Three-dimensional Diffusion Model Research Articles

Flash calcines of kaolinite: kinetics of isothermal dehydroxylation of partially dehydroxylated flash calcines and of flash calcination itself

Kaolinite has been flash calcined to produce calcines kinetically frozen at different levels of dehydroxylation. The kinetics of subsequent isothermal dehydroxylation of the calcines were consistent with a three-dimensional diffusion model. Activation energies and rate constants generally decrease as dehydroxylation of the calcine increases. A decrease in reaction rate at high levels of dehydroxylation is consistent with collapse of the interlamellar space, restricting diffusion of water out of the particles. The kinetics of flash calcination were shown to obey the same principles as isothermal dehydroxylation.

The relationship of surface reflectance measurements to optical properties of layered biological media.

Reflectance from a turbid biological tissue is discussed for a diffusive light source illuminating the surface of the medium, and is related to the optical property distribution within the medium and to photon propagation through the medium. A three-dimensional photon diffusion model with closed form is developed to describe the photon diffuse intensity in a homogeneous medium. The solution is extended by numerical methods to the medium with layered structure. The concepts of photon flux paths and of reflectance indexes are utilized, together with reflectance data, to extract information about the internal optical properties of a medium. The flux path concept was corroborated by successfully detecting in vivo and ex vivo layered differences in optical properties within the biological medium. These studies suggest that the optical properties of subdermal tissue can be measured from light reflectance and that the effect of the upper skin layers can be eliminated.

A Dispersion Model Evaluation Study for Real-Time Application in Complex Terrain

A few tracer experiments were carried out in autumn 1984 and summer 1985 at the Lago Brasimone site, on the Appennini Mountains approximately 50 km south of Bologna with the purpose assessing the atmospheric dispersion of pollutants under drainage flow conditions. The three-dimensional transport and diffusion model MATHEW/ADPIC (M/A) has been applied to selected tracer and meteorological data with the aim of assessing the model performance under complex terrain and meteorological conditions, and its sensitivity to input data available in real-time applications. Boundary layer input parameters were derived through standard algorithms based on tethersonde and pilot balloon measurements. Model simulations of the most significant tracer experiments have been assessed by means of several evaluation criteria, and the sensitivity to some input data has been investigated. The results show that if a limited spatial uncertainty in the computed concentration pattern is taken into account, M/A provides a good agreement with observed concentrations. The quality of the results is very sensitive to the presence of wind measurements where the deviation of the flow due to the shape of the valley is observed.

Meteorological Modeling of Arrival and Deposition of Fallout at Intermediate Distances Downwind of the Nevada Test Site

A three-dimensional atmospheric transport and diffusion model is used to calculate the arrival and deposition of fallout from 13 selected nuclear tests at the Nevada Test Site (NTS) in the 1950s. Results are used to extend NTS fallout patterns to intermediate downwind distances (300 to 1200 km). The radioactive cloud is represented in the model by a population of Lagrangian marker particles, with concentrations calculated on an Eulerian grid. Use of marker particles, with fall velocities dependent on particle size, provides a realistic simulation of fallout as the debris cloud travels downwind. The three-dimensional wind field is derived from observed data, adjusted for mass consistency. Terrain is represented in the grid, which extends up to 1200 km downwind of NTS and has 32-km horizontal resolution and 1-km vertical resolution. Ground deposition is calculated by a deposition-velocity approach. Source terms and relationships between deposition and exposure rate are based on work by Hicks. Uncertainty in particle size and vertical distributions within the debris cloud (and stem) allow for some model "tuning" to better match measured ground-deposition values. Particle trajectories representing different sizes and starting heights above ground zero are used to guide source specification. An hourly time history of the modeled fallout pattern as the debris cloud moves downwind provides estimates of fallout arrival times. Results for event HARRY illustrate the methodology. The composite deposition pattern for all 13 tests is characterized by two lobes extending out to the north-northeast and east-northeast, respectively, at intermediate distances from NTS. Arrival estimates, along with modeled deposition values, augment measured deposition data in the development of data bases at the county level; these data bases are used for estimating radiation exposure at intermediate distances downwind of NTS. Results from a study of event TRINITY are also presented.

