ALBERT

Notes: Summary Intestinal transport of PteGlu was studied using BBMV from rat small intestine. Transport was neither coupled to a specific cation gradient nor was it influenced by variations of the membrane potential. In the presence of a transmembrane pH gradient (pHout 〈 pHin) initial transport was significantly higher compared to studies without pH gradient. Under these conditions transport could be inhibited by pretreating the vesicles with DIDS, an inhibitor of anion exchange systems. Uptake of PteGlu could not be enhanced by preloading the BBMV with HPO 4 2− and Cl− and was not sensitive to DIDS under these conditions. Uptake studies using different concentrations of PteGlu revealed dual transport kinetics in the presence of a pH gradient and linear uptake in its absence. It could be concluded that uptake is mediated by a PteGlu−/OH−-antiporter at low substrate concentrations and occurs by non-ionic diffusion at higher concentrations or in the absence of a pH gradient. In an additional series of experiments it could be shown that about one-third of the substrate is bound to the membrane and is not transported. The biological significance of this binding remains unclear.

Notes: Abstract Diffusion, density, and viscosity data are collected for the systems α-cyclodextrin and β-cyclodextrin in water. Frictional coefficients were computed with the help of literature activity data and a qualitative discussion of their concentration dependence was attempted.

Notes: Abstract The evolution of free diffusion boundaries with various initial perturbations is described and compared with a set of experimental data for the system KCl-Water. The necessity of extrapolating to infinite time of not only the experimental diffusion coefficient (as a function of 1/t'), but also the experimental Q quantily (as a function of 1/t'2) is stressed.

Notes: Abstract Diffusion in a boundary between a polymer+solvent solution and non-solvent was treated by accounting for the presence of the four diffusion coefficients that describe the isothermal transport process in a three component system. Diffusion equations were integrated assuming a concentration dependence of diffusion coefficients that account for the thermodynamic conditions on the cross diffusion terms of Eq. (1). The presence of non-zero cross terms promotes an incongruent diffusion of polymer whose concentration increases at the boundary between the polymer+solvent solution and the non-solvent. Although our model describes diffusion in the range of homogeneous solution, this incongruent polymer diffusion is a process similar to that promoted by the solvent evaporation from the polymer+solvent film that some authors suggested as an intermediate step before the film immersion into the coagulation bath to obtain good asymmetric membranes.

Notes: Abstract The free diffusion coefficients of aqueous solutions of methyl-, 1,3-dimethyl-, ethyl-, and 1,3-diethylurea have been measured at 25°C by the Gouy interferometric technique. With the help of literature activity data the thermodynamic diffusion and the frictional coefficients are computed and a qualitative discussion of their concentration dependence is attempted.

Notes: Abstract The diffusion coefficients of tris(acetylacetonato)-cobalt(III) in water (5, 15, 25, and 40°C), methanol (25°C), ethanol (15, 25, and 45°C), 1-propanol (25°C), 1-butanol (45°C), acetone (25 and 40°C), 2-butanone (25°C), acetonitrile (25°C), tetrahydrofuran (25°C), benzen (25°C), toluene (25°C), and carbon tetrachloride (25°C) have been measured at concentrations close to infinite dilution. The Stokes-Einstein coefficient (f=kT/Dπηr) has been calculated for Co(acac)3 in each solvent and is found to be larger in water than in organic solvents. Furthermore, it increases as the temperature is lowered (or as the viscosity is increased) in water while it decreases with increasing viscosity of organic solvents. The differences are discussed in terms of the enhancement of the water structure by the solute.

Notes: Abstract The four diffusion coefficients describing the isothermal interdiffusion transport in the three-component system BaCl2(1)-KCl(2)-H2O(3) at one concentration were measured. The conditions for the growth of convection inside the diffusion boundary (double diffusive convection) were computed according to the theory proposed by McDougall and compared with the experimental results. Good agreement was found between theory and experimental results. In this system, convection at the borders of the boundary grows even if the heavier components BaCl2 and KCl are more concentrated at the bottom of the diffusion boundary.

Notes: Abstract The polarographic behaviour of fluoro, chloro, bromo and iodobenzene in dimethylformamide, dimethylsulfoxide and acetonitrile at 25 °C is reported. The viscosities and densities of these species in the three solvents have been measured and the corresponding viscosityB-coefficients and molar partial volumes at infinite dilution for halobenzenes are reported. The results, which show a clear dependence upon solvent nature, are analysed in terms of solute-solvent interactions and solvent structure.

Notes: Abstract This paper approaches strategic pricing over the product life cycle while considering the impact of dynamic price elasticities. Extending the work of Simon (1979), a general optimal control formulation is proposed which relies on functional forms which have empirical foundations and can be calibrated in a managerial context. In addition to typical skimming and penetration strategies, dynamic elasticities can lead to “saw tooth” strategies; optimal prices may, for example, decrease, then increase, then decrease over the life cycle. Several normative results, based on numerical simulations, are presented and compared to those found in the literature.

Notes: Abstract We consider the problem of the first passage times for absorption (trapping) of the firstj (j = 1,2, ....) ofk, j 〈k, identical and independent diffusing particles for the asymptotic case k≫〉1. Our results are a special case of the theory of order statistics. We show that in one dimension the mean time to absorption at a boundary for the first ofk diffusing particles, μ1,k , goes as (lnk)−1 for the set of initial conditions in which none of thek particles is located at a boundary and goes ask −2 for the set of initial conditions in which some of thek particles may be located at the boundary. We demonstrate that in one dimension our asymptotic results (k21) are independent of the potential field in which the diffusion takes place for a wide class of potentials. We conjecture that our results are independent of dimension and produce some evidence supporting this conjecture. We conclude with a discussion of the possible import of these results on diffusion-controlled rate processes.

Notes: Abstract The velocity and the diffusion constant are obtained for a periodic onedimensional hopping model of arbitrary periodN. These two quantities are expressed as explicit functions of all the hopping rates. The velocity and the diffusion constant of random systems are calculated by taking the limit N→Β. One finds by varying the distribution of hopping rates that the diffusion constant and the velocity are singular at different points. Lastly, several possible applications are proposed.

