Mathematical Models of Skin Permeability: Microscopic Transport Models and Their Predictions

Mathematical models of skin permeability: An overview

International Journal of Pharmaceutics ◽

10.1016/j.ijpharm.2011.02.023 ◽

2011 ◽

Vol 418 (1) ◽

pp. 115-129 ◽

Cited By ~ 187

Author(s):

Samir Mitragotri ◽

Yuri G. Anissimov ◽

Annette L. Bunge ◽

H. Frederick Frasch ◽

Richard H. Guy ◽

...

Keyword(s):

Mathematical Models ◽

Skin Permeability

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Description and Verification of the Contaminat Transport Models in Groundwater (Theory And Practice)

Archives of Environmental Protection ◽

10.2478/aep-2013-0021 ◽

2013 ◽

Vol 39 (3) ◽

pp. 3-21 ◽

Cited By ~ 1

Author(s):

Andrzej Aniszewski

Keyword(s):

Mathematical Models ◽

Contaminant Transport ◽

Organic Contaminants ◽

Radioactive Decay ◽

Theory And Practice ◽

Transport Models ◽

Measured Concentration ◽

Calculated Concentration ◽

Dimensionless Concentration ◽

Measurement Series

Abstract This paper presents a general overview of 2D mathematical models for both the inorganic and the organic contaminants moving in an aquifer, taking into consideration the most important processes that occur in the ground. These processes affect, to a different extent, the concentration reduction values for the contaminants moving in a groundwater. In this analysis, the following processes have been taken into consideration: reversible physical non-linear adsorption, chemical and biological reactions (as biodegradation/biological denitrification) and radioactive decay (for moving radionuclides). Based on these 2D contaminant transport models it has been possible to calculate numerically the dimensionless concentration values with and without all the chosen processes in relation to both the chosen natural site (piezometers) and the chosen contaminants.In this paper, it has also been possible to compare all the numerically calculated concentration values to the measured concentration ones (in the chosen earlier piezometers) in relation to both the new unpublished measurement series of May 1982 and the new set of parameters used in these 2D contaminant transport models (as practical verification of these models).

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A review of models for investigating the behaviour of nitrogen in soil

Philosophical Transactions of the Royal Society of London Series B Biological Sciences ◽

10.1098/rstb.1982.0010 ◽

1982 ◽

Vol 296 (1082) ◽

pp. 341-349 ◽

Cited By ~ 14

Keyword(s):

Organic Matter ◽

Mathematical Models ◽

Nitrogen Cycle ◽

Statistical Treatment ◽

Scientific Understanding ◽

Data Series ◽

Transport Models ◽

Management Models

An efficient way to integrate knowledge on the behaviour of nitrogen in soil is by the development of mathematical models. Models are developed for several aims, such as prediction, management or scientific understanding. Prediction and management models are mainly based on a statistical treatment of data series from preceding years. Models that have been made to obtain a better understanding of the nitrogen cycle are usually based on a mechanistic description of processes such as leaching, volatilization of ammonia, mineralization, immobilization, nitrification, denitrification and uptake by the roots. Differences between models occur because these processes are described with varying degrees of sophistication; often, the description of one or two of the processes dominate the entire model. Thus, a classification of models can be based on the processes that are emphasized. A useful categorization distinguishes between transport models, organic matter models and soil-plant relation models.

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