Ionic diffusion in voltage-clamped isolated cardiac myocytes. Implications for Na,K-pump studies

The whole-cell voltage-clamp technique employing electrolyte-filled micro-pipette suction electrodes is widely used to investigate questions requiring an electrophysiological approach. With this technique, the ionic composition of the cytosol is assumed to be strongly influenced (as result of diffusion) by the ionic composition of the solution contained in the electrode. If this assumption is valid for isolated cardiac myocytes, the technique would be particularly powerful for studying the dependence of their Na,K-pump on the intracellular [Na+]. However, the relationship between the concentrations of ions in the solution filling the electrode and those in the cytosol has not been established. The relationship was investigated to determine in particular whether the [Na+] at the intracellular cation ligand binding sites for the Na-pump ([ Na+]ps) can be set and clamped by [Na+] in the pipette electrode ([ Na+]pip). If [Na+]pip can set and clamp [Na+]ps, this would provide a means for defining the dependence of the Na,K-pump on intracellular [Na+]. The relationship between [Na+]pip and [Na+]ps was analyzed using two approaches. First, a mathematical model of three-dimensional ionic diffusion within a whole-cell patch-clamped myocyte was developed and the effects of experimental parameters on mean [Na+]ps were investigated. When typical experimental values were simulated, the time course to achieve steady state mean [Na+]ps was found to be most sensitive to variations in electrode pore size, cell length and the Na+ pumping rate, but at steady state, mean [Na+]ps varies from [Na+]pip by 5% or less depending on pump rate. Second, to provide experimental support for the validity of the simulations, isolated ventricular myocytes were voltage-clamped and the reversal potential for the Na current was determined in order to estimate steady state intracellular [Na+]. The results of the mathematical and experimental analyses suggest that steady state [Na+]ps can be regulated by the [Na+] in suction pipette electrodes. These findings, while also having a broader significance, indicate for isolated cardiac myocytes that whole-cell suction micro-electrodes can provide a means to assess the dependence of the Na,K-pump on [Na+]ps.

Effect of Ca2+ diffusion on the time course of neurotransmitter release

The three-dimensional (3D) diffusion model of Fogelson, A. L., and R. S. Zucker (1985. Biophys. J. 48: 1003-1017) has been employed as the basis of a refined version of the "Ca theory" for neurotransmitter release. As such, it has been studied here as to its ability to predict the time course of release under various conditions. In particular, conditions were chosen in which the temporal variations in intracellular Ca2+ concentration, the sole factor controlling the release according to the Ca theory, were modified and tested experimentally. The predictions of this model were compared with the experimental results. It is shown that the 3D diffusion model, similarly to earlier simpler versions of the Ca theory, predicts that the time course of release is highly sensitive to both the level of depolarization and the level of the resting concentration of intracellular Ca2+ Moreover, the 3D diffusion model predicts that the time course of release is insensitive to changes in temperature. In contrast, the experimental results show that the time course of release is invariant to the level of depolarization and to the resting level in intracellular Ca2+, but highly sensitive to variations in temperature.

Experimental Verification Study for System for Prediction of Environmental Emergency Dose Information: SPEEDI, (III)

The performance of a three-dimensional atmospheric transport and diffusion model to simulate an accidental release of radioactivity was evaluated by data sets from field tracer experiments over a mountain and valley area. The model consists of a mass-consistent model for wind fields and a particle random-walk model for atmospheric dispersion. Model simulations of tracer concentrations were compared with observed values from eleven experiments; four were conducted in down-valley winds; two were in up-valley winds and five were in cross-valley winds. The calculated results almost agreed reasonably with observed concentration patterns. However, it became apparent that the model is subject to err from real dispersions in down-valley winds induced by nocturnal drainage flows.

Experimental verification study for system for prediction of environmental emergency dose information: SPEEDI. (III). Simulation of field tracer experiments in mountain and valley area.

The performance of a three-dimensional atmospheric transport and diffusion model to simulate an accidental release of radioactivity was evaluated by data sets from field tracer experiments over a mountain and valley area. The model consists of a mass-consistent model for wind fields and a particle random-walk model for atmospheric dispersion. Model simulations of tracer concentrations were compared with observed values from eleven experiments; four were conducted in down-valley winds; two were in up-valley winds and five were in cross-valley winds. The calculated results almost agreed reasonably with observed concentration patterns. However, it became apparent that the model is subject to err from real dispersions in down-valley winds induced by nocturnal drainage flows.