Notes: Abstract An exact solution is obtained for the survival fraction in the one-dimensional diffusion problem with randomly distributed deep traps. The time decay is studied both with and without a bias field. The small concentration (x) long time (t) decay behaves as exp[-(x 2 t/t 0)1/3]. The exact results are compared with the coherent potential approximation (CPA) and the first passage time approach (FPT). We find that in most cases of practical interest the FPT is superior to the CPA.

Notes: Abstract This paper deals with independent particles diffusing on a line with traps at random positions. It is shown how the long-time decay of the survival probability is exhanced when particles do not necessarily disappear upon hitting a trap. The results are compared with predictions for a model where particles are either absorbed or reflected by traps.

Notes: Abstract The first purpose of this paper is to present a class of algorithms for finding the global minimum of a continuous-variable function defined on a hypercube. These algorithms, based on both diffusion processes and simulated annealing, are implementable as analog integrated circuits. Such circuits can be viewed as generalizations of neural networks of the Hopfield type, and are called “diffusion machines.” Our second objective is to show that “learning” in these networks can be achieved by a set of three interconnected diffusion machines: one that learns, one to model the desired behavior, and one to compute the weight changes.

Notes: Summary If hydrogen is diffused electrolytically in a metal, it subsequently escapes out if the metal is left to itself. However this hydrogen-treated metal does not totally regain the original magnitudes of its various physical properties,e. g., thermo e.m.f., electrical resistivity, elastic modulii etc. This effect has also been observed in the second-order elastic effect (the Poynting effect) in nickel and two varieties of steel. Measurements were carried out first before hydrogen diffusion. The samples were electrolytically diffused with hydrogen and the left to themselves for a few days and the measurements were repeated. The changed values of the coefficient of Poynting effect are discussed in terms of the dislocations created by in-and out-going hydrogen.

Notes: Abstract Water-well-level fluctuations associated with episodic creep are studied using a coupled deformation-diffusion solution for the pore pressure produced by a plane-strain shear dislocation moving steadily at a speedV in a linear elastic, saturated porous medium. For largeVr/2c, wherer is distance from the dislocation andc is diffusivity, the solution approaches the form of the uncoupled elastic solution used by Wesson (1981) to analyze water-level changes due to creep events. The differences between the two solutions are significant within 10 diffusion lengths (20c/V) from the fault plane. More specifically, the pore pressure predicted by the coupled solution reverses sign behind the dislocation and is much smaller in magnitude than that predicted by the uncoupled solution. For an undrained Poisson ratio of 0.3, Skempton's coefficient of 0.8 and a shear modulus of 30 GPa, the coupled solution predicts a peak pore-pressure change of 13.7 kPa (137 mbar) per millimeter of slip forV=1 km/day andc=1.0 m2/sec. The spectrum of the coupled solution is limited to a band of frequencies, centered at a value proportional toV and approximately inversely proportional to the distance from the observation point to the fault plant. Thus, close to the fault plane the frequency band occupied by the coupled solution may lie above the range at which water wells can respond. The coupled solution is used in interpreting the same creep-associated water-level change observed by Johnson (1973) and modeled by Wesson (1981) using the uncoupled solution. Although there are uncertainties in properties of the rock material and in the speed of the creep event, the coupled solution predicts a water-level change comparable in magnitude to the observed change.

Notes: Abstract Dye plumes were generated at three depths in the seasonal thermocline between 7 and 11 m, 22 km south of Key West on 21 August 1980 and photographed at about 10 second intervals with an underwater camera system. Eleven pairs of consecutive pictures are analyzed to determine the mean current vertical shear and the width of the plumes by positioning reference points relative to the rod attached to the camera system. The relative distances of reference points are calibrated with the stereophotogrammetric method for one pair. The eddy diffusivity is calculated by use of a model of turbulent diffusion developed byTaylor (1921). Its values range from 5 to 25 cm2s−1 for the plume widths ranging from 33 to 132 cm. The Richardson number is calculated for each pair of pictures with the vertical density gradient estimated from temperature profiles. Its values are higher than the critical value of 0.25 except for one case. The diffusivity was higher by orders of magnitude than the molecular one and indicates the presence of turbulence together with billow like features of the plumes in spite of high Richardson numbers. This suggests that the billow turbulence might be caused by effects of surface gravity waves and not by the Kelvin-Helmholtz instability.

Notes: Summary The rates of diffusion of small ions and neutral molecules through isolated calvaria have been determined. Compared with data published on self-diffusion and diffusion through cartilage, H2O, 3-O-methylglucose, lactate, sulfate, and methylamine diffuse at approximately 2/3 the expected rate. Diffusion of H2O and sulfate was unaffected by the administration of the diphosphonate 1-hydroxyethane-1,1-diphosphonate (EHDP), although phosphate fluxes are markedly diminished. Diffusion of water was nearly doubled by vitamin D deficiency. A 1-week treatment with 1,25(OH)2D3 had no effect on H2O diffusion while returning calcium influx to normal. It is concluded that bone matrix permits a flow of small neutral and ionized molecules nearly comparable to that in cartilage. When changes in calcium and phosphate influx are observed, they can be ascribed to the exchange properties of bone mineral and not to changes in matrix permeability.

