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Results for “Spatiotemporal variation”

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PubMed2003

Dissipating step bunches during crystallization under transport control.

In studies of crystal formation by the generation and spreading of layers, equidistant step trains are considered unstable-bunches and other spatiotemporal patterns of the growth steps are viewed as ubiquitous. We provide an example to the opposite. We monitor the spatiotemporal dynamics of steps and the resulting step patterns during crystallization of the proteins ferritin and apoferritin using the atomic force microscope. The variations in step velocity and density are not correlated, indicating the lack of a long-range attraction between the steps. We show that (i) because of its coupling to bulk transport, nucleation of new layers is chaotic and occurs at the facet edges, where the interfacial supersaturation is higher; (ii) step bunches self-organize via the competition for supply from the solution; and, (iii) bunches of weakly interacting steps decay as they move along the face. Tests by numerical modeling support the conclusions about the mechanisms underlying our observations. The results from these systems suggest that during crystallization controlled by transport, with weakly or noninteracting growth steps, the stable kinetic state of the surface is an equidistant step train, and step bunches only arise during nucleation of new layers. Since nucleation only occurs at a few sites on the surface, the surface morphology may be controllably patterned or smoothened by locally controlling nucleation.

Journal Article↗

PubMed2000

Calcium dynamics associated with action potentials in single nerve terminals of pyramidal cells in layer 2/3 of the young rat neocortex.

Calcium dynamics associated with a single action potential (AP) were studied in single boutons of the axonal arbor of layer 2/3 pyramidal cells in the neocortex of young (P14-16) rats. We used fluorescence imaging with two-photon excitation and Ca2+-selective fluorescence indicators to measure volume-averaged Ca2+ signals. These rapidly reached a peak (in about 1 ms) and then decayed more slowly (tens to hundreds of milliseconds). Single APs and trains of APs reliably evoked Ca2+ transients in en passant boutons located on axon collaterals in cortical layers 2/3, 4 and 5, indicating that APs propagate actively and reliably throughout the axonal arbor. Branch point failures are unlikely to contribute to differences in synaptic efficacy and reliability in the connections made by layer 2/3 pyramidal cells. AP-evoked Ca2+ transients in boutons were mediated by voltage-dependent Ca2+ channels (VDCCs), predominantly by the P/Q- and N-subtypes. Ca2+ transients were, on average, of significantly larger amplitude in boutons than in the flanking segments of the axon collateral. Large amplitude Ca2+ transients in boutons were spatially restricted to within <= 3 m of axonal length. Single AP-evoked Ca2+ transients varied up to 10-fold across different boutons even if they were located on the same axon collateral. In contrast, variation of Ca2+ transients evoked by successive APs in a given single bouton was small (coefficient of variation, c.v. <= 0.21). Amplitudes of AP-evoked Ca2+ signals did not correlate with the distance of boutons from the soma. In contrast, AP-evoked Ca2+ signals in spines of basal dendrites decreased slightly (correlation coefficient, r2 = -0.27) with distance from the soma. Measurements with the low-affinity Ca2+ indicator Magnesium Green suggest that the volume-averaged residual free [Ca2+]i in a bouton increases on average by 500 nM following a single AP. Higher concentrations of indicator caused, on average, a decrease in the amplitude and an increase in the decay time constant of Ca2+ transients. Assuming a single-compartment model the concentration dependence of decay time constants suggests a low endogenous Ca2+ binding ratio close to 140, indicating that of the total Ca2+ influx ( approximately 2 fC) less than 1% remained free. The indicator concentration dependence of decay time constants further suggests that the residual free Delta[Ca2+]i associated with an AP decays with a time constant of about 60 ms (35 C) reflecting a high Ca2+ extrusion rate of about 2600 s(-1). The results show that AP-evoked volume-averaged Ca2+ transients in single boutons are evoked reliably and, on average, have larger amplitudes than Ca2+ transients in other subcellular compartments of layer 2/3 pyramidal cells. A major functional signature is the large variation in the amplitude of Ca2+ transients between different boutons. This could indicate that local interactions between boutons and different target cells modify the spatiotemporal Ca2+ dynamics in boutons and cause target cell-specific differences in their transmitter release properties.

Action Potentials↗

PubMed1984

Model of electroretinogram b-wave generation: a test of the K+ hypothesis.

