Local Growth Rate Research Articles

The onset of longitudinal vortex rolls in the thermal entrance region of plane Poiseuille flow heated with a constant heat flux

The onset of longitudinal vortex rolls in the thermal entrance region of plane Poiseuille flow heated from below with a constant heat flux is investigated theoretically. In the present study, the Boussinesq equations are solved numerically by using the finite volume method to analyze the onset of secondary flow. The local growth rates of the mean temperature and its fluctuations are examined, and the three characteristic distances, which are those to exhibit the onset of intrinsic instability, the detection of secondary flow, and the minimum Nusselt number under mixed convection, are suggested. They are discussed in comparison with available experimental data for water and air.

Dust confinement and dust-acoustic waves in weakly magnetized anodic plasmas

Experiments on dust-acoustic waves (DAW) in a magnetized anodic plasma are presented for the regime of low collisionality. The dust trapping and the self-excited and synchronized DAW dynamics are studied. Based on Langmuir and emissive probe measurements the dust confinement is found to be well described with respect to size, stability, and position of the dust cloud by an effective potential well formed by ion drag and Coulomb forces. Moreover, the measurements indicate the necessity for a kinetic model for the wave dispersion. By means of singular value decomposition the local wavelengths and growth rates of the waves are measured systematically. It is found that the measured mean wave number is well described by kinetic theory, while the theoretical growth rates overestimate the experiments. A novel observation for the DAW is a systematic variation of the wavelength inside the dust cloud.

Asymmetric distribution of auxin correlates with gravitropism and phototropism but not with autostraightening (autotropism) in pea epicotyls.

The relationships between the distribution of the native auxin indole-3-acetic acid (IAA) and tropisms in the epicotyl of red light-grown pea (Pisum sativum L.) seedlings have been investigated. The distribution measurement was made in a defined zone of the third internode, using (3)H-IAA applied from the plumule as a tracer. The tropisms investigated were gravitropism, pulse-induced phototropism, and time-dependent phototropism. The investigation was extended to the phase of autostraightening (autotropism) that followed gravitropic curvature. It was found that IAA is asymmetrically distributed between the two halves of the zone, with a greater IAA level occurring on the convex side, at early stages of gravitropic and phototropic curvatures. This asymmetry was found in epidermal peels and, except for one case (pulse-induced phototropism), no asymmetry was detected in whole tissues. It was concluded, in support of earlier results, that auxin asymmetry mediates gravitropism and phototropism and that the epidermis or peripheral cell layers play an important role in the establishment of auxin asymmetry in pea epicotyls. During autostraightening, which results from a reversal of growth asymmetry, the extent of IAA asymmetry was reduced, but its direction was not reversed. This result demonstrated that autostraightening is not regulated through auxin distribution. In this study, the growth on either side of the investigated zone was also measured. In some cases, the measured IAA distribution could not adequately explain the local growth rate, necessitating further detailed investigation.

A Numerical Study of the Effects of Operating Conditions and Coal Properties on Cavity Growth in Underground Coal Gasification

Underground coal gasification is a candidate process for converting the world's coal resources into energy, liquid fuels, and chemicals. In this article, a one-dimensional model of a reacting coal block called COALGAS is used to investigate the effects of operating conditions and coal properties on the local rate of cavity growth and energy effectiveness in underground coal gasification. The investigation has revealed that the cavity growth rate is most sensitive to the operating temperature, water influx, and gas pressure. The coal properties that most affect the cavity growth rate are the thermomechanical spalling behavior, the behavior of the ash, and the amount of fixed carbon in the coal. Many trends observed in the field trials are reproduced by the model simulations, and predicted cavity growth rates for six field trials are comparable to those observed.

Model-supported optimization of phototrophic growth in a stirred-tank photobioreactor

A fuzzy-logic light attenuation model was developed and validated for a stirred-tank photobioreactor. Based on this model, local light intensities were used to calculate local specific growth rates of the cyanobacteria Synechococcus PCC 7942. The light regime for maximization of biomass space-time yield in a batch process was estimated using a genetic algorithm taking into account the integral average of the individual growth rates.

Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production. We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations.

The Fate of Mutations Surfing on the Wave of a Range Expansion

Many species, including humans, have dramatically expanded their range in the past, and such range expansions had certainly an impact on their genetic diversity. For example, mutations arising in populations at the edge of a range expansion can sometimes surf on the wave of advance and thus reach a larger spatial distribution and a much higher frequency than would be expected in stationary populations. We study here this surfing phenomenon in more detail, by performing extensive computer simulations under a two-dimensional stepping-stone model. We find that the probability of survival of a new mutation depends to a large degree on its proximity to the edge of the wave. Demographic factors such as deme size, migration rate, and local growth rate also influence the fate of these new mutations. We also find that the final spatial and frequency distributions depend on the local deme size of a subdivided population. This latter result is discussed in the light of human expansions in Europe as it should allow one to distinguish between mutations having spread with Paleolithic or Neolithic expansions. By favoring the spread of new mutations, a consequence of the surfing phenomenon is to increase the rate of evolution of spatially expanding populations.

Stalactite growth as a free-boundary problem

Stalactites, the most familiar structures found hanging from the ceilings of limestone caves, grow by the precipitation of calcium carbonate from within a thin film of fluid flowing down their surfaces. We have recently shown [M. B. Short, J. C. Baygents, J. W. Beck, D. A. Stone, R. S. Toomey III, and R. E. Goldstein, “Stalactite growth as a free-boundary problem: A geometric law and its Platonic ideal,” Phys. Rev. Lett. 94, 018501 (2005)] that the combination of thin-film fluid dynamics, calcium carbonate chemistry, and carbon dioxide diffusion and outgassing leads to a local geometric growth law for the surface evolution which quantitatively explains the shapes of natural stalactites. Here we provide details of this free-boundary calculation, exploiting a strong separation of time scales among that for diffusion within the layer, contact of a fluid parcel with the growing surface, and growth. When the flow rate, the scale of the stalactite, and the chemistry are in the ranges typically found in nature, the local growth rate is proportional to the local thickness of the fluid layer, itself determined by Stokes flow over the surface. Numerical studies of this law establish that a broad class of initial conditions is attracted to an ideal universal shape, whose mathematical form is found analytically. Statistical analysis of stalactite shapes from Kartchner Caverns (Benson, AZ) shows excellent agreement between the average shape of natural stalactites and the ideal shape. Generalizations of these results to nonaxisymmetric speleothems are discussed.

Numerical Model for Bridgman-Stockbarger Crystal Growth with a Magnetic Field

This paper presents a model for the unsteady species transport for the growth of doped semiconductor crystals during the vertical Bridgman‐Stockbarger process with a steady axial magnetic field. This dilute species transport depends on the convective and diffusive species transport of the dopant. This convective species transport is driven by buoyant convection in the melt, which produces compositional nonuniformities in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal grown in a steady axial magnetic field. The present study presents results of concentration in the crystal and in the melt at several different stages during crystal growth. I. Introduction D URING crystal growth without a magnetic field or with a weak magnetic field, turbulent or oscillatory melt motions can produce undesirable spatial oscillations of the concentration, or microsegregation, in the crystal. 1 Turbulent or oscillatory melt motions lead to fluctuations in the heat transfer across the growth interface from the melt to the crystal. Because the local rate of crystallization depends on the balance between the local heat fluxes in the melt and the crystal, fluctuations in the heat flux from the melt create fluctuations in the local growth rate, which create microsegregation. A moderate magnetic field can be used to create a body force that provides an electromagnetic (EM) damping of the melt motion can to eliminate oscillations in the melt motion and thus in the concentration of the crystal. Unfortunately, the elimination of mixing and a moderate or strong EM damping of the residual melt motion can lead to a large variation of the crystal’s composition in the direction perpendicular to the growth direction (radial macrosegregation). On the other hand, if the magnetic field strength is so strong that the melt motion is reduced sufficiently so that it has no effect on the composition in the crystal, then this diffusion-controlled species transport can produce a radially and axially uniform composition in the crystal grown. 2 To achieve diffusion-controlled species trans�

