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

1990 ◽  
Vol 195 ◽  
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.

New Mathematical Models for Effective Drug Diffusivity Estimation in 2D

2007 ◽  
Vol 561-565 ◽  
pp. 1557-1560 ◽  
Author(s):  
Song Wang ◽  
Xia Lou
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mathematical Models ◽  
Analytical Solutions ◽  
Least Squares Method ◽  
Effective Diffusivity ◽  
Data Set ◽  
Initial Burst ◽  
Effective Boundary ◽  
Effective Diffusivities

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.

scholarly journals Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications

2015 ◽  
Vol 52 (04) ◽  
pp. 1076-1096
Author(s):  
Aleksandar Mijatović ◽  
Martijn R. Pistorius ◽  
Johannes Stolte
Keyword(s):  
Monte Carlo ◽  
Lévy Processes ◽  
Variance Reduction ◽  
First Passage Time ◽  
Passage Time ◽  
Levy Processes ◽  
Weak Approximation ◽  
Occupation Times ◽  
First Passage ◽  
Exponential Lévy Models

We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Lévy bridge process that relies in part on a randomisation of the time parameter. We establish this recursion for general Lévy processes and derive its explicit form for mixed-exponential jump-diffusions, a dense subclass (in the sense of weak approximation) of Lévy processes, which includes Brownian motion with drift, Kou's double-exponential model, and hyperexponential jump-diffusion models. We present a highly accurate numerical realisation and derive error estimates. By way of illustration the method is applied to the valuation of range accruals and barrier options under exponential Lévy models and Bates-type stochastic volatility models with exponential jumps. Compared with standard Monte Carlo methods, we find that the method is significantly more efficient.

scholarly journals Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation

2011 ◽  
Vol 48 (3) ◽  
pp. 699-712 ◽  
Author(s):  
Tomoyuki Ichiba ◽  
Constantinos Kardaras
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Kernel Smoothing ◽  
Brownian Bridge ◽  
First Passage Time ◽  
Passage Time ◽  
Efficient Estimation ◽  
Cumulative Distribution ◽  
First Passage ◽  
One Dimensional

We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as the expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order 1 / √N, where N is the sample size, is achieved, which is in sharp contrast to the slower nonparametric rates achieved by kernel smoothing of cumulative distribution functions.

scholarly journals Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation

2011 ◽  
Vol 48 (03) ◽  
pp. 699-712
Author(s):  
Tomoyuki Ichiba ◽  
Constantinos Kardaras
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Kernel Smoothing ◽  
Brownian Bridge ◽  
First Passage Time ◽  
Passage Time ◽  
Efficient Estimation ◽  
Cumulative Distribution ◽  
First Passage ◽  
One Dimensional

We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as the expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order 1 / √N, where N is the sample size, is achieved, which is in sharp contrast to the slower nonparametric rates achieved by kernel smoothing of cumulative distribution functions.

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