Generation of the electroretinogram b-wave is simulated with a computer model representing a dark-adapted amphibian retina. The simulation tests the K+ hypothesis of b-wave generation, which holds that b-wave currents arise from localized Müller cell depolarizations generated by light-evoked increases in extracellular K+ concentration, [K+]o. The model incorporates the following components and processes quantitatively: 1) two time-dependent K+ sources representing the light-evoked [K+]o increases in the inner and outer plexiform layers, 2) a time- and [K+]o-dependent K+ sink representing the [K+]o decrease in the rod inner segment layer, 3) diffusion of released K+ through extracellular space, 4) active K+ reuptake and passive K+ drift across the Müller cell membrane, 5) spatial variations in the tortuosity factor and the volume fraction of extracellular space, 6) an extraretinal shunt resistance. Müller cells are modeled with 1) cytoplasmic resistance, 2) spatial variations in membrane permeability to K+, and 3) a membrane potential specified by the Nernst equation and transmembrane current flow. For specified K+ source and sink densities, the model computes [K+]o variations in time and retinal depth. Based on these [K+]o distributions, Müller cell potentials, current source-density profiles, and intraretinal and transretinal voltages are calculated. Imposed [K+]o distributions similar to those seen experimentally during the b-wave lead to the generation of a transient b-wave response and to a prolonged Müller response in the model system. These response time courses arise because the b-wave is dominated by the short-lived distal [K+]o increase, while the Müller response primarily reflects the long-lived proximal [K+]o increase. Current source-density distributions and intraretinal voltage profiles that are generated by the model at the peak of the b-wave closely resemble experimental results. The model generates a realistic slow PIII potential in response to prolonged [K+]o decreases in the distal retina and reproduces the K+ ejection results of Yanagida and Tomita (50) accurately. Simulations also suggest that tissue damage caused by K+-selective micropipettes in experimental preparations can lead to an underestimation of the distal [K+]o increase. The simulations demonstrate that the spatiotemporal properties of intraretinal b-wave voltages and currents and Müller cell responses can be generated according to the K+ hypothesis: by passive Müller cell depolarization driven by variations in [K+]o.

Animals↗

PubMed2006

El Niño effects on influenza mortality risks in the state of California.

Recent El Niño events have emphasized the need to develop modelling techniques to assess climate-related health events. Experts agree that climate changes affect the spread of infectious diseases and that the geographic range of infectious diseases may expand as a result of these changes. Nevertheless, the world health modelling community cannot yet predict, with reasonable accuracy, when or where exactly these effects will occur or how large the threat of these diseases will be to particular populations. This study compared the spatiotemporal patterns of influenza mortality risk in the state of California during El Niño vs normal weather periods. By applying a stochastic methodology to county-specific mortality data, various sources of uncertainty were accounted for, and informative influenza mortality maps and profiles were generated. This methodology enabled the detection of significant effects of climate change on the influenza risk distributions. Geographical maps of risk variation during El Niño differed from those during normal weather, the corresponding covariances exhibited distinct space-time dependence features, and the temporal mean mortality profiles were considerably higher during normal weather than during El Niño. These rather unexpected results of spatiotemporal analysis are worth further investigation that seeks substantive and biologically plausible explanations. The findings of this study can offer a methodological framework to evaluate public health management strategies.

Aged↗

PubMed2005

Frequency bands and spatiotemporal dynamics of beta burst stimulation induced afterdischarges in hippocampus in vivo.

Temporal and spatial characteristics of hippocampal neuronal network activation are modified during epileptiform afterdischarges. We developed a beta burst stimulation protocol to investigate subregional variations and substrates of rhythmic population spike discharges in vivo in urethane anesthetized Wistar rat hippocampus with a 14-electrode recording array and extracellular single electrode recordings. Our 64 pulse beta burst stimulation protocol was constructed from electrical pulses delivered at intervals corresponding to beta (14-25 Hz), Delta (2 Hz), and slow (0.5 Hz) frequencies. In each experiment these interleaved pulses were all repeated four times with unchanged intervals. Stimulation of either perforant path or fimbria fornix induced a prolonged afterdischarge pattern peaking at 200 Hz fast, 20 Hz beta, and 2 Hz Delta frequencies. Analysis of variance confirmed that the response pattern of the discharges remained constant regardless of the stimulation beta frequency. Within the afterdischarge the fast frequencies were restricted to independent hippocampal subfields whereas beta and slow frequencies correlated across the subfields. Current source density (CSD) analysis revealed that the original signal propagation through subfields of the hippocampus was compromised during the beta burst stimulation induced afterdischarge. In addition, the CSD profile of the epileptiform afterdischarge was consistently similar across the different experiments. Time-frequency analysis revealed that the beta frequency afterdischarge was initiated and terminated at higher gamma (30-80 Hz) frequencies. However, the alterations in the CSD profile of the hippocampus coincided with the beta frequency dominated discharges. We propose that hippocampal epileptiform activity at fast, beta and Delta frequencies represents coupled oscillators at respectively increasing spatial scales in the hippocampal neuronal network in vivo.