Heuristic theory of nonlocally broken gyro-Bohm scaling

Global gyrokinetic simulations of ion temperature gradient turbulent transport with piecewise-flat profiles are given to illustrate the breaking of gyro-Bohm scaling by a nonlocal mechanism. The nonlocal drainage of the turbulence from unstable regions spreading into stable (or less unstable) regions breaks the gyro-Bohm scaling toward Bohm in unstable regions and toward super-gyro-Bohm in stable (or less unstable) regions. A heuristic model for this nonlocal process is formulated in terms of a nonlocal growth rate resulting from a locally weighted radial average of the local linear ballooning mode growth rate. A nonlocality length L measured in ion gyroradii provides the exponential scale for the local weighting. The nonlocal growth rate can be incorporated into a local gyro-Bohm-scaled transport model in place of the local growth rate. The resulting nonlocal transport model will provide some transport in stable regions. A heuristic theory of this nonlocal transport mechanism based on the partial formation of global modes in toroidal geometry is detailed. The theory argues that the nonlocality length L increases with relative gyroradius and decreases with the linear growth rate.

Temporal Autocorrelation Can Enhance the Persistence and Abundance of Metapopulations Comprised of Coupled Sinks

In spatially heterogeneous landscapes, some habitats may be persistent sources, providing immigrants to sustain populations in unfavorable sink habitats (where extinction is inevitable without immigration). Recent theoretical and empirical studies of source-sink systems demonstrate that temporally variable local growth rates in sinks can substantially increase average abundance of a persisting population, provided that the variation is positively autocorrelated--in effect, temporal variation inflates average abundance. Here we extend these results to a metapopulation in which all habitat patches are sinks. Using numerical studies of a population with discrete generations (buttressed by analytic results), we show that temporal variation and moderate dispersal can jointly permit indefinite persistence of the metapopulation and that positive autocorrelation both lowers the magnitude of variation required for persistence and increases the average abundance of persisting metapopulations. These effects are weakened--but not destroyed--if variation in local growth rates is spatially synchronized and dispersal is localized. We show that the inflationary effect is robust to a number of extensions of the basic model, including demographic stochasticity and density dependence. Because ecological and environmental processes contributing to temporally variable growth rates in natural populations are typically autocorrelated, these observations may have important implications for species persistence.

FEG-SEM investigation of α-alumina scales formed on FeCrAlY alloys oxidised at 1200○C

This work is part of an ongoing European funded project, SMILER, with the aim of improving the performance of alumina forming Fe-20Cr-5Al-Y alloys for high temperature industrial applications. One aspect of the project is to investigate the influence of additives on the oxidation behaviour of these alloys. During this study a LEO 1550 FESEM (field emission scanning electron microscope), equipped with INCA X-ray microanalysis facilities was used. Ultra-high-purity model alloys, where the levels of additives (Hf, Zr, Ti, Si, La and Y) were carefully controlled, and two commercial Aluchrom YHfAl and Kanthal AMPT alloys were oxidised at 1200°C for up to 3100h (100h/cycle). The YHfAl, (Y+Ti+Zr)- and (Y+Zr+Hf)-containing alloys showed the highest oxidation rates when oxidised, whereas the La-containing alloy showed the lowest oxidation rate. However, the La-containing alloy spalled the most, while the (Y+Zr+Hf)-containing and YHfAl alloys showed little spallation, and the additives appeared to have a major influence on the spallation of the α-alumina scale formed. On the alloys with La and Si respectively, the scale spalled at the scale/metal interface (adhesively), whereas on alloys containing (Y+Hf+Ti) and (Y+Hf+Zr) and the YHfAl alloy, the scale spalled mainly in a cohesive manner (within the scale). Also, the added elements affected the scale topography. In general the scale had a columnar structure at the scale/metal interface, whereas the grains were equiaxed at the scale/gas interface. However, in the case of YHfAl and (Y+Zr+Hf)-containing alloys, a sunflower type structure was observed in both fractured samples, in the regions where the scale spalled cohesively. Preliminary EDX analyses revealed that, in the case of YHfAl, for example, the center of the sunflower structure was rich in Mg. This suggests that there may be inhomogeneities in the metal substrate, prior to oxidation, where high concentrations of Mg increase the local oxide growth rate.

