Analytical Diffusion Model Research Articles

Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo

Diffuse reflectance spectra were collected from adenomatous colon polyps (cancer precursors) and normal colonic mucosa of patients undergoing colonoscopy. We analyzed the data by using an analytical light diffusion model, which was tested and validated on a physical tissue model composed of polystyrene beads and hemoglobin. Four parameters were obtained: hemoglobin concentration, hemoglobin oxygen saturation, effective scatterer density, and effective scatterer size. Normal and adenomatous tissue sites exhibited differences in hemoglobin concentration and, on average, in effective scatterer size, which were in general agreement with other studies that employ standard methods. These results suggest that diffuse reflectance can be used to obtain tissue information about tissue structure and composition in vivo.

Inhibited Carbon-Carbon Composites: Isothermal and Fatigue Exposure

The oxidation process is examined under isothermal, cyclic thermal and thermomechanical fatigue conditions for inhibited carbon-carbon composites. Mass loss and material property degradation assessment is undertaken with subsequent exploratory nondestructive testing utilizing DMA and PUCOT techniques. An analytical diffusion model is developed to evaluate oxidation degradation for selected exposure conditions. The results are then compared with the experimental data generated. Nondestructive testing techniques introduced along with the diffusion model successfully trace the shear and axial modulus degradation of inhibited carbon-carbon composite as oxidation progresses. These results when compared with thermomechanical data establish the significance of the combined temperature and mechanical load on the overall material characterization of carbon-carbon laminates.

Water dynamics in human blood via combined measurements of T2 relaxation and diffusion in the presence of gadolinium.

An analytical model of tissue relaxation and restricted diffusion in human blood is presented. The blood tissue model is composed of three different compartments: red blood cells, plasma, and macromolecular protons. The relaxation rate constants and free diffusion coefficients of intracellular and extracellular water may differ. Analytical formulas for signal loss due to relaxation and diffusion in the Carr-Purcell Meiboom-Gill and pulsed-field-gradient multispin echo experiments for this tissue model are derived. The model is fitted to the experimental data for human blood with various concentrations of Gadolinium contrast agent. The obtained model parameters are realistic. The validity and sensitivity of the model are also discussed.

An analytical model of restricted diffusion in bovine optic nerve.

An analytical model of restricted diffusion in bovine optic nerve is presented. The nerve tissue model is composed of two different objects: prolate ellipsoids (axons) and spheres (glial cells) surrounded by partially permeable membranes. The free diffusion coefficients of intracellular and extracellular water may differ. Analytical formulas for signal loss due to diffusion in the pulsed gradient spin echo (PGSE) experiment for this tissue model are derived. The model is fitted to experimental data for bovine optic nerve. The obtained model parameters are shown to be reasonable. The model describes all of the characteristics of the PGSE data: anisotropy, upward curvature of decay curves, and diffusion time dependence. The validity and sensitivity of the model are also discussed.

Transmitter concentration profiles in the synaptic cleft: an analytical model of release and diffusion

A three-dimensional model for release and diffusion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a diffusion function describing the spread of transmitter in the cleft. Concentration profiles of transmitter at the postsynaptic side were calculated for different transmitter concentrations in a vesicle, release scenarios, and diffusion coefficients. From the concentration profiles the receptor occupancy could be determined using alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor kinetics. It turned out that saturation of receptors and sufficiently fast currents could only be obtained if the diffusion coefficient was one order of magnitude lower than generally assumed, and if the postsynaptic receptors formed clusters with a diameter of roughly 100 nm directly opposite the release sites. Under these circumstances the gradient of the transmitter concentration at the postsynaptic membrane outside the receptor clusters was steep, with minimal cross-talk among neighboring receptor clusters. These findings suggest that for each release site a corresponding receptor aggregate exists, subdividing an individual synapse into independent functional subunits without the need for specific lateral diffusion barriers.

Polyethylene exposed to liquid propane: Sorption and permeation kinetics and mechanical properties

AbstractData obtained by sorption and permeation measurements of liquid propane in medium‐density polyethylene were analyzed with an analytical diffusion model, assuming a constant diffusion coefficient, and a numerical model, based on the free volume theory of Fujita. The stress‐strain properties of propane‐swollen medium‐density polyethylene were recorded in an Instron tensile tester. The sigmoid sorption curves (modeled here for the first time) were adequately described using nonstationary boundary conditions. The numerical model was capable of representing sorption, desorption, and permeation data, whereas the analytical technique gave satisfactory results only for sorption/desorption data in the initial, transient stage. The difference between diffusion coefficients determined from sorption and desorption measurements and the time dependence of the modulus‐solute concentration relationship can be explained by assuming a relaxation of constrained amorphous chain segments. The penetrant‐induced structure rearrangement is, according to differential scanning calorimetry measurements, confined to the amorphous phase.