Action Potentials↗

PubMed2006

Compound response of marine and terrestrial ecosystems to varying climate: pre-anthropogenic perspective from bivalve shell growth increments and tree-rings.

Annual growth increments were examined from shells of the ocean quahog (Arctica islandica L.) from northwest Norway and from tree-ring samples of the Scots pine (Pinus sylvestris L.) from nearby coastal areas. The reconstructed annual growth increments were used to compare growth variability in marine and terrestrial ecosystems. Spatiotemporal comparison of the growth records showed statistically significant correlation during the 19th century A.D., indicative of ecosystem-independent response to pre-anthropogenic climate variations. Geographical correlation between marine and terrestrial records was only observed at the local scale. Years with particularly low winter or high summer North Atlantic Oscillation (NAO) indices showed the best synchronization of marine and terrestrial growth. Despite strong correlation during historical time, our palaeoecological evidence suggests that marine and terrestrial ecosystems may show dissimilar growth reaction to recently observed positive winter-NAO phases.

Animals↗

PubMed1997

Assessment of stenosis severity using a novel method to estimate spatial and temporal variations of blood flow velocity in biplane coronarography.

The authors present a novel method to estimate absolute blood flow velocity in coronary arteries from biplane angiograms. Spatial and temporal velocity variations are derived giving simultaneously a direct geometric and an indirect functional index of stenosis severity, stenosis ratio and coronary flow reserve. No prior assumption concerning stenosis geometry is made. Deformable models are used to track a coronary artery segment dynamically in three dimensions. A densitometric map is obtained by summing densities across sections at every position along the previously calculated path and at every time of the cardiac cycle. An advection relationship between density and velocity is observed. The spatiotemporal velocity map is a solution of a nonlinear least-squares scheme. A simulation protocol based on simple geometric conformations and blood flow properties is used to assess numerical stability and immunity towards noise. Predicted results for temporal velocity variations are compared with the intracoronary Doppler recordings to test the model assumptions for basal state and hyperaemia examinations of the same patient. The stenosis ratio was accurate to within 3% for a simulated additive Gaussian noise with a standard deviation of 0.14. The limits of agreement between angiographic and Doppler velocities were -11.4 and 11.8 cm s-1 for a peak value of 23 cm s-1 (basal state) and -16.8 and 13.5 cm s-1 for a peak value of 52 cm s-1 (hyperaemia), corresponding to 18 and 3.5% errors on the average peak values and a 16% error on the coronary flow reserve. To summarize, the advection model derivation and its solution are presented. Simulated and experimental results corroborate the validity of the numerical schemes and support clinical applicability.

Blood Flow Velocity↗

PubMed1995

Characterizing dynamic brain responses with fMRI: a multivariate approach.

In this paper we present a multivariate analysis of evoked hemodynamic responses and their spatiotemporal dynamics as measured with fast fMRI. This analysis uses standard multivariate statistics (MANCOVA) and the general linear model to make inferences about effects of interest and canonical variates analysis (CVA) to describe the important features of these effects. We have used these techniques to characterize the form of hemodynamic transients that are evoked during a cognitive or sensorimotor task. In particular we do not assume that the neural or hemodynamic response reaches some "steady state" but acknowledge that these physiological changes could show profound task-dependent adaptation and time-dependent changes during the task. To address this issue we have modeled hemodynamic responses using appropriate temporal basis functions and estimated their exact form within the general linear model using MANCOVA. We do not propose that this analysis is a particularly powerful way to make inferences about functional specialization (or more generally functional anatomy) because it only provides statistical inferences about the distributed (whole brain) responses evoked by different conditions. However, its application to characterizing the temporal aspects of evoked hemodynamic responses reveals some compelling and somewhat unexpected perspectives on transient but stereotyped responses to changes in cognitive or sensorimotor processing. The most remarkable observation is that these responses can be biphasic and show profound differences in their form depending on the extant task or condition. Furthermore these differences can be seen in the absence of changes in mean signal.

Arousal↗

PubMed1997

Variability and uncertainty in spatial, temporal and spatiotemporal crop-yield and related data.

