Random walk to describe diffusion phenomena in three-dimensional discontinuous media: Extension to anisotropic phases and nonplane interfaces

2020 ◽  
Vol 101 (2) ◽  
Author(s):  
Yutaka Maruyama
Keyword(s):  
Random Walk ◽  
Three Dimensional ◽  
Diffusion Phenomena

Modeling and Assessment of the Produced Water Discharges from Offshore Petroleum Platforms

2007 ◽  
Vol 42 (4) ◽  
pp. 303-310 ◽  
Author(s):  
Zhi Chen ◽  
Lin Zhao ◽  
Kenneth Lee ◽  
Charles Hannath
Keyword(s):  
Random Walk ◽  
Produced Water ◽  
Model Development ◽  
Three Dimensional ◽  
Monitoring Program ◽  
Ecological Monitoring ◽  
Numerical Approach ◽  
Ocean Model ◽  
Scale Model ◽  
Water Stream

Abstract There has been a growing interest in assessing the risks to the marine environment from produced water discharges. This study describes the development of a numerical approach, POM-RW, based on an integration of the Princeton Ocean Model (POM) and a Random Walk (RW) simulation of pollutant transport. Specifically, the POM is employed to simulate local ocean currents. It provides three-dimensional hydrodynamic input to a Random Walk model focused on the dispersion of toxic components within the produced water stream on a regional spatial scale. Model development and field validation of the predicted current field and pollutant concentrations were conducted in conjunction with a water quality and ecological monitoring program for an offshore facility located on the Grand Banks of Canada. Results indicate that the POM-RW approach is useful to address environmental risks associated with the produced water discharges.

An Approach Toward Emulating Molecular Interaction with a Graph

2006 ◽  
Vol 59 (12) ◽  
pp. 869 ◽  
Author(s):  
Hideaki Suzuki
Keyword(s):  
Random Walk ◽  
Molecular Interaction ◽  
Hard Sphere ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Atomic Clusters ◽  
Experimental Results ◽  
Random Walk Simulation ◽  
Mathematical Graph ◽  
Three Dimensional Space

Network artificial chemistry (NAC) uses a mathematical graph to emulate molecular interaction in a solvent. To emulate molecules' movement in a three-dimensional space, rewiring rules for NAC graphs’ edges must be designed to enable the edges to imitate the relations between molecules or atomic clusters. Our research formulated the ‘network energy’ representing this constraint and rewired the NAC graph to minimize the required energy. Experimental results for the NAC rewiring are compared with a hard-sphere random walk simulation.

scholarly journals Simulating the Gluing of Wood Particles by Lattice Gas Cellular Automata and Random Walk

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 988
Author(s):  
Carina Rößler ◽  
Felix Breitenecker ◽  
Martin Riegler
Keyword(s):  
Mathematical Model ◽  
Random Walk ◽  
Cellular Automata ◽  
Lattice Gas ◽  
Three Dimensional ◽  
Three Dimensional Model ◽  
Model And Simulation ◽  
Wood Particles ◽  
Lattice Gas Cellular Automata ◽  
Modelling Methods

In this work a mathematical model and simulation for the gluing of wood particles designated for particleboards is presented. The aim is to obtain a better understanding of the gluing process. Thus, the behaviour of wood particles during gluing is investigated and the resulting adhesive distribution across the surface of the wood particles is analysed. For developing a mathematical model, the modelling methods “lattice gas cellular automata” and “random walk” were used. The model was implemented in MATLAB and different scenarios were simulated for answering the main questions of the behaviour during gluing. The influences of different parameters on the adhesive distribution were investigated and quantitatively determined by several key figures. Based on these key figures, the effects of the mixing arm, realistic size distributions of wood particles and adhesive droplets, the transfer of adhesive, and the total mass of adhesive are discussed. Furthermore the results are compared with experimental measurements. The simulation results show that the model can feasibly be used for studying the gluing of wood particles. For a possible industrial application, additional research for developing a three-dimensional model is needed.

Random walk method for the two‐ and three‐dimensional Laplace, Poisson and Helmholtz's equations

2001 ◽  
Vol 51 (10) ◽  
pp. 1133-1156 ◽  
Author(s):  
Mandar K. Chati ◽  
Mircea D. Grigoriu ◽  
Salil S. Kulkarni ◽  
Subrata Mukherjee
Keyword(s):  
Random Walk ◽  
Three Dimensional ◽  
Random Walk Method

scholarly journals Scaling limits of the three-dimensional uniform spanning tree and associated random walk

2021 ◽  
Vol 49 (6) ◽  
Author(s):  
O. Angel ◽  
D. A. Croydon ◽  
S. Hernandez-Torres ◽  
D. Shiraishi
Keyword(s):  
Random Walk ◽  
Spanning Tree ◽  
Three Dimensional ◽  
Scaling Limits ◽  
Uniform Spanning Tree

A random walk on small spheres method for solving transient anisotropic diffusion problems

2019 ◽  
Vol 25 (3) ◽  
pp. 271-282
Author(s):  
Irina Shalimova ◽  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
Anisotropic Diffusion ◽  
First Passage Time ◽  
Three Dimensional ◽  
Passage Time ◽  
Exit Point ◽  
Stochastic Algorithm ◽  
Probability Densities ◽  
Spatially Varying ◽  
Diffusion Problems

Abstract A meshless stochastic algorithm for solving anisotropic transient diffusion problems based on an extension of the classical Random Walk on Spheres method is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have derived approximations of the probability densities for the first passage time and the exit point on a small sphere. The method can be conveniently applied to solve diffusion problems with spatially varying diffusion coefficients and is simply implemented for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We present some simulation results in the case of cathodoluminescence and electron beam induced current in the vicinity of a dislocation in a semiconductor material.

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