Search results for "Diffusion equation"

showing 6 items of 56 documents

Oxygen Consuming Regions in EMT60/Ro Multicellular Tumour Spheroids Determined by Nonlinear Regression Analysis of Experimental PO2 Profiles

1987

Malignant cells can be studied in vitro, in a tumour-like microenvironment, by growing multicellular tumour spheroids in culture (Sutherland, McCredie and Inch, 1971). Franko and Sutherland (1979) utilized diffusion theory to explain the viable rim thicknesses of spheroids measured histologically. Without PO2 profiles, however, an unequivocal interpretation of their results was not possible. Systematic studies of the PO2 profiles in spheroids have since been made with oxygen microelectrodes by several groups (Carlsson et al., 1979; Kaufman et al., 1981; Mueller-Klieser and Sutherland, 1982a,b). Based on these measurements, new analyses utilizing diffusion theory are being developed to chara…

Steady stateMaterials scienceDiffusion equationStereochemistryMathematical analysisSpheroidOxygen transportRadiusDiffusion (business)Fick's laws of diffusionNonlinear regression
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Transport coefficients in desalting processes by electrodialysis

2011

Abstract In this work a thermodynamic analysis on the transport equations in the processes of electrodiffusion (EF) and electrodialysis (ED) has been developed. The transport equations are classified in two sets according to the information they contain: i ) fundamental and ii ) complementary. We determine that there are four fundamental transport coefficients needed to characterize these membrane systems. We also conclude that this number is not reduced to three when the Onsager reciprocal relation (ORR) is assumed. I have also obtained a new expression for the concentration rate in EF and ED processes from the mass and volume balance. This relation provides a new way for evaluating the ap…

Work (thermodynamics)ChemistryMechanical EngineeringGeneral Chemical EngineeringThermodynamicsNon-equilibrium thermodynamicsGeneral Materials ScienceGeneral ChemistryElectrodialysisConvection–diffusion equationVolume balanceWater Science and TechnologyMembrane technologyDesalination
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Electromagnetic scattering solutions for digital signal processing

2010

electromagnetic wavesscattering theoryfractional diffusion equationelectromagnetic scatteringdigital signal processingsähkömagnetismisirontainverse scatteringsignal processingelectromagnetic imagingsähkömagneettinen säteily
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A CNN Adaptive Model to Estimate PM10 Monitoring

2006

In this work we introduce a model for studying the distribution and control of atmospheric pollution from PM10. The model is based on the use of a cellular neural network (CNN) and more precisely on the integration of the mass-balance equation; at the same time it simulates the scenario regarding a planar grid describing the whole studied area (the city of Palermo) by means of a CNN and a set of Bayesian networks. The CNN allows us to define a grid system whose dynamic evolution is a redefinition of the diffusion equation that considers contributions coming from near cells for each element of the grid. Dynamics of each cell is influenced by meteorological effects and by parameters related t…

particulate matterPolynomialAdaptive controlDiffusion equationbusiness.industryComputer scienceMass balanceAir pollutionAir pollutionBayesian networkAtmospheric pollutionFunction (mathematics)ParticulatesGridmedicine.disease_causeUrban structureCellular neural networkAir qualitymedicineArtificial intelligencebusinessAlgorithmAir quality index
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Itô-Stratonovitch Formula for the Wave Equation on a Torus

2010

We give an Ito-Stratonovitch formula for the wave equation on a torus, where we have no stochastic process associated to this partial differential equation. This gives a generalization of the classical Ito-Stratonovitch equation for diffusion in semi-group theory established by ourself in [18], [20].

symbols.namesakePartial differential equationDiffusion equationMathematics::ProbabilityDifferential equationMathematical analysisFirst-order partial differential equationsymbolsFokker–Planck equationFisher's equationWave equationd'Alembert's formulaMathematics
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Random Walk and Diffusion

2014

The concept of random walk as introduced by Einstein is introduced. It is shown that a random walk on a lattice can be descrbed by a difference equation, which becomes a partial differential equation (diffusion equation) in the continuum limit. The equation is solved with the help of Fourier and Laplace transformations.

symbols.namesakePartial differential equationHeterogeneous random walk in one dimensionDiffusion equationFourier transformLaplace transformDifferential equationMathematical analysissymbolsEinsteinRandom walkMathematics
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