Application of the theories of precision agriculture to the practicalities of broad-acre farming relies on successful handling of the ramifications of uncertainty in information, i.e. information pertaining to the spatial and temporal variation of those factors which determine yield components and/or environmental losses. This paper discusses the uncertainty of yield and related variables as measured by their spatial and temporal variance. The magnitude of these two components gives a suggestion as to the appropriate scale of management. Simultaneous reporting on spatial and temporal variation is rare and the theory of these types of process is still in its infancy. Some brief theory is presented, followed by several examples from the Rothamsted classic experiments, yield-monitoring experiments in Australia, a long-term barley trial in Denmark, and a soil moisture monitoring network. It is clear that annual temporal variation is much larger than the spatial variation within single fields. This leads to the conclusion that if precision agriculture is to have a sound scientific basis and ultimately a practical outcome then the null hypothesis that still remains to be seriously researched is: 'given the large temporal variation in yields relative to the scale of a single field, then the optimal risk aversion strategy is uniform management.'

Crops, Agricultural↗

PubMed2004

Influence of speed variation and age on the asymmetry of ground reaction forces and stride parameters of normal gait in children.

The purpose of this study was to assess the influence of age and speed on the asymmetry of ground reaction forces (GRFs) and spatiotemporal parameters (STPs) during normal gait in 4- to 10-year-old children. Forty-seven children walked at three speeds on a treadmill dynamometer (ADAL; Tecmachine, Andrézieux Bouthéon, France). Thirty steps were recorded at each speed for each foot for each child. The GRF and stride parameters were normalized to body weight and to body height, respectively. A left-right symmetry index (SI) was calculated for each parameter. The influence of both age and speed on the different SI was examined with a two-way analysis of variance. GRF and STP were asymmetric (SI ranged from +/- 1.92% to +/- 45.05%). The SI of forces Fz1 and Fy1 are negative in children aged 4-6 years, indicating that left Fz1 and Fy1 are higher than right Fz1 and Fy1. The cross effect of age and speed on the asymmetries of gait parameters was not significant There was no significant effect of age on the asymmetries of vertical GRF and STP. The asymmetry of vertical propulsive force (Fz3) alone increased with the speed (P < 0.05). This study showed that the different tasks performed by the lower limbs could be responsible for the asymmetry of GRF and STP in children aged 4-6 years. It also shows that upper and lower limits of normal asymmetry of gait parameters are different. Therefore no single criterion value can be used to assess the symmetry of several gait parameters. The small values of upper and lower limits of symmetry indices of vertical forces and stride duration show that the symmetry indices of these variables are reliable measurements and should thus be used in symmetry analysis of gait in normal and disabled children.

Acceleration↗

PubMed2005

Stable spatiotemporal solitons in bessel optical lattices.

We investigate the existence and stability of three-dimensional solitons supported by cylindrical Bessel lattices in self-focusing media. If the lattice strength exceeds a threshold value, we show numerically, and using the variational approximation, that the solitons are stable within one or two intervals of values of their norm. In the latter case, the Hamiltonian versus norm diagram has a swallowtail shape with three cuspidal points. The model applies to Bose-Einstein condensates and to optical media with saturable nonlinearity, suggesting new ways of making stable three-dimensional solitons and "light bullets" of an arbitrary size.

Journal Article↗

PubMed1997

Experimental analysis of neuronal dynamics in cultured cortical networks and transitions between different patterns of activity.

Experimental investigation of the dynamics of biological networks is a fundamental step towards understanding how the nervous system works. Spontaneous activity in cultured networks of cortical neurons has been investigated by using a multisite recording technique with planar electrode arrays. In these networks, the spatiotemporal firing patterns were studied in the presence of different extracellular solutions. Transitions from asynchronous firing dynamics to synchronous firing dynamics were observed when the extracellular Ca2+ concentration was increased from 0.1 mM to 1 mM. Addition of extracellular Mg2+ reduced the spontaneous activity at any Ca2+ concentration, and an increase in the extracellular K+ concentration enhanced the frequency of periodical synchronous bursts. N-methyl-D-aspartate (NMDA) and non-NMDA glutamate receptor antagonists inhibited synchronous activity. A spatiotemporal analysis of the data has been performed, and the properties of the network such as the synchronization and the periodicity have been quantified in order to clarify how variations of intrinsic parameters of the network can induce structural transitions in the neural dynamics. This experimental study is a possible approach to investigate the computational properties of a neuronal network.

