimentally, with good resolution in both space and time.

In the accompanying article, Part I, we have described the basic mechanism of chaotic mixings due to a new “Chaos Screw” in single-screw extrusion processes, and presented experimental evidence of the chaotic mixing in a single-screw extruder with a typical Chaos Screw installed. The present article, Part II, will be focused on the numerical investigations of the chaotic flows via the Chaos Screw in a single-screw extruder. The three-dimensional velocity fields in both the no-barrier and barrier regions were separately calculated via a finite element analysis of the quasi–three-dimensional flow in each region, and were subsequently used in the numerical simulations of chaotic flow behaviors. Extensive numerical simulation results will be presented in terms of particle trajectories, Poincare sections, and mixing patterns for several dimensionless parameters. It was found that invariant manifolds obtained by numerical simulations were in good agreement with those from experiments. © 1996 John Wiley & Sons, Inc.

As far as the mixing performance in single-screw extrusion processes is concerned, it is well known that the deformation measure or stretching which materials undergo due to the regular flows inside a conventional screw channel increases linearly with the extruder channel length. In general, the chaotic mixing is far superior to the regular mixing. Therefore, it would be fascinating if one could make the chaotic mixing possible in single-screw extruders with a special, and yet easily manufacturable screw without sacrificing the pumping performance of single-screw extruders. With this purpose in mind, we have developed a new screw (termed “Chaos Screw”) for the single-screw extrusion process to enhance the mixing performance via the chaotic flows. The main idea of the Chaos Screw design lies in the spatially periodic barriers inserted in the channel to break closed streamlines in regular flows, which induces the chaotic mixing. The present article describes the basic mechanism of the chaotic mixing in a single-screw extruder and presents experimental evidence of the chaotic mixing using the Chaos Screw. Experimental mixing patterns due to the chaotic flow clearly indicate that the Chaos Screw drastically enhances the mixing performance in a single-screw extruder. It may be mentioned that the accompanying article, Part II, presents numerical investigation which shows that the chaotic mixing was successfully predicted by numerical simulations. © 1996 John Wiley & Sons, Inc.

As numerical simulations in mixing become pervasive, an analysis of errors becomes crucial. Purposely discretized examples with exact analytical solutions provide a reference point from which to judge the soundness of numerical solutions. Three types of errors are identified and examined: discretization, time integration, and round-off, with emphasis on the first two. Theoretical derivations and numerical examples for 2-D, steady (regular) and time-periodic (chaotic) flows indicate that errors, in general, behave as material lines. In regular flows, their magnitude increases, on the average, with at most t{sup 2}, while in chaotic flows it increases exponentially. Errors tend to align with the direction of the streamlines in regular flows and with manifolds in chaotic flows. As a result, even though exact and calculated trajectories diverge exponentially fast in chaotic flows, overall mixing patterns are reproduced, at least qualitatively, even when the velocity fields do reproduce qualitatively the main features of a line as it is deformed by the flow, although the error in its length may be more than 100%. It is concluded that accurate quantitative information, such as the location of periodic points or the length of a deformed line, can be obtained from numerical simulations. However, robust application ofmore » standard numerical analysis tools, such as mesh refinement, is necessary, which in turn, can lead to nearly prohibitive computational costs.« less

In dynamic models of infectious disease transmission, typically various mixing patterns are imposed on the so-called Who-Acquires-Infection-From-Whom matrix (WAIFW). These imposed mixing patterns are based on prior knowledge of age-related social mixing behavior rather than observations. Alternatively, one can assume that transmission rates for infections transmitted predominantly through non-sexual social contacts, are proportional to rates of conversational contact which can be estimated from a contact survey. In general, however, contacts reported in social contact surveys are proxies of those events by which transmission may occur and there may exist age-specific characteristics related to susceptibility and infectiousness which are not captured by the contact rates. Therefore, in this paper, transmission is modeled as the product of two age-specific variables: the age-specific contact rate and an age-specific proportionality factor, which entails an improvement of fit for the seroprevalence of the varicella-zoster virus (VZV) in Belgium. Furthermore, we address the impact on the estimation of the basic reproduction number, using non-parametric bootstrapping to account for different sources of variability and using multi-model inference to deal with model selection uncertainty. The proposed method makes it possible to obtain important information on transmission dynamics that cannot be inferred from approaches traditionally applied hitherto., 25 pages, 6 figures

A finite element analysis was carried out to study the mixing patterns of a viscous Newtonian fluid into a stirred tank. A helical ribbon screw impeller (HRS) was used as the mixing device. The numerical simulation involved the full three-dimensional resolution of the equations of change governing the flow in the tank. The circulation time and the torque were determined and compared with experimental data. A good agreement was found, showing the usefulness of the numerical approach for design purposes.

SUMMARY 1. The influence of solar heating on the formation of temperature and density profiles of ice-covered lakes is considered. 2. Mathematical models are derived to quantify the effect of solar heating on vertical stability and its dependence on critical parameters, 3. Solar heating is shown to be able to account for the thermal structure and mixing patterns of certain ice-covered lakes. 4. The importance of convective mixing is discussed in relation to the distribution of phytoplankton and nutrients.

A 50 mm twin screw extruder was used to study the melting profiles of various PVC formulations. Melt temperature and degree of flux are measured axially along various mixing paddle arrangements. The viscous work is correlated with the rheology of the PVC mass and effective shear rate of the intermeshing co-rotating screws. The results of this investigation are used to develop a conceptual model of compounding PVC formulations. The radial mixing patterns in paddle segments down the barrel length are analyzed by introduction of trace quantities of pigment added to the dry blend. The resulting residence time distributions coupled with localized shear rate distributions give a numerical evaluation of shear strain required to flux PVC particles into a continuous fluid mass. By proper agitator design, compounding of PVC formulations can be accomplished with minimal thermal history.

Mathematical modeling approaches are being developed to better understand and describe the overall performance of large-scale agitated fermentors. These new approaches are based upon subdividing the fermentor into various mixing cells, or stages. The further development of these models requires information on the power input per stage, its effect on mass transfer within the stage, fluid mixing patterns between stages, and the distribution of gas in the fermentor stages. The following discussion presents data and comments related to these topics for aerobic fermentations of low to medium viscosity.

Mixing of viscous fluids in an annular channel is analyzed theoretically. Four basic mixing patterns are described which can be generated by altering the relative rotational velocities of the annular boundaries. Only one aspect of the mixing problem is isolated, i.e., reduction in striation thickness. Problems of front to back mixing to iron out variations of feed stream composition and mixing of solid particles are not considered. The theory was verified experimentally using molten polystyrene.

Temperature profiles of water in a spray column heat exchanger, 15 cm. in diameter and 150 cm. long, operating with a dense packing of kerosene drops, were measured. The range of superficial velocities was 0 to 0.8 cm./sec. of water and 0.5 to 1.7 cm./sec. of kerosene. The bottom of the dense packing was either slightly above or 15 cm. below the bottom of the column proper. The physical picture of heat transfer is similar to that for dispersed packings of drops and emphasizes the dominant role of wakes in the heat transfer mechanism. The mathematical equations for dispersed packings of drops were modified to take into account the reduction of wake size at the interface of the two packings and the difference in the mixing patterns at the top of the column. An empirical allowance for the effect of bypassing is suggested. The volume of the wakes and the rate of wake shedding were estimated from the temperature profiles. General agreement was found between the theory and the experimental data of this and three other studies.