Development of a mathematical eutrophication model of the lagoon of Venice

Integrated research on pollution and eutrophication problems in the central part of the lagoon of Venice is reported, together with a three-dimensional diffusion model. The latter was developed through preliminary elaboration of two other two-dimensional models of the same area, a diffusion and a advection-diffusion model. It was used to estimate, by calibration, the eddy diffusion constant incorporating the dispersive action of the tide. Both research and model were finalized with the objective of studying the temporal evolution and steady-state condition of the dispersion of pollutants and nutrients in the lagoon. The three-dimensional model is applied to simulate dispersion of eight representative variables: phytoplankton, zooplankton, NH 4 +, NO x −, PO 4 3−, dissolved oxygen, degradable organic compounds and temperature. Computer outputs, displaying the spatial distribution of the considered variables under peculiar hypereutrophic conditions, are presented. Additional detailed notes are introduced concerning the more relevant steps of the global study.

Steady-state achievement by introduction of true tidal velocities in a pollution model of the Venice Lagoon

Data on the velocities of tidal currents to be used as input for an advection-diffusion model of the central part of the Venice Lagoon are obtained through interpolation by means of a pre-existing hydrodynamic model. Problems discussed include interpolating procedure and choice of points to calculate velocity vectors for the integration formula ‘donor cell’, as well as the least square optimization of both position and mutual orientation of the two grids. Using interpolated velocities, a steady state was attained after about forty semidiurnal tidal cycles; spatial distributions of pollutant at different tidal stages, as well as their arithmetic mean, are reported. Concentration profiles of the averaged distribution are shown to be substantially similar to those caused by a pure eddy-diffusion process originating from an apparent source spatially shifted from the real one. Causes for the shift are analyzed and the development of a three-dimensional diffusion model is anticipated, with tide-vorticity embodying an eddy-diffusion constant, calibrated upon the achieved steady state. The effect of ‘numerical diffusion’ is also discussed: this effect, in spite of the rather high Reynold's cell number involved in the numerical integration, is shown to be negligible in real circumstances.

ESR determination of lipid translational diffusion coefficients at low spin-label concentrations in biological membranes, using exchange broadening, exchange narrowing, and dipole-dipole interactions

Spin-spin interactions between phosphatidylcholine nitroxide spin labels in fluid-phase dimyristoyl phosphatidylcholine bilayers have been studied in the concentration range 0.1–2.0 mol%. The total line broadening has been separated into its Gaussian and Lorentzian components. The Gaussian linewidth exhibits exchange narrowing of the unresolved proton hyperfine structure, with an approximate quadratic concentration dependence for the square of the linewidth, over this spin-label concentration range. The Lorentzian linewidth has a linear dependence on the spin-label concentration over the same range. The temperature dependence of the gradient of the Lorentzian broadening with respect to spin-label concentration is biphasic over the range 30–80°C, indicating a dominant contribution from magnetic dipole-dipole broadening at the lower temperatures. The contributions from the dipole-dipole and exchange interactions to the Lorentzian broadening have been separated by fitting the temperature dependence using an unconstrained optimization procedure and assuming a single effective activation energy for both diffusion-controlled processes. The lipid lateral diffusion coefficient has been determined from the concentration dependence of both the exchange broadening of the nitrogen hyperfine structure and the exchange narrowing of the proton hyperfine structure using a two-dimensional lattice diffusion model, and also from the concentration dependence of the dipole-dipole interaction using a three-dimensional Fick's law diffusion model. All three methods yield consistent values for the diffusion coefficient, although because of the approximate nature of some of the theoretical models the exchange broadening is expected to give the most reliable results. An experimental protocol for determining the actual spin concentration in the membrane sample is also presented.

Relationship between transmitter release and presynaptic calcium influx when calcium enters through discrete channels.

We have used a three-dimensional diffusion model of calcium entering the presynaptic nerve terminal through discrete channels to simulate experiments relating transmitter release to presynaptic calcium current. The relationship will be less than linear, or will curve downward, if calcium channels are well separated. It will resemble a power-law function with exponent less than the cooperativity of calcium action if channels are clustered closer together. Large presynaptic depolarizations elicit more release than small depolarizations admitting the same calcium influx. This occurs because large pulses open more channels near each other, with the result that the calcium concentration near release sites is greater, due to overlap of calcium diffusing from adjacent channels.