Notes: Abstract Photosynthesis was studied in four species of red marine macroalgae: Palmaria palmata, Laurencia pinnatifida, Lomentaria articulata and Delesseria sanguinea. The rate of O2 evolution for submersed photosynthesis was measured as a function of incident photon flux density at normal pH and inorganic carbon concentration (pH 8.0, 2 mol m−3), and as a function of inorganic carbon concentration at pH 8.0 at saturating and at limiting photon flux density. The rate of CO2 uptake was measured for emersed photosynthesis as a function of CO2 partial pressure at saturating photon flux density. Previous pH-drift results suggest that Palmaria and Laurencia are able to use HCO inf3 sup− as well as CO2 whereas Lomentaria and Delesseria are restricted to CO2. None of the algae are saturated by 2 mol m−3 inorganic carbon at high light (400 μmol m−2 s−1) but are saturated at low light (35 μmol m−2 s−1). The inorganic C concentration at which half the light-saturated rate of O2 evolution is achieved is higher for Palmaria and Laurencia (1.51 and 1.85 mol m−3) than for Lomentaria and Delesseria (0.772 and 0.841 mol m−3). The lower values for the latter two species could reflect their putative restriction to CO2. If expressed in terms of CO2, the half-saturation values yield 7.2 and 7.8 mmol m−3 respectively, which are very similar to values obtained previously during pH-drift experiments but at lower concentrations of HCO inf3 sup− , consistent with restriction to CO2. The photosynthetic conductance (m s−1), calculated from the initial slope for photosynthesis at low concentrations of inorganic carbon, correlates with the suggested ability to extract inorganic carbon based on pH-drift results. Calculations made assuming that CO2 is the only species diffusing across the boundary layer are consistent with boundary layer thicknesses of 20 and 19 μm for Lomentaria and Delesseria respectively, which is feasible given the rapid water movement in the experiments. For Laurencia however, an unreasonably small boundary layer thickness of 6 μm is necessary to explain the flux, which indicates co-diffusion by HCO inf3 sup− . In the apparent absence of external carbonic anhydrase, direct uptake of HCO inf3 sup− , rather than external conversion to CO2 is indicated in this species. In air, the CO2 concentration at which photosynthesis is half-maximal increases in the same order as the ability to raise pH in drift experiments. At 21 kPa the CO2 compensation partial pressures for Palmaria and Laurencia at 0.56 and 1.3 Pa are low enough to suggest a carbon-concentrating mechanism is operating, while those of Lomentaria at 1.8 Pa and particularly that of Delesseria at 4.5 Pa could be explained without a carbon-concentrating mechanism. The algae tested (all except Delesseria) showed more O2 evolution than could be accounted for with a photosynthetic quotient of 1.0 and uncatalysed conversion of HCO inf3 sup− to CO2 outside the cell in high light at pH 8.0 when high algal fresh weight per unit medium was used. These results are concordant with other data suggesting use of HCO inf3 sup− by Palmaria and Laurencia, but discordant with the rest of the available information in indicating use of HCO inf3 sup− by Lomentaria. The reason for this is unclear. The lightsaturated rate of O2 evolution on an algal area basis and the photon flux density needed to saturate photosynthesis were related partly to the habitat from which the seaweeds were collected, but more strongly to the ability to use HCO inf3 sup− . Values for the two users of HCO inf3 sup− , Palmaria (population used was intertidal; also occurs subtidally) and Laurencia (intertidal/shaded intertidal), were greater than for Lomentaria (shaded intertidal), which was greater than Delesseria (subtidal), both of which are believed to be restricted to CO2. In accordance with earlier δ13C data and, for Delesseria, estimates of the achieved growth rates in situ, carbon is likely to be saturating and use of HCO inf3 sup− is unlikely to occur in the normal low-light habitats of Lomentaria and Delesseria. Analysis of N-use efficiencies show that they are closer to the low-CO2-affinity Laminariales than the high-CO2-affinity Fucaceae.

Notes: Abstract Molecular dynamics simulations were performed on a 20-residue polyalanine helix and a spontaneous transition from a kinked to a straight conformation was observed. The kinetics of the transition was analyzed within the framework of the Kramers model for chemical reactions and within a random walk model. The Kramers model which is based on diffusion along a one-dimensional reaction pathway and the crossing of an energy barrier was found to be inadequate. Instead, a random walk model based on diffusion in the high-dimensional phase space of the system was found to be compatible with the data. The high dimensionality of the phase space permits the system to circumvent high energy barriers and diffuse rapidly at about constant energy, but decelerates the reaction since in the labyrinth of pathways the transition state is reached rarely.

Notes: Abstract A recently described self-consistent effective binary diffusion approximation is applied to ambipolar diffusion in a neutral multicomponent plasma in zero magnetic field, where forced diffusion due to the electric field E plays an essential role. The field E is determined by the constraint that the net current flow produced by the diffusion fluxes must be zero. The resulting effective binary diffusion fluxes are the sum of those that would obtain for E=0 and ambipolar correction terms proportional to E. The formulation is .self=consistent with respect to both mass and charge, the net diffusional fluxes of which are both identically zero. The results may be further simplified due to the small mass of the electrons. The effective binary diffusivity De of the electrons no longer appears in the simplified expressions. They are therefore well suited to numerical calculations, where the large value of De, might otherwise have resulted in unacceptable stability or accuracy restrictions. The well-known effective doubling of ion diffusivities due to ambipolar diffusion occurs in simple situations but is not a general feature.

Notes: Abstract A recent formulation of multicomponent diffusion in multitemperature gas mixtures [J. D. Ramshaw, J. Non-equilib. Thermodyn. 18. 121 (1993)] is applied to ambipolar diffusion in two-temperature multicomponent plasmas in zero magnetic field. Simplifications chic to the small electron muss are systematically exploited. A general expression is derived for the ambipolar electric field E. In the special case where the electron and heavy-particle temperatures are equal, this expression reduces to a result previously obtained using a self-consistent effective binary diffusion (SCEBD) approximation [J. D. Ramshaw and C. H. Chang,Plasma Chem. Plasma Process.11. 395 (1991)]. When thermal diffusion due to electrons is neglected, the heavy particles are shown to diffuse precisely as they would in the same E field if the electrons were entirely removed from the system. Finally, the SCEBD approximation for ambipolar diffusion in multicomponent plasmas is generalized to the case, of unequal electron and heavy-particle temperatures.

Notes: Abstract The growth of a defective scale is analyzed in terms of an idealized, singlelayer, moving-boundary problem with constant diffusivity. The form of the solution is chosen to emphasize the magnitude of the departure from a linear concentration gradient of the diffusing species in the growing scale. The departure is shown to be a function of the k p /D ratio (where kp is the parabolic rate constant, and D is the chemical diffusivity), and thus is directly related to the defect concentration. For iron sulfide under most conditions, and for other compound scales with defect concentrations less than about 10%, the linear gradient assumption is shown to be reasonable.