Morphological stability of a two-dimensional cylindrical crystal with a square-lawsupersaturation dependence of the growth rate

The morphological stability of a two-dimensional cylindrical crystal growing in a solution atthe local growth rate proportional to the squared supersaturation has been analysed for thefirst time by the weakly nonlinear technique. A correction to the stability size, which wasdetermined from the linear stability theory, was found and analysed. It was shown that inmost cases the critical size of the crystal stability decreased with growing perturbationamplitude. This result has been discussed in terms of the nonequilibrium phase transitiontheory.

TROUT PREDATORS AND DEMOGRAPHIC SOURCES AND SINKS IN A MAYFLY METAPOPULATION

Habitat patches often differ in environmental conditions, and the degree of environmental heterogeneity among patches is thought to influence population dynamics at the regional (metapopulation) scale. In a previous study, I found evidence of a source– sink dynamic in a metapopulation of the mayfly Callibaetis ferrugineus hageni occupying beaver ponds with or without brook trout predators, where adult females frequently dispersed among ponds, and frequently oviposited in ponds with trout. Here, I tested the hypothesis that trout create habitat sinks by manipulating trout densities and estimating local population growth rates (λ) of Callibaetis. In addition, Callibaetis emergence rates were estimated in the mayfly generation before the manipulation. Among ponds, λ ranged from 0.062 to 2.631, and nine Monte Carlo simulations scenarios revealed that four ponds had λ significantly below replacement (sinks) while the presence of source ponds was less conclusive. The manipulation of trout did not result in a detectable treatment effect, perhaps because of low statistical power resulting from high within-treatment variation in trout densities. However, point estimates of λ and emergence rates were negatively and exponentially related to trout density, such that nearly all ponds with more than 1 trout/100 m2 were sinks. Further, multiple regression analyses were consistent with the hypothesis that trout reduced λ and emergence rates, while other biotic and abiotic factors did not provide explanatory power. The results support the hypothesis that source–sink population dynamics may be common in freshwater habitats, and that prey metapopulation dynamics may be predicted from the distribution of predators, prey movement and habitat selection behaviors, and factors influencing the outcome of predator–prey interactions.

Dynamics of turbulence spreading in magnetically confined plasmas

A dynamical theory of turbulence spreading and nonlocal interaction phenomena is presented. The basic model is derived using Fokker–Planck theory, and supported by wave-kinetic and K-ϵ type closures. In the absence of local growth, the model predicts subdiffusive spreading of turbulence. With local growth and saturation via nonlinear damping, ballistic propagation of turbulence intensity fronts is possible. The time asymptotic front speed is set by the geometric mean of local growth and turbulent diffusion. The leading edge of the front progresses as the turbulence comes to local saturation. Studies indicate that turbulence can jump gaps in the local growth rate profile and can penetrate locally marginal or stable regions. In particular, significant fluctuation energy from a turbulent edge can easily spread into the marginally stable core, thus creating an intermediate zone of strong turbulence. This suggests that the traditional distinction between core and edge should be reconsidered.