A simplified model for radiant heating and cooling panels

Radiant panel heating and cooling systems for sensible space conditioning have several attributes. These include, but are not limited to, energy savings potential and ability to favorably tie-in with moderate temperature, low-intensity energy sources like solar systems and heat pumps. In order to predict and incorporate such attributes of panel systems, a comprehensive, yet simple model is necessary so that the designers will find it practical to use. Part of this model is the heat diffusion in the panel. An analytical heat diffusion model was developed which is applicable to heating and cooling. Sample designs indicated that this model has an accuracy comparable to that of a finite element model and can be used easily by the design engineer for practical purposes.

An exploratory econometric analysis of shared electronic banking network adoption

This paper focuses on a specific kind of interorganizational system — shared electronic banking networks — and identifies firm characteristics that are likely to influence the perceived business value of network membership and thus lead to early adoption. We undertake an exploratory econometric analysis of the adoption of Yankee 24, a large shared electronic banking network in the northeastern USA. Using Bass's analytical diffusion model, we categorize Yankee 24 members into earlier and later adopters. Probit models are estimated to assess the impact of explanatory variables on network adoption. We find that a bank's total demand deposits have a positive impact on early adoption, while the number of a bank's branch offices, a proxy for the size of its proprietary network, has a negative impact on early adoption.

Analysis of threshold modulations in one-dimensional error diffusion

Error diffusion is a numerical method for the binarization of continuous tone data. Modified error diffusion algorithms exist that introduce threshold modulations into the process. this article generalizes an analytical model of error diffusion to include those threshold modulated algorithms. The agreement between analytical prediction and the result of numerical error diffusion is shown.

Diffusion thermique non-stationnaire dans des milieux multicouches et problème aux valeurs propres—1. Une paroi unique multicouches

An analytical model for the transient heat diffusion in one-dimensional multilayered slabs, cylinders and spheres, is proposed. This model is based on the finite integral transform and the transfer matrix formalism for solving the boundary homogeneous problem and the eigenvalue problem that is not of the conventional Sturm- Liouville type in this case. For the computation of the eigenvalues in order to obtain the numerical solution, a reliable procedure is presented because the conventional techniques cannot prevent from missing eigenvalues in the course of the computation.

Calculated intra- and extracellular PO2 gradients in heavily working red muscle

A recently introduced three-dimensional analytical model of O2 diffusion to heavily working muscle that considers myoglobin-facilitated O2 diffusion inside the muscle fiber and a carrier-free layer separating erythrocytes and fiber is able to furnish the following new insights in O2 supply to red muscle at high performance. 1) Fiber PO2 profiles are essentially flat, and the major PO2 gradients are located in the perierythrocytic region, in good agreement with experimental findings [T. E. J. Gayeski and C. R. Honig, Am. J. Physiol. 251 (Heart Circ. Physiol. 20): H789-H799, 1986]. No specialized anatomical pericapillary barrier structure is required to explain these results. 2) A functional barrier to O2 diffusion has been identified that consists of the carrier-free layer and of the pericapillary muscle fiber portions. There are three reasons that make these structures act as a diffusion barrier: a "geometric reason," a "diffusivity-related reason," and a "myoglobin-related reason." 3) PO2 fields of adjacent red blood cells (RBCs) practically do not interact. 4) Small scale heterogeneities in capillary and RBC spacing are compensated for by high myoglobin-facilitated fiber diffusivity. Limiting factor for diffusional O2 transport is the number of RBCs present on the fiber surface.

Kinetics of layer growth and multiphase diffusion in ion- nitrided titanium

Pure titanium specimens were ion nitrided in a nitrogen plasma in the temperature range of 800 ‡C to 1080 ‡C at various nitrogen partial pressures. During ion nitriding, titanium nitrides TiN and Tiin2N and nitrogen solid solution layers (α and Β) were formed consistent with the equilibrium phase diagram. The kinetics of growth of these layers were studied as a function temperature and ion-nitriding parameters. An analytical diffusion model for multiphase diffusion was used to calculate the diffusion coefficients of nitrogen in the phases of the Ti-TiN system from layer growth experiments. Using the layer growth data, the temperature dependence of nitrogen diffusion in TiN (δ), Ti2N (e), and α titanium was found to obey the following relations: Dinδ=4.4±1.62 × 10su-5 exp-36,500±1400/RT Dine=2.7±1.05 ×10su-3 exp-35,760±2500/RT Dinα=0.96±0.08 × exp-51,280-505/RT

Analytical air pollution advection and diffusion models

A review of non-Gaussian analytical solutions of the advection diffusion equation is presented. Their utilization to mathematical models of air pollution diffusion is discussed and the application of a particular solution is suggested. The suggested KAPPAG model uses the Demuth's (1978) solution and can incorporate smoothed observed vertical wind and diffusion coefficient profiles. It is shown that Demuth's solution can represent the realistic situations of the diminishing vertical exchange coefficient at the top of boundary layer.