Notes: Summary Molecular dynamics has been used to study the diffusion of xenon in ferrierite and zeolite-L. It was found that at 298 K and a loading level of 1.33 atoms per unit cell, diffusion down the 10-ring channel in ferrierite is a more facile process than down the wider 12-ring channel in zeolite-L (D = 8.90 x 10-9 m2/s for ferrierite vs. 1.78 x 10-9 m2/s for zeolite-L). This effect can be rationalised by consideration of the effect of channel shape on the diffusion pathway. Under the same conditions, the heat of sorption was calculated to be more favourable for ferrierite (ΔUads = -25.7 kJ/mol vs. -20.0 kJ/mol).

Notes: Abstract Models for a single species that inhabits an environment that is spatially varying are presented. Simple necessary and sufficient conditions for stability, which are independent of the exact details of the dispersal process, are developed in the case of large diffusion rates. The results highlight the important stabilizing nature of diffusion in a spatially varying environment.

Notes: Abstract We first treat the Gierer-Meinhardt equations by linear stability analysis to determine the critical parameter, at which the homogeneous distributions of activator and inhibitor concentrations become unstable. We find two types of instabilities: one leading to spatial pattern formation and another one leading to temporal oscillations. We consider the case where two instabilities are present. Using the method of generalized Ginzburg-Landau equations introduced earlier we then analyze the nonlinear equations. As we are mainly interested in spatial pattern formation on a sphere we consider the problem under an appropriate constraint. Combining the two occurring solutions we find patterns well-known in biology, such as a gradient system and temporal oscillations.

Notes: Abstract Integrodifference equations are discrete-time models that possess many of the attributes of continuous-time reaction-diffusion equations. They arise naturally in population biology as models for organisms with discrete nonoverlapping generations and well-defined growth and dispersal stages. I examined the varied travelling waves that arise in some simple ecologically-interesting integrodifference equations. For a scalar equation with compensatory growth, I observed only simple travelling waves. For carefully chosen redistribution kernels, one may derive the speed and approximate the shape of the observed waveforms. A model with overcompensation exhibited flip bifurcations and travelling cycles in addition to simple travelling waves. Finally, a simple predator-prey system possessed periodic wave trains and a variety of travelling waves.

Notes: Abstract Wyman's equation for facilitated diffusion of a ligand through a solution slab containing a carrier is recast and solved by means of a regular perturbation expansion in the parameter representing the driving force for facilitation. This new solution is complementary to the previously exploited singular perturbation solution due to Murray and represents facilitation in the low facilitation parameter regime. The most significant physical realization of this regime occurs when there is a large affinity between ligand and carrier, as in the carbon monoxide-hemoglobin system. The validity domains of the regular perturbation solution and the singular perturbation solution of Mitchell and Murray and Rubinow and Dembo are delineated. The equation for facilitated diffusion is solved numerically for parameter values appropriate to the oxygen-myoglobin experiments of Wittenberg, and to the carbon monoxide-hemoglobin experiments of Mochizuki and Forster, and Wittenberg. This solution provides a norm for comparison of the utility of the perturbation solutions. We show how the theory explains the apparent contradiction between the positive observations of Mochizuki and Forster and the negative observations of Wittenberg on facilitation of carbon monoxide transport through a slab of hemoglobin solution.

Notes: Abstract This paper studies the classical single locus, diallelic selection model with diffusion for a continuously reproducing population. The phase variables are population density and allele frequency (or allele density). The genotype fitness depend only on population density but include one-hump functions of the density variable. With mild assumptions on genotype fitnesses, we study the geometry of the nullclines and the asymptotic behavior of solutions of the selection model without diffusion. For the diffusion model with zero Neumann boundary conditions, we use this geometric information to show that if the initial data satisfy certain conditions then the corresponding solution to the reaction-diffusion equation converges to the spatially constant stable equilibrium which is closest to the initial data.

Notes: Abstract A non-linear partial differential equation is analyzed using multiple scale techniques and similarity transformations in order to examine the role of hemoglobin and myoglobin in facilitating oxygen transport to tissue.

Notes: Summary A simulation model is presented for the distribution and consumption of O2 in infected cells of soybean root nodule central tissue. It differs from earlier models in closer adherence to observed structure and embodies new morphometric data about the distribution of 〉 12,000 mitochondria per cell and about the geometry of the gas-filled intercellular spaces near which the mitochondria are located. The model cell is a rhombic dodecahedron and O2 enters only through interfaces (totalling 26% of the cell surface) with 24 gas-filled intercellular spaces. These spaces are located at the edges of each rhombic face of the cell, forming an interconnected network over the cell suface. Next, O2 is distributed through the cytoplasm by a leghaemoglobin-facilitated diffusive process, initially between the mitochondria and amyloplasts in the outer layers of the cell and then between 〉 6,000 symbiosomes (each containing 6 bacteroids) towards the central nucleus. The symbiosomes and mitochondria consume O2, but impede its diffusion; all O2 entering symbiosomes is considered to be consumed there. For the calculations, the cell is considered to consist of 24 structural units, each beneath one of the intercellular spaces, and each is divided into 126 layers, 0.2 μm thick, in and through which O2 is consumed and diffused. Rates of consumption of O2 and of N2 fixation in each diffusion layer were calculated from previously-established kinetics of respiration by mitochondria and bacteroids isolated from soybean nodules and from established relationships between bacteroid respiration and N2 fixation. The effects of varying the O2-supply concentration and the concentration and type of energy-yielding substrates were included in the simulations. When the model cell was supplied with 0.5 mM malate, mitochondria accounted for a minimum of 50% of the respiration of the model cell and this percentage increased with increased concentration of the O2 supply. Gradients of concentrations of free O2 dissolved in the cytoplasm were steepest near the cell surface and in this location respiration by mitochondria appeared to exert a marked protective effect for nitrogen fixation in layers deeper within the cell. Estimates of N2 fixation per nodule, calculated from the model cell, were similar to those calculated from field measurements.