Animals↗

PubMed1998

Variability in spatiotemporal gait characteristics over the course of the L-dopa cycle in people with advanced Parkinson disease .

BACKGROUND AND PURPOSE: Understanding the nature and extent of fluctuations in spatial and temporal variables of gait (eg, speed, stride length [SL], stride time [ST]) over the course of the levodopa (L-dopa) cycle of individuals with advanced Parkinson disease (PD) is important in order to assess patients and examine the effectiveness of interventions. The purpose of this study was to determine whether gait variables are sufficiently stable to be used as outcome measures in a clinical trial involving patients with advanced PD. SUBJECTS: Five volunteers (3 male, 2 female; mean age=67.8 years; Hoehn and Yahr stages 3-4) with idiopathic PD of a mean duration of 15.0 years participated. METHODS: Gait speed, SL, and ST were measured as the subjects walked 7.2 m at self-selected speeds. To evaluate the full "on-off" sequence of the L-dopa response, this analysis was repeated 11 times, at intervals of 10% of the L-dopa cycle. Each subject was analyzed on 3 separate days, with approximately 1 month between tests. Two-way repeated-measures analyses of covariance, with 2 within-subject factors (percentage of L-dopa cycle and day) and 1 covariate (height), were applied, and coefficients of variation were calculated to determine the extent of change in speed, SL, and ST over the L-dopa cycle and over the 3 days. RESULTS: The subjects' overall mean gait speed was 70.39 cm/s, representing 55.4% of the age-related normative values. There were no effects of percentage of the L-dopa cycle or day or of the interaction of percentage of the L-dopa cycle and day on speed, SL, and ST. The coefficients of variation for speed and SL were consistently higher than the normative values, ranging from 13.5% to 23.8% and from 13.9% to 23.3% at 20% of the L-dopa cycle, respectively. CONCLUSION AND DISCUSSION: When interpreting spatiotemporal measurements of gait of patients with advanced PD, fluctuations can be extensive and may not follow a predictable pattern.

Aged↗

PubMed2025

Genomic Insights Into Local Adaptation Across Heterogeneous Understory Habitats and Climate Change Vulnerability.

Understanding adaptive evolution and survival risks in understory herbs is crucial for the effective conservation of biodiversity. How environmental gradients shape species local adaptation patterns is not well understood, nor is how populations of understory herbs respond to a changing climate. In this study, we conducted population genomic analyses of Adenocaulon himalaicum (Asteraceae) with a pan-East Asian distribution, representing a good model for dominant understory herbs to elucidate adaptation mechanisms in heterogeneous forest ecosystems. Based on 34,398 putatively neutral single nucleotide polymorphisms (SNPs) across 27 populations, we identified three genetic lineages accompanied by high levels of genetic differentiation between populations. Our isolation by environment results (IBE) indicated a significant effect of environmental gradients on genomic variation of A. himalaicum (r = 0.18, p = 0.03). To decompose the relative contributions of climate, geography and population structure in explaining genetic variance, our partial RDA found that the prominent contribution of environmental effects (climatic and soil variables) explained 29% and 36% of the neutral and adaptive genetic variation, respectively. Using two genotype-environment association (GEA) methods, we identified 13 SNPs as candidates for core climate-related adaptation loci, with two of these loci further validated by qRT-PCR experiments. Projections of spatiotemporal genomic vulnerability under different future climate scenarios revealed that populations in the southeastern edge of the Himalayas, near the Sichuan Basin, the southernmost region of Northeast China and the northern Korean Peninsula, as well as northern Japan, were identified as the most vulnerable and should be prioritised for conservation. Therefore, our current study provides the genomic foundations for conservation and management strategies to elucidate how these understory herbs cope with future climate changes.

Climate Change↗

PubMed1993

Optical tearing in spatiotemporal boundary formation: when do local element motions produce boundaries, form, and global motion?

Perception of continuous boundaries, shape, and global motion can be produced by transformations in local elements separated in both space and time, a process here called spatiotemporal boundary formation (SBF). Prior research has shown that a broad class of element transformations gives rise to SBF. The present work used the transformation of local element displacement to explore the initiating conditions for SBF. Three experiments assessed SBF using a 10-alternative, forced-choice, shape identification task. Experiment 1a showed that large element displacements, but not small ones, produced high accuracy in shape identification. Experiment 1b tested the detectability of the small and large element displacements in an unrelated task, indicating that the results of Experiment 1a were not due to poor detectability for small displacements. Experiment 2 found no variation in SBF performance with changes in viewing distance. Experiment 3 provided evidence that initiating SBF depends on a ratio of element displacement to element separation. These results support an interpretation of SBF as a process geared to detection of object boundaries from spatiotemporal change. Initiating SBF requires transformations in local elements that are classified as spatiotemporal discontinuities (STDs). Small element displacements in a display of a given density do not register as STDs because they are classified as local deformations in an intact, implicit surface connecting visible elements. Complementarity is suggested between element changes which preserve continuity with their neighbors (optic flow) and those comprising spatiotemporal discontinuities (optic tearing). Classification of element transformations as optic flow or tearing may determine whether they provide information about surface form (e.g., through structure-from-motion) or about object boundaries, through SBF.