Persistence, spread and the drift paradox

We derive conditions for persistence and spread of a population where individuals are either immobile or dispersing by advection and diffusion through a one-dimensional medium with a unidirectional flow. Reproduction occurs only in the stationary phase. Examples of such systems are found in rivers and streams, marine currents, and areas with prevalent wind direction. In streams, a long-standing question, dubbed ‘the drift paradox’, asks why aquatic insects faced with downstream drift are able to persist in upper stream reaches. For our two-phase model, persistence of the population is guaranteed if, at low population densities, the local growth rate of the stationary component of the population exceeds the rate of entry of individuals into the drift. Otherwise the persistence condition involves all the model parameters, and persistence requires a critical (minimum) domain size. We calculate the rate at which invasion fronts propagate up- and downstream, and show that persistence and ability to spread are closely connected: if the population cannot advance upstream against the flow, it also cannot persist on any finite spatial domain. By studying two limiting cases of our model, we show that residence in the immobile state always enhances population persistence. We use our findings to evaluate a number of mechanisms previously proposed in the ecological literature as resolutions of the drift paradox.

Monte Carlo Simulation of Thin Film Growth with Defect Formation: Application to Via Filling

The filling process of via holes in damascene electroplating is investigated with the use of kinetic Monte Carlo method. As a model for damascene plating, we included additives in the Solid-by-Solid model which we developed to study the correlation between the surface and void structures during the crystal growth. Two kinds of additives, inhibitors and accelerators, are taken into account to control the local growth rate and to find out the condition for avoiding the void formation during the filling. A series of simulations have been performed by changing the parameters which characterize the additives to see their influence on the filling mechanism. The distribution of additives, the correlation with the resulting surface and void structures are discussed.

Morphological phase diagram of a spherical crystal growing under nonequilibrium conditions at the growth rate as a quadratic function of supersaturation

The complete morphological diagram of a spherical nucleus growing from a solution under nonequilibrium conditions at a local growth rate as a quadratic function of supersaturation is calculated for the first time on the basis of a linear analysis for morphological stability and the principle of maximum entropy production. The results of calculations are compared with those obtained previously for a spherical particle in the case of a linear dependence of the growth rate on the supersaturation.

Observation of strain field fluctuation in SiGe-relaxed buffer layers and its influence on overgrown structures

We investigated in-plane strain field distribution in strained-Si/strain-relaxed SiGe buffer layers by spatially resolved micro-Raman spectroscopy. Crosshatch-like strain distribution was observed in both the strained-Si and SiGe layer, indicating that strain field coming from underlying misfit dislocations reaches the SiGe surface and causes the strain fluctuation in the strained-Si layer. The wavelength of the distribution was found to strongly depend on the SiGe thickness. The amount of the fluctuation corresponded to 13% of the strain that strained-Si layer inherently had. It was also found that the strain field modulated the local growth rate of overgrown layer and caused the enhancement of the surface roughness. The strain fluctuation, therefore, should be carefully taken into account for device applications.

A modelling study of the activity and structure of biofilms in biological reactors

In spite of the large range of morphologies observed for biofilms, there is strong experimental and theoretical evidence that the complex nature of biofilm structure dynamics is primarily a consequence of the effect of environmental conditions on biofilm development. It has been observed from the operation of industrial and laboratory-scale biofilm reactors that the structure of biofilms results from a balance of the detachment forces and the regimen of transport of a growth-limiting substrate. The overall performance of biofilm reactors is intrinsically dependent on biofilm morphology. The spatial distribution of the diverse dissolved and particulate components through the biofilm matrix and the shape of its external surface influence the rates of the occurring bioconversions, and structure also influences the stability of the biofilm in terms of resistance to mechanical stress. Individual-based modelling (IbM) of biofilms structure dynamics is used here to unify observations from the operation of biofilm reactors by simulating biofilm growth under variable detachment forces and mass transport regimens for a growth-limiting substrate. The IbM is a bottom-up approach, where the global system behaviour is derived from the local interactions of multiple elements acting independently. Transport and reaction of a solute species, local microbial growth rates and the effect of external detachment forces applied to the biofilm are modelled using differential approaches. Simulations carried out in two-dimensional space using this model illustrate a range of biofilm morphologies that emerge from different reactor operation parameters, reproducing trends observed experimentally. Comparison of multi-dimensional modelling results with those obtained using one-dimensional approaches enforces the need to use multi-dimensional modelling to predict properties that derive from the spatial biofilm structure.