Notes: Abstract In a captive group of Japanese monkeys, a juvenile female spontaneously began standing poles against a concrete wall and climbing up them in 1983. By 1987, 3 juvenile females out of 39 monkeys had acquired the behavior. They stood rather heavy poles, weighing 2.6 kg, against the wall and climbed up them without training. At the top of the poles, they often explored the smooth wall by licking or touching it.

Notes: Abstract A mathematical model of deoxygenation of blood in the microcirculation is used to estimate the mass transfer resistance in the blood and to examine certain assumptions used in prior work on simulation of the microcirculation: the treatment of blood as a continuum and the use of a single-step reaction kinetics model. The erythrocytes are treated as cylindrical slugs which alternate with plasma gaps such that oxygen transport is by radial diffusion in the cell. The system of equations including reaction kinetics and oxyhemoglobin diffusion is solved numerically. The results are of direct applicability in estimation of oxygen concentration profiles in tissue. The results also indicate that the resistance to oxygen transport in the capillary (relative to that in the surrounding tissue) is much higher than predicted by the continuum approach used by most prior workers. The resistance in the capillary is a significant fraction of the overall resistance. Other results give quantitative estimates of the error incurred from use of a single-step kinetic model.

Notes: Abstract A theoretical model of high-frequency ventilation (HFV) is presented based on the physical convective exchange process that occurs due to the irreversibility of gas velocity profiles in oscillatory flow through the bronchial airways. Mass transport during the convective exchange process can be characterized by a convective exchange length, $$\bar L_E $$ , which depends only on the irreversibility of bronchial velocity profiles and can be measured by the experimental technique of photographic flow visualization in bronchial tree models. Using the exchange length and the molecular diffusivity, a simple model of overall bronchial mass transfer is developed. The model allows a prediction of the mean gas concentration profiles along the airways, the site of maximum mass transfer resistance, and overall flow rate of the gas of interest in or out of the lung as functions of the parameters of HFV. The results predicted by the model agree with the limited experimental data available for animals and humans. For normal unassisted ventilation, total bronchial cross-sectional area around the 15th Weibel bronchial generation is predicted to be the single most important parameter in controlling the total gas transport rate along the airways. For the breathing of room air, values of the respiratory quotient around 0.78 are predicted, which are insensitive to VT and f. The model represents a fruitful combination of fluid mechanical theory and experiment with physiologic data to yield new and deeper insight into the operation of the human respiratory system during HFV and normal breathing.

Notes: Abstract Translational and rotational diffusion equation of single elements in solution in the external orienting potential forces has been formulated. The equation should govern long-range diffusion effects in the kinetics of nucleation and crystal growth. Boundary conditions, adequate to the reversible reaction of cluster growth typical for kinetic model of nucleation and accounting for steric limitations, has been proposed. Uniaxial single elements in uniaxial orienting force field are considered. Depression of the concentration of single elements at the cluster boundary as controlled by kinetic factors, is predicted i. e., chemical rate constants, finite translational and rotational diffusion, supercolling, and steric limitations. Effective rate constants, controlled by long-range diffusion of single elements at steric limitations present, have been used. Two dimensionless kinetic factors (i. e., reduced addition-reaction rate constant and reduced rotational diffusion constant), supercooling, and steric tolerance anlge range, control process kinetics and distribution of single elements in the cluster's surroundings. Rate reduction factor responsible for the effects of long-range diffusion at steric limitations present is defined and applied for kinetic models of nucleation and crystal growth in unoriented and oriented systems. Computation examples are performed for a wide range of the model variables, and rate reduction effects of several orders of magnitude are predicted. The dominating role ranges of particular model variables, i. e., kinetic, thermodynamic, or steric variables, are discussed.

Notes: Abstract Diffusion of linear aliphatic mono- and diesters (C N ) havingN main chain atoms (N=13–68) in bulk medium-density polyethylene (MDPE) has been studied under hydrostatic pressures up to 2500 bar at temperatures between 60°C and 125°C. Three triglycerides, phenyl stearate, and p-aminoazobenzene (pAAB, 80°C) as the diffusants and low-density (LDPE) and high-density (HDPE) polyethylenes as polyethylene substrate were used for comparison. Diffusion coefficientD was determined from concentration distribution of the diffusants through stacked PE sheets as substrate. Regarding the linear esters at 90°C, the relationshipD ∝N α holds at constant pressures. Under the atmospheric pressure, α became −2.10 in accordance with de Gennes's proposal (1971)D ∝N −2 as well as with the experimental results reported by Klein and Briscoe (1979) forN larger than 30.D's for the glycerides deviate from the relationshipD ∝N −2 toward the smaller values by comparison at the sameN. The exponent α is pressure-dependent. It decreases with increasing pressure according to α=−2.10−0.000942P, whereP is measured by the unit of bar. Plots of lnD vsP for all the diffusants show linear relationships with negative slopes, from which activation volume for the diffusion ΔV

Notes: Zusammenfassung Die Permeabilität von Polybutylenterephthalat wurde für He, Ne, Ar und CO2 im Temperaturbereich von 293–338 K und Druckdifferenzen bis 1,2 bar untersucht. Die Aktivierungsenergien der Permeation und Diffusion von Ne, Ar und CO2 sind oberhalb der Einfriertemperatur größer als unterhalb, während sie für He nahezu konstant bleiben. Die Temperaturabhängigkeit der Löslichkeitskoeffizienten ändert sich bei der Einfriertemperatur nicht.

Notes: Summary Root hairs increase phosphorus, P, uptake over that due to the plant root alone. A mechanistic model using 16 parameters was developed to describe this process. The model was verified with an experiment using six species that varied widely in root hair length, density and radius. A sensitivity analysis was conducted and the results are included to illustrate the situations where root hairs contribute significantly to P uptake. Length of root hair, root hair density and root hair radius all influenced predicted P uptake with root hair length being particularily significant.