Numerical analysis on steady-state characteristics of wide range air-fuel ratio sensor by using three-dimensional diffusion model.

Various types of sensors to measure wide range air-fuel rations have currently been developed. Most are composed of an electrochemical oxygen pumping cell and a diffusion controlling part. This paper presents a numerical method to analyze the steady-state characteristics of such sensors, using a three-dimensional diffusion model and considering electrochemical reactions. The following results are obtained, considering serveral kinds of gas components: Sensor characteristics are simulated under both λ≥1 and λ<1 conditions; the current value Ip* at the pumping cell is consistent with the experimental value, as is the sensor output. Calculations are also made of several sensor model types by changing the size of some of their parts. It is clear that the Ip* value depends on the gas diffusion, controlled either by the leak aperture or by the diffusion chamber of the sensor.

Presynaptic calcium diffusion from various arrays of single channels. Implications for transmitter release and synaptic facilitation

A one-dimensional model of presynaptic calcium diffusion away from the membrane, with cytoplasmic binding, extrusion by a surface pump, and influx during action potentials, can account for the rapid decay of phasic transmitter release and the slower decay of synaptic facilitation following one spike, as well as the very slow decline in total free calcium observed experimentally. However, simulations using this model, and alternative versions in which calcium uptake into organelles and saturable binding are included, fail to preserve phasic transmitter release to spikes in a long tetanus. A three-dimensional diffusion model was developed, in which calcium enters through discrete membrane channels and acts to release transmitter within 50 nm of entry points. Analytic solutions of the equations of this model, in which calcium channels were distributed in active zone patches based on ultrastructural observations, were successful in predicting synaptic facilitation, phasic release to tetanic spikes, and the accumulation of total free calcium. The effects of varying calcium buffering, pump rate, and channel number and distribution were explored. Versions appropriate to squid giant synapses and frog neuromuscular junctions were simulated. Limitations of key assumptions, particularly rapid nonsaturable binding, are discussed.

Influence of crystallinity on the kinetics of the litharge-massicot phase transition

The kinetics of the thermal transformation of litharge to massicot were studied by the analysis of isothermal data. A diffusion mechanism, formally three-dimensional, seems to be adequate to describe the kinetic data as deduced from reduced time and log-log plots. Comparison of two samples differing in particle size and crystallinity indicated the influence of preliminary grinding on the values of activation energy calculated with the Arrhenius equation. This value changed from 543.4 to 681.3 kJ mol −1 for a three-dimensional diffusion model as the erystallinity decreases. The determination of crystallite size and microstrains for the original and partially converted samples of litharge showed that a recrystallization process occurs simultaneously with the phase transition. This process is responsible for the change in activation energy and diminution of the peak area in the differential thermal analysis curves as the crystallinity decreases.

Chlorination of irradiated polyethylene single crystals: 1: Analysis of alkyl radical decay kinetics

The chlorination of electron beam-irradiated polyethylene (PE) single crystals was studied for a range of irradiation doses, temperatures and chlorine interaction times. The results of this work are presented in two parts: (1) Electron paramagnetic resonance (e.p.r.) analysis of irradiated PE without chlorination and (2) characterization of chlorine uptake in irradiated PE by use of X-ray energy of spectroscopy (XES) and electron spectroscopy for chemical analysis (e.s.c.a.). Spectra were obtained for 75 – 600 Mrad doses over 136 to 333 K temperature range. Alkyl radical concentrations and decay kinetics were derived from e.p.r. spectra and provided a basis for the chlorination analysis in Part II. A first-order alkyl radical decay constant of 4.3 × 10 −5s −1 at 298 K was determined in agreement with previous research. Alkyl radical migration was modelled as a one, two or three-dimensional unsteady-state Fickian diffusion process. E.p.r. alkyl radical concentration data was used to estimate alkyl radical diffusion coefficients yielding values of 10 to 4 × 10 −18cm 2−1 at 298 K for the three models evaluated, respectively. These values are consistent with a diffusivity estimated by Seguchi and Tamura based on a 3-D model. A three-dimensional diffusion model seems to be the most realistic since it permits a zig-zag radical trajectory due to the staggered arrangement of −CH 2- units in crystalline PE. Although a 3-D model would allow diffusion in all directions, it is still consistent with the observation that consecutive migration steps are most likely intermolecular.

