New Mathematical Models for Effective Drug Diffusivity Estimation in 2D

In this paper we propose several new mathematical models for estimating effective diffusivities of a drug released from a cylinder device to an external finite volume. These models can handle problems with ‘initial burst’ and boundary layers. Analytical solutions to the models are derived. To determine the unknown effective diffusivity, time of a initial burst and width of the effective boundary layer, a least-squares method can be used for a given experimental data set. The models were tested using experimental data and the numerical results show the usefulness and accuracy of these models.

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Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽

10.11145/j.biomath.2016.04.231 ◽

2016 ◽

Vol 5 (1) ◽

pp. 1604231

Author(s):

A.N. Pete ◽

Peter Mathye ◽

Igor Fedotov ◽

Michael Shatalov

Keyword(s):

Experimental Data ◽

Mathematical Models ◽

Least Squares ◽

Numerical Method ◽

Least Squares Method ◽

Algebraic Equations ◽

Systems Of Odes ◽

Determination Of Parameters ◽

Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

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Calibration of stormwater quality regression models: a random process?

Water Science & Technology ◽

10.2166/wst.2010.324 ◽

2010 ◽

Vol 62 (4) ◽

pp. 875-882 ◽

Cited By ~ 4

Author(s):

A. Dembélé ◽

J.-L. Bertrand-Krajewski ◽

B. Barillon

Keyword(s):

Experimental Data ◽

Least Squares ◽

Regression Models ◽

Linear Models ◽

Least Squares Method ◽

Weighted Least Squares ◽

Ordinary Least Squares ◽

Data Sets ◽

Data Set ◽

Urban Catchments

Regression models are among the most frequently used models to estimate pollutants event mean concentrations (EMC) in wet weather discharges in urban catchments. Two main questions dealing with the calibration of EMC regression models are investigated: i) the sensitivity of models to the size and the content of data sets used for their calibration, ii) the change of modelling results when models are re-calibrated when data sets grow and change with time when new experimental data are collected. Based on an experimental data set of 64 rain events monitored in a densely urbanised catchment, four TSS EMC regression models (two log-linear and two linear models) with two or three explanatory variables have been derived and analysed. Model calibration with the iterative re-weighted least squares method is less sensitive and leads to more robust results than the ordinary least squares method. Three calibration options have been investigated: two options accounting for the chronological order of the observations, one option using random samples of events from the whole available data set. Results obtained with the best performing non linear model clearly indicate that the model is highly sensitive to the size and the content of the data set used for its calibration.

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Utilização de soluções numéricas e analíticas na descrição da secagem do eixo central de jaca

Revista Verde de Agroecologia e Desenvolvimento Sustentável ◽

10.18378/rvads.v11i3.4314 ◽

2016 ◽

Vol 11 (3) ◽

pp. 131 ◽

Cited By ~ 1

Author(s):

Hyago Costa Sousa ◽

Nathan José Pereira da Silva ◽

Emmanuel Moreira Pereira ◽

Carlos Roberto Marinho da Silva Filho ◽

Weysser Felipe Cândido de Souza

Keyword(s):

Experimental Data ◽

Mathematical Model ◽

Data Analysis ◽

Mathematical Models ◽

Analytical Solutions ◽

Central Axis ◽

Page Model ◽

Different Temperatures ◽

Best Fit ◽

Air Exchange

Objetivou-se descrever o processo de secagem do eixo central de jaca por modelos matemáticos e determinar qual modelo matemático apresentou os melhores ajustes para as características avaliadas. Foi estudado a secagem do eixo central de jaca em estufa com circulação e renovação de ar em quatro temperaturas diferentes 50, 60 70 e 80 °C utilizando modelos matemáticos para a descrição da quantidade de água no eixo central de jaca, foram utilizados frutos adquiridos no pomar do Centro de Ciências Humanas, Sociais e Agrarias, Bananeiras-PB pertencente a Universidade Federal da Paraíba. De acordo com a análise de dados o modelo de Page foi o que apresentou os melhores coeficientes de determinação e os melhores ajustes aos dados experimentais.Use of numerical and analytical solutions in the description of the drying of the central axis of jackfruitAbstract: This study aimed to describe the process of drying the central axis of jackfruit by mathematical models and determine which mathematical model presented the best fit for the characteristics. This study investigated the drying of the central axis of jackfruit in an oven with circulation and air exchange at four different temperatures 50, 60, 70 and 80 ° C using mathematical models to describe the amount of water in the central axis of jackfruit, fruits were utilized acquired in orchard Humanities Center, Social and Agricultural, Bananeiras-PB belonging to the Federal University of Paraíba. According to the data analysis the Page model showed the best determination coefficients and the best fit to the experimental data.

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Monte Carlo Simulations of Effective Diffusivities in Three—Dimensional Pore Structures

MRS Proceedings ◽

10.1557/proc-195-553 ◽

1990 ◽

Vol 195 ◽

Cited By ~ 3

Author(s):

Sebastian C. Reyes ◽

Enrique Iglesia ◽

Yee C. Chiew

Keyword(s):

Boundary Layer ◽

Monte Carlo ◽

Pore Space ◽

First Passage Time ◽

Effective Diffusivity ◽

Passage Time ◽

Gas Diffusion ◽

Random Motion ◽

Porous Solids ◽

Effective Diffusivities

ABSTRACTA hybrid discrete/continuum Monte Carlo technique combining random walk simulations with first passage time (FPT) concepts is developed here in order to estimate diffusion properties of randomly-assembled sintered porous structures. This work combines the creation of realistic porous solid structures with controlled pore size, shape, and tortuosity features with the application of an efficient algorithm for calculating effective diffusivities in all diffusion regimes (Knudsen, transition, and molecular). The hybrid simulation technique consists of creating a “protective” boundary layer surrounding solid surfaces within which discrete random motion simulations are performed while continuum FPT results are used in the remaining pore space. The boundary layer thickness reflects a characteristic length scale, of the order of a few mean free paths, over which the FPT approximation breaks down. This procedure significantly reduces the computations required to cover statistically representative regions of the porous structure,a serious shortcoming in previous studies of gas diffusion through porous solids; it leads to effective diffusivity estimates that are in excellent agreement with experimental measurements.

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