Notes: Summary In relation to explanations of anaerobiosis in the field, mathematical models presented in part I are evaluated in the light of the disparity between the low oxygen pressure required by plant roots in well-stirred nutrient solutions and the rather high values apparently required in the field. Water film and rhizosphere respiration do not fully explain this disparity. Soil-root contact as described in part I is shown to considerably affect the partial pressure of oxygen required for unrestricted aerobic respiration.

Notes: Summary A mathematical model is presented for diffusive transport of oxygen inside the root, for the case that oxygen can enter only through part of the root's perimeter because the remainder is blocked by soil-root contact. Without soil-root contact, concentration profiles inside the root can be shown to converge rapidly to a steady-state solution. For the case of soil-root contact a steady-state solution is presented. Steady-state solutions have also been obtained for the presence of a water film, with and without rhizosphere respiration inside the water film. Results are presented in the form of isoconcentration lines.

Notes: Abstract Existing studies that deal with the diffusion of durable good innovations have been criticized for their lack of an explicit testable theory of new product growth. This paper attempts to remedy this situation by providing a theoretical model of market penetration of new durable goods derived from The basic assumption that potential users of the new intermediate product attempt to minimize costs. The resulting model defines a time path of short-run equilibrium market shares determined by the cost characteristics of both the new innovation and the equipment that it is designed to replace, the age distribution of the existing capital stock, and the growth rate of the adopting sector.

Notes: Abstract Calculations of effective diffusivities in three-dimensional, spatially periodic porous media are performed. For isotropic systems, it is found that, for a given porosity, the predicted value of the effective diffusivity matches experimental results for randomly-packed beds of spheres. Furthermore, the three-dimensional geometry yields approximately the same results as previous calculations employing two-dimensional representations, indicating a relative insensitivity of the effective diffusivity to local geometry. Regarding anisotropic systems, for which two-dimensional modes fail, it is found that there is a significant improvement in the prediction of the effective diffusivity perpendicular to the bedding plane when the three-dimensional model is employed using one adjustable parameter. However, the three-dimensional model overestimates the effective diffusivity parallel to the bedding plane.

Notes: Abstract We review and discuss diffusion and hydrodynamic dispersion in a heterogeneous porous medium. Two types of heterogeneities are considered. One is percolation disorder in which a fraction of the pores do not allow transport to take place at all. In the other type, the permeabilities of various regions of the pore space are fractally distributed with long-range correlations. Both systems give rise to unusual transport in which the mean square displacement 〈r 2(t)〉 of a particle grows nonlinearly with time. Depending on the heterogeneities and the mechanism of diffusion and disperison, we may havefractal transport in which 〈r 2〉 growsslower than linearly with time, orsuperdiffusive transport in which 〈r 2〉 growsfaster than linearly with time. We show that percolation models can give rise to both types of transport with scale-dependent transport coefficients such as diffusivity and dispersion coefficients, which are consistent with many experimental observations.

Notes: Abstract We show that it is possible to change the space of diffusion to determine the diffusion controlled apparent rate constant of reaction k a (t). The most important result is that k a (t) can be always expressed by a simple law which will be used for reactions in an infinite plane to an infinite 3D spherical space.

Notes: Zusammenfassung Bei der Ausheilung von Brüchen in thermoplastischen Polymeren spielen der Grenzflächenkontakt, gegebenenfalls die Durchmischung während erzwungener Fließprozesse, vor allem jedoch die Interdiffusion eine Rolle. In dieser Arbeit wird eine kurze Übersicht über Untersuchungen der ersten beiden Phänomene gegeben. Ausführlicher wird dann auf bruchmechanische Untersuchungen der Grenzflächenfestigkeit (G c ) eingegangen. Die Beobachtung, daßG c mit der Quadratwurzel aus der Ausheilzeitt p zunimmt, läßt sich durch ein Diffusionsmodell der Bildung von Kettenverschlaufungen erklären. Die Aktivierungsenergie des Diffusionsprozesses wurde für PMMA und SAN direkt (zu 274 kJ mol−1) bestimmt, die Diffusionskonstante und die mittlere Eindringtiefe (2 bis 3 nm) der Molekülknäuel über die Grenzfläche hinweg aus einem Reptationsmodell berechnet. Infrarotspektroskopische Messungen der Interdiffusion von SAN in PMMA führen zu vergleichbaren Diffusionskonstanten.

Notes: Abstract Recent treatments of diffusion in a one-dimensional disordered lattice by Machta using a renormalization-group approach, and by Alexander and Orbach using an effective medium approach, lead to a frequency-dependent (or non-Markoffian) diffusion coefficient. Their results are confirmed by a direct calculation of the diffusion coefficient.

Notes: Abstract Diffusion on the one-dimensional lattice ℤ is described by a master equation with nearest-neighbor transfer rates (symmetric or asymmetric). The transfer rates associated with bonds are assumed to be independent, equally distributed random variables. Under various conditions on their common distribution the large time behavior of averaged site probabilities and/or related quantities is exhibited.

Notes: Abstract A simple anisotropic diffusion model, according to semiphenomenological arguments, exhibits long-ranged spatial correlations in uniform stationary states.

Notes: Abstract We show in this paper how the segregation of reactants in the diffusion-limited reaction A+B→0 on a fractal substrate arises. For spectral dimensions ds ⩽ 2 we obtain segregation controlled by the source and/or the intrinsic lifetime of the particles.

Notes: Abstract The flux of particles to a single trap is investigated for two systems: (1) particles in 3D space which jump a fixed step lengthl (the Rayleigh flight) and are adsorbed by a spherical surface, and (2) particles on a lattice, jumping to nearest neighbor sites, with a single adsorbing site. Initially, the particles are uniformly distributed outside the traps. When the jump length goes to zero, both processes go over to regular diffusion, and the first case yields the diffusive flux to a sphere as solved by Smoluchowski. For nonzero step length, the flux for large times is given by a modified form of Smoluchowski's result, with the effective radius replaced byR-cl, wherec=0.29795219 andcl is the Milne extrapolation length for this problem. For the second problem, a similar expression for the flux is found, with the effective trap radius a function of the lattice (sc, bcc, fcc) being considered.