A PROPOSED DUAL ROLE OF ODOR IN FORAGING BY THE CALIFORNIA SPINY LOBSTER,PANULIRUS INTERRUPTUS(RANDALL)

A dual influence of odor on foraging is proposed for Panulirus interruptus, on the basis of laboratory and field tests using abalone muscle effluence as a stimulant. Food search consisted of three major components: detection (increased antennule flicking), locomotion, and non-locomotor probing by pereiopod dactyls. Detection occurred at lower concentrations (l0-8 to 10-10 g/l) and was initiated before probing and locomotion in laboratory tests. Probing occurred at concentrations ≥ 10-6 g/l and was initiated before locomotion. Locomotion was limited to higher concentrations (≥ 10-4 g/l) and its induction frequently followed introduction of an effective chemical stimulus by 60 s or longer. The response hierarchy in Panulirus indicates that concentrated chemical stimuli may initiate only local searches for food.Traps were baited with abalone muscle for field experiments. Effective effluent concentrations in immediate trap environments were estimated by a three-dimensional Fickian diffusion model. The minimum concentration attracting lobsters was estimated to be nearly identical to the laboratory-determined threshold for detection, 4-6 log units lower than the threshold for induction of locomotion. Lobsters were captured in traps primarily at night, the period of greatest normal, endogenously initiated activity. Consequently, low concentrations may act by modifying behavior of animals already aroused, rather than by initiating foraging or feeding from the quiescent state.

Quantitative aspects of 119Sn-CIDNP

Enhancement factors of the 119Sn-CIDNP signals observed in hexamethylditin — the recombination product of trimethyltin radicals — are determined. The enhanced absorption in the main 119Sn signal, which cannot be explained by Kaptein's rules based on a first order perturbation treatment of the radical pair theory, can be described by applying the high field approximation of the radical pair model if second order perturbation theory is used. The A/E type multiplet effect in the satellites arising from coupling with 117Sn nuclei which is in accordance with Kaptein's rules is not affected by the second order treatment. Pedersen's analytical expressions derived from the three-dimensional diffusion model describe the 119Sn-CIDNP effects using p = 0.32 and Λ = 1 or p = 0.5 and Λ = 0.56. During the photochemical decomposition of hexamethylditin and octamethyltritin, the main 119Sn signals show enhanced absorption. Enhancement factors found experimentally are compared with values calculated using the second order treatment. It follows that both compounds mainly decompose from triplet states.

Dielectric and ultrasonic relaxation of lithium thiocyanate and lithium perchlorate in dimethoxymethane

Ultrasonic absorption at radio frequencies, complex dielectric permittivities at microwave frequencies, electrical conductances, and infrared spectra of solutions of LiSCN and LiClO/sub 4/ in dimethoxymethane are reported. The conductance data, analyzed in the concentration range 7 X 10/sup 14/ to 10/sup -2/ M, indicate that the major species are neutral pairs of ions although a significant amount of triple ions are present. Band analysis of the ir spectra of solutions with concentrations equal and above 0.05 M reveal the presence of three major species, ion-pairs quadrupoles and chains, the latter with Li/sup +/ bound also to the S-end of the SCN ion. The dielectric spectra indicate that there are three dipolar species present, the solvent and two solute species, in accord with information from the ir spectra. Alternate analysis of the dielectric spectra in terms of a Cole-Davidson distribution does not seem to be consistent with the ir findings. Consequently a possible theoretical interpretation of the Cole-Davidson spectrum (based on our earlier proposed mechanism of collisional diffusion and rotation of ion pairs) is considered as unlikely to be relevant. The same applies to recent improvements on our proposal based on a three-dimensional diffusion model. With the aid of the structuralmore » information above, the ultrasonic spectra at c approx. 0.1 M for both LiSCN and LiClO/sub 4/ are interpreted as due to an ion-pair-quadrupole equilibrium involving cation desolvation. At higher concentrations a new relaxation process centered at approx. 10 MHz appears.« less

On an Elliptic Boundary Value Problem with Mixed Boundary Conditions, Arising in Suspended Sediment Transport Theory

In this paper we prove the existence of an equilibrium distribution in the three-dimensional diffusion model for suspended sediment transport. Mathematically, this means that we solve an elliptic boundary value problem with mixed boundary conditions in a domain with corners. We use Riesz–Schauder theory and some of the classical Agmon–Douglis–Nirenberg estimates, among other things.