Form Perception↗

PubMed1994

The spatiotemporal transfer function of crayfish lamina monopolar neurons.

1. The graded, synaptic potentials of first-order visual interneurons (lamina monopolar cells) were examined with intracellular recordings. The spatiotemporal properties were characterized with drifting sine wave gratings and annuli. 2. Annulus-elicited inhibition is maximal for annulus-test pulse intervals of approximately 140 ms and declines exponentially. The inhibition declines with increasing annular internal radii (ri). 3. Grating responses were examined with respect to spatial and temporal frequency. The gratings elicit sinusoidal signals that are approximately linear with contrast. 4. Variations in spatial frequency produce response functions with a low-pass or modest band-pass characteristic, which are described by a difference of Gaussians sensitivity profile. The central Gaussian approximates the sensitivity profile of photoreceptors. The inhibitory Gaussian is similar to the inhibitory field estimated with annulus pulses. The peak of the inhibitory Gaussian is approximately 18% of the peak excitatory Gaussian. 5. Variations in temporal frequency generally produce transfer functions with a band-pass characteristic and a peak at 1.0 Hz. These data were described by a difference of exponentials function convolved with a low-pass filter that approximates the photoreceptor response. The inhibitory time course estimated from these data was similar to that of the annulus measurements. 6. The spatiotemporal properties of lateral inhibition are consistent with inhibitory action by the lamina amacrine neurons. The proposed model is spatiotemporally inseparable and nonrecurrent. 7. Eleven of 20 monopolar cells tested exhibited a strong orientation preference with a bias to the vertical. Photoreceptors exhibit little or no orientation preference.

Animals↗

PubMed2004

Real-time ozone mapping using a regression-interpolation hybrid approach, applied to Tucson, Arizona.

Real-time ozone (O3) maps, intended for public access and mass media, are generated from spatially interpolating (i.e., kriging) sparse monitoring data and are typically characterized by over-smoothed surfaces that inadequately represent local-scale spatial patterns (e.g., averaged over 1 km2). In this paper, a hybrid regression-interpolation methodology is developed to enhance the representation of local-scale spatiotemporal patterns with an application to Tucson, Arizona. The mapping of local patterns is enhanced with pre-interpolation regression modeling of local-scale deviation-from-mean variability, preserving variation in the monitor data that is ubiquitous across the modeling domain (i.e., the areal mean). The model is trained on several years of deviation-from-mean hourly O3 data, and predictor variables are developed using theoretically and empirically derived proxy regression variables. The regression model explains a significant proportion of the variation in the data (r2 = 0.54), with an average error of 7.1 ppb. When augmented with the areal mean, the r2 of the pre-interpolation model increases to 0.847. Model residuals are then spatially interpolated to the extents of the modeling domain. Final concentration estimate maps are the summation of areal mean, regression, and spatially interpolated surfaces, preserving absolute values at monitor locations.

Air Pollutants↗

PubMed2003

Standing waves in flow between finite counterrotating cylinders.

Experimental evidence for standing waves resulting from a supercritical Hopf bifurcation that appears as the first pattern-forming instability in counterrotating Taylor-Couette flow is presented. Depending on the aspect ratio two different types of standing waves, denoted as SW0 and SW(pi), could be observed. Both modes have an azimuthal wave number m=1 but differ in symmetry. While for SW(pi), a spatiotemporal glide-reflection symmetry could be found, SW0 is purely spatial reflection symmetric. The transition between the two modes is found to be organized in a cusp bifurcation unfolded by variations of the aspect ratio. The "classical" spiral vortex flow appears in this control parameter regime only as a result of a secondary steady bifurcation from SW0. This transition is found to be either subcritical or supercritical. The experimentally observed bifurcation structure has been predicted by theory of Hopf bifurcation to spiral vortex flow in finite counterrotating Taylor-Couette systems.

Journal Article↗