Notes: Abstract We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 108 collisions of the diffusive particle. We find that 〈νν(t)〉 ∼ 1/t δ fort large enough, and a crossover from an M ≠ m regime whereδ=2 toδ=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments 〈x(t)2〉 and 〈x(t)4〉, and examine the behavior ofq 2 (t)=〈x(t)4〉/3〈x(t)2〉2. We find thatq(t)→1 (consistent with a normal distribution) in theM →∞ limit (for all timest) and in the t→∞ limit for allM.

Notes: Abstract We study classical diffusion of particles in random media. Although many of our results are general, we focus on the case of an ion in a three-dimensional medium with random, quenched charge centers obeying bulk charge neutrality. Within a functional-integral framework, we calculate the effective diffusion coefficients by first-order and second-order self-consistent perturbation theory (with a Gaussian reference in both cases). We also carry out a one-loop order momentum space renormalization group calculation. The self-consistent methods are complicated numerically and fail beyond intermediate disorder strengths. In contrast, the renormalization group calculation gives an analytical result that appears valid even to high disorder strengths. The methodology, generally applicable to a quantitative calculation of effective diffusion coefficients in disordered media, resolves deficiencies in self-consistent perturbation theory approaches to this class of problems.

Notes: Abstract We construct a bridge between the standard diffusion-to-traps mathematical model of stretched exponential relaxation and the modern experimental database on both electronic and structural relaxation.

Notes: Abstract Diffusion of moving particles in stationary disordered media is studied using a phenomenological mode-coupling theory. The presence of disorder leads to a generalized diffusion equation, with memory kernels having power law long time tails. The velocity autocorrelation function is found to decay like t−(d/2+1), while the time correlation function associated with the super-Burnett coefficient decays liket −d/2 for long times. The theory is applicable to a wide variety of dynamical and stochastic systems including the Lorentz gas and hopping models. We find new, general expressions for the coefficients of the long time tails which agree with previous results for exactly solvable hopping models and with the low-density results obtained for the Lorentz gas. Finally we mention that if the moving particles are charged, then the long time tails imply that there is an ω d/2 contribution to the low-frequency part of the frequency-dependent electrical conductivity.

Notes: Abstract The three topics discussed in this paper are largely independent. Part 1: Fractal “squig clusters” are introduced, and it is shown that their properties can match to a remarkable extent those of percolation clusters at criticality. Physics on these new geometric shapes should prove tractable. As background, the author's theories of squig intervals and squig trees are reviewed, and restated in more versatile form. Part 2: The notion of “latent” fractal dimensionality is introduced and motivated by the desire to simplify the algebra of dimensionality. Scaling noises are touched upon. A common formalism is presented for three forms of anomalous diffusion: the ant in the fractal labyrinth, fractional Brownian motion, and Lévy stable motion. The fractal dimensionalities common to diverse shapes generated by diffusion are given, in Table I, as functions of the latent dimensionalities of the support of the motion and of the diffusion itself. Part 3: It is argued that every fractal point set has a unique fractal dimensionality, but it is pointed out that many fractals involve diverse combinations of many fractal point sets. Such is, in particular, the case for fractal measures and for fractal graphs, often called hierarchical lattices. The fractal measures that the author had introduced in the early 1970s are described, including new developments.

Notes: Abstract A study is presented of migration of optical or magnetic excitations on percolation clusters which terminates upon reaching a trapping site. The theory is based on the extension of results from the theory of random walks to systems without translational invariance, together with the use of scaling concepts. For the case of an excitation which resides on one type of atom in a randomly mixed crystal near the percolation threshold, new power laws for the time and concentration dependences of the mean number of sites visited at timet of the kinetics of arrival at traps are obtained. Some of these results are also tested for the first time by numerical simulations.

Notes: Abstract A diffusion equation including source terms, representing randomly distributed sources and sinks is considered. For quasilinear growth rates the eigenvalue problem is equivalent to that of the quantum mechanical motion of electrons in random fields. Correspondingly there exist localized and extended density distributions dependent on the statistics of the random field and on the dimension of the space. Besides applications in physics (nonequilibrium processes in pumped disordered solid materials) a new evolution model is discussed which considers evolution as hill climbing in a random landscape.

Notes: Abstract We study the superlinear diffusion 〈x 2(t) 〉 ∼t α,α 〉 1, in layered media containing random velocity fields. The superlinear behavior holds in the case of random velocities along thex direction accompanied by diffusional motion in the space transverse to it. The transverse space can be either Euclidean, fractal, or ultrametric. For a one-dimensional transverse space we derive exact expressions for the higher moments of the displacement. Furthermore, we investigate the propagatorP(x, t) along thex direction and establish its scaling behavior. Our analysis highlights the resemblance between the stretched-Gaussian behavior of the propagator and the stretched-exponential form of the survivial probability in the trapping problem; both show late crossover behavior.

Notes: Abstract Diffusion and reaction in heterogeneous media arise in a host of phenomena in the physical and biological sciences. The determination of the mean survival timeτ (i.e., inverse trapping rate) and relaxation timesT n, n=1,2,3,... (i.e., inverse eigenvalues), associated with diffusion among partially absorbing, static traps with surface rate constantk are problems of long-standing interest. The limitsk=∞ andk=0 correspond to the diffusion-controlled case (i.e., perfect absorbers) and reaction-controlled case (i.e., perfect reflectors), respectively. This paper reviews progress we have made on several basic aspects of this problem: (i) the formulation of rigorous bonding techniques and computational methodologies that enable one to estimate the mean survival time τ and principal relaxation timeT 1 (ii) the quantitative characterization of the microstructure of nontrivial continuum (i.e., off-lattice) models of heterogeneous media; and (iii) evaluation of τ and T1 for the same models. We also describe a rigorous link between the mean survival time t and a different effective parameter of the system, namely the fluid permeability tensork associated with Stokes flow through the same porous medium.