Analytical two-dimensional model for minority-carrier diffusion from small-geometry pn junction

A model is developed for the current in a small-geometry p+n junction. It is based on a two-dimensional analytical solution for the continuity equation in low-injection regime. Results for both the minority-carriers concentration and current are presented.

Analytical Diffusion Model for Flood Routing

An analytical diffusion model for flood routing which can take into account backwater effect and lateral flows has been developed. The model is applied to route the floods in a hypothetical rectangular channel with different upstream, downstream, and lateral boundary conditions. Different channel characteristics are assumed and the results obtained are found to check well with those obtained by the finite difference method of implicit scheme based on the complete Saint‐Venant equations for unsteady open channel flow. The model shows good results when applied to simulate flood flow conditions in 1980 and 1981 in the Lower Mun River, in Northeast Thailand. The model cannot be incorporated with detailed data of cross sections or river bed geometry but requires only their average values. The Chézy, C and the diffusivity, k due to channel irregularities are used in the model and are determined by trial and error during model calibration. The model provides an excellent means to analyze individual or overall effects of the boundary conditions and requires much less effort and time for computation at a particular station.

An Analytical Model of Thermal and Vapor Diffusion in Freezing of Wet Coal

An analytical study is presented for the freezing of a semi-infinite domain of wet coal particles with special attention to the role of the airborne water vapor diffusion process. The results indicate that energy transport in this multiphase system can occur by means of thermal diffusion or mass diffusion. The magnitude of the Lewis number can be used to determine the mechanism. For a Lewis number smaller than 1, water vapor will evaporate from the coal particles, condense on the wall, and increase the freezing rate in the system.

An analytical solution to time-dependent fission-product diffusion in an HTGR core

An analytical time-dependent fission-product diffusion model is solved for the fuel-moderator regions of a high temperature gas-cooled reactor (HTGR) during a hypothetical loss of forced circulation (LOFC) accident. A conservative approximate 1-D model is developed for the fuel and moderator regions, represented in cylindrical and slab geometries, from consideration of the hexagonal fuel-element symmetry. Transport is assumed along the shortest diffusion path and the concentration change across the fuel-moderator interface is approximated by a jump condition. The model is solved by construction of the Green's functions for the Laplace-transformed equations and identification of the pole structure. The concentration and current inverse Laplace transforms are obtained by the Cauchy residue theorem in each region for cubic piecewise polynomial initial conditions. A computer program was developed and validated to evaluate the solution, serve as a benchmark for more sophisticated numerical models and to investigate 90Sr diffusion during a hypothetical LOFC.

Turbulent mixing in the hypolimnion of Baldeggersee (Switzerland) traced by natural radon‐2221

Three analytical diffusion models are used to describe the distribution of a nonconservative tracer in the hypolimnion of a lake: The one‐dimensional vertical (1‐DV) model, developed for tracers in the deep sea, leads to a significant overestimation of vertical diffusivity Kz in lakes; the one‐dimensional topographic vertical (1‐DTV) model, applicable if horizontal mixing is fast compared to in situ decay, demonstrates that, except for the deepest layers, vertical tracer distributions are insensitive to Kz; the one‐dimensional topographic horizontal (1‐DTH) model, in which horizontal mixing is incomplete and vertical diffusion is disregarded, is the appropriate model for the interpretation of vertical excess 222Rn profiles a few meters above the lake bottom. The radon flux F from the bottom is calculated from 226Ra in the sediments and corrected for depth variation of porosity and radium activity. In Baldeggersee (Switzerland), F is 390 ± 70 dpm·m‒2·d‒1. Radium activities in the sediments are 0.7 ± 0.2 dpm·g‒1 dry mass, similar to those in other Swiss lakes and in coastal areas of the ocean but 20–50 times smaller than in the deep Pacific. Horizontal diffusivity in the hypolimnion decreases from June (5,000 m2·d‒1) to October (1,000 m2·d‒1); vertical diffusivity is between 1 and 10 m2·d‒1, roughly 10 times larger than values calculated from temperature in the upper hypolimnion. Vertical buoyancy flux is between 10‒11 and 10‒10 m2·s‒3, i.e. between values for the deep ocean and the small ELA lakes in Canada. The large Kz and the transient, often irregular shape of the radon profiles are the result of horizontal bottom currents previously measured by other methods.

Two-dimensional numerical analysis of impurity atom diffusion in semiconductors

Linear two-dimensional diffusion of impurity atom through finite-dimension masks has been numerically examined. Numerical simulation results demonstrate the limits of the two-dimensional analytical diffusion model which was first employed in the well-known paper by Kennedy and O'Brien [1].

To the Corrosion of Austenitic Steel in Sodium Loops

We investigated whether it is possible to predict corrosion effects for austenitic steels exposed to liquid sodium with an analytical diffusion model The comparison between experimental measurement...