Notes: Abstract For diffusion in a monotonie potential field the probability distribution of first-passage times is computed in the limit of short times. The relation to the familiar long-time regime is pointed out.

Notes: Summary Freshly harvested wheat straw contained 0.096 g water g−1 dry straw and 180 mM acetic acid. The straw absorbed water more rapidly from wet soil. The concentration of acetic acid fell to about 10 mM within 6 h of incorporation of straw in the soil and then remained relatively constant for a period of 12 days, irrespective of soil moisture content. In soil at its maximum water holding capacity after gravitational drainage, the decline in acetic acid concentration (c) with distance (d) from wheat or barley straw was exponential, with c=co e−nd where co is the concentration of acetic acid at the straw surface and n is a constant (0.46 for barley and 0.42 for wheat straw). The presence of acetic acid seems to be a major cause of poor establishment and growth when seeds and seedling roots come into contact with straw.

Notes: Abstract With the roots assumed growing at an exponential rate the effects of the diffusive and convective components of flux and nutrient uptake are examined in a non-dimensional setting. Two cases considered are root-root on no root-root competition. Several examples are presented to illustrate the general effects of interroot competition.

Notes: Abstract A hydrogel basedin vivo reference electrode catheter has been developed. A simple diffusion model of ion transport was applied to study chloride ion transport through polyhydroxyethylmethacrylate (pHEMA) membranes. Based on an experimentally derived effective diffusion coefficient of Deff=4·04±0·5×10−8 cm2s−1, a reference electrode catheter was fabricated featuring a dimensionally appropriate pHEMA porous liquid junction, a gelled Ringer's solution internal electrolyte compartment and a Ag/AgCl internal half cell. The reference electrode potential is not a function of pH from pH6 to pH9 and is linearly related to temperature by 0·33 m VoC−1. In animal trials, the intravascular catheter electrodes exhibit an average stability of ±0·92mV for 6–8h. Stability in blood can be attributed to the haemocompatibility and transport properties of pHEMA.

Notes: Abstract The dispersion of I 131 and I 131 -HSA in plasma and whole pig's blood has been studied by observing the clearance of a well mixed bolus, containing the radioactive labelled solute, at a point downstream, during flow through flexible straight and curved tubes. The dispersion of I 131 -HSA in plasma flow through a straight tube is consistent with a mechanism of diffusion superimposed on a parabolic velocity profile. In curved tubes, secondary flows produce additional dispersion of I 131 -HSA in plasma. With whole blood additional dispersion of I 131 -HSA occurs in straight tubes owing to the tumbling and rolling of red blood cells near the vessel wall. The onset of secondary flows and increased dispersion in curved tubes requires a relatively high flow rate with whole blood owing to its increased viscosity at low shear rates. At high flow rates, above a velocity of 10 cm s−1, a phase separation of cells and plasma occurs, with the formation of a relatively stagnant cell-free plasma layer on the inner wall of the bend.

Notes: Abstract Transport chamber experiments were conducted to elucidate the role of surface-oriented blood cell/serum protein interactions in modulating the potassium ion (K+) transport properties of poly (2-hydroxyethylmethacrylate) (pHEMA) membranes. The effects were achieved by carefully exposing one side of pHEMA membranes to freshly drawn whole blood for a period of 10 min. A simple steady-state diffusion model is presented and verified for both the control and experimental membranes. The results indicate that the presence of blood components rapidly decreases the rate of K+ transport to a new steady-state value which is described by a surface area multiplication factor of γT≃0.60. This observation is useful in the design of medical devices for biomedical electroanalysis and haemodialysis, where ion transport is the main function. This transport chamber approach is flexible and useful in measuring the effects of various microenvironmental manipulations to simulate variousin vivo conditions.

Notes: Abstract A numerical solution of the convection-diffusion equation with an alveolar source term in a single-path model (SPM) of the lung airways simulates steady state CO2 washout. The SPM is used to examine the effects of independent changes in physiologic and acinar structure parameters on the slope and height of Phase III of the single-breath CO2 washout curve. The parameters investigated include tidal volume, breathing frequency, total cardiac output, pulmonary arterial CO2 tension, functional residual capacity, pulmonary bloodflow distribution, alveolar volume, total acinar airway cross sectional area, and gas-phase molecular diffusivity. Reduced tidal volume causes significant steepening of Phase III, which agrees well with experimental data. Simulations with a fixed frequency and tidal volume show that changes in blood-flow distribution, model airway cross section, and gas diffusivity strongly affect the slope of Phase III while changes in cardiac output and in pulmonary arterial CO2 tension strongly affect the height of Phase III. The paper also discusses differing explanations for the slope of Phase III, including sequential emptying, stratified inhomogeneity, and the issue of asymmetry, in the context of the SPM.

Notes: Abstract Biosensing is widely recognised to be of potentially major importance to medicine and related fields, but in spite of a large number of impressive and important advances, widespread practical application has lagged. We examine the thesis that ‘sampling’ is a process which involves all of the phenomena which are associated with the transport of analyte molecules to the active sensor site, and that problems associated with this process are now the limiting factor in further use of many existing biosensors. We conclude that an integrated process of sampling and sensing should be emphasised in developing new biosensing systems, and propose several new approaches.

Notes: Abstract A novel design for the internally charged palladium hydride α—β electrode is proposed, based on the Wheatstone-bridge principle. The construction of the electrode and electronic control circuit require little specialist skills. Both long- and short-term tests have shown that the proposed reference electrode system possesses remarkable stability and response time in changing conditions. The design permits a number of improvements to be made in the construction and optimisation of the performance.

Notes: Abstract The diffusion of glucose, inulin and dextran into adult bovine articular cartilage was studied as a function of temperature, solute concentration and articular surface integrity. One-dimensional, transient solute diffusion experiments were performed for 5, 15 and 60 min. The diffusion and interface partition coefficients increased with increasing temperature, but exhibited no concentration dependency when the solute concentration was increased 100-fold. Relative to intact tissue, removal of the uppermost articular surface resulted in decreased solute concentrations within the tissue for all solutes and time periods tested.