scholarly journals Diffusion models for mixtures using a stiff dissipative hyperbolic formalism

2019 ◽  
Vol 16 (02) ◽  
pp. 293-312 ◽  
Author(s):  
Laurent Boudin ◽  
Bérénice Grec ◽  
Vincent Pavan
Keyword(s):  
Relaxation Parameter ◽  
Diffusion Models ◽  
Bulk Velocity ◽  
Diffusion Type ◽  
Relaxation Term ◽  
Fluid Equations ◽  
Stiff Relaxation

We consider a system of fluid equations for mixtures with a stiff relaxation term of Maxwell–Stefan diffusion type. We use the formalism developed by Chen et al. and derive a limiting system of Fick type, in which the species velocities tend to align with a bulk velocity when the relaxation parameter remains small.

scholarly journals Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

2020 ◽  
Vol 66 (4) ◽  
pp. 773-793 ◽  
Author(s):  
Arman Shojaei ◽  
Alexander Hermann ◽  
Pablo Seleson ◽  
Christian J. Cyron
Keyword(s):  
Boundary Conditions ◽  
Materials Science ◽  
Unbounded Domains ◽  
Diffusion Models ◽  
Absorbing Boundary Conditions ◽  
The Finite Element Method ◽  
Absorbing Boundary ◽  
Diffusion Type ◽  
2D And 3D ◽  
Accuracy And Stability

Abstract Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.

A system of conservation laws including a stiff relaxation term; the 2D case

1996 ◽  
Vol 36 (4) ◽  
pp. 786-813 ◽  
Author(s):  
Wen Shen ◽  
Aslak Tveito ◽  
Ragnar Winther
Keyword(s):  
Conservation Laws ◽  
Relaxation Term ◽  
System Of Conservation Laws ◽  
Stiff Relaxation

A quasi-likelihood approach to estimating parameters in diffusion-type processes

1994 ◽  
Vol 31 (A) ◽  
pp. 283-290 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Maximum Likelihood ◽  
Diffusion Models ◽  
Estimation Of Parameters ◽  
Likelihood Methods ◽  
Diffusion Type ◽  
Langevin Model ◽  
Likelihood Approach ◽  
Basic Ideas ◽  
Nikodym Derivative ◽  
General Conditions

Estimation of parameters in diffusion models is usually handled by maximum likelihood and involves the calculation of a Radon–Nikodym derivative. This methodology is often not available when minor changes are made to the model. However, these complications can usually be avoided and results obtained under more general conditions using quasi-likelihood methods. The basic ideas are explained in this paper and are illustrated through discussion of the Cox–Ingersoll–Ross model and a modification of the Langevin model.

A quasi-likelihood approach to estimating parameters in diffusion-type processes

1994 ◽  
Vol 31 (A) ◽  
pp. 283-290 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Maximum Likelihood ◽  
Diffusion Models ◽  
Estimation Of Parameters ◽  
Likelihood Methods ◽  
Diffusion Type ◽  
Langevin Model ◽  
Likelihood Approach ◽  
Basic Ideas ◽  
Nikodym Derivative ◽  
General Conditions

Estimation of parameters in diffusion models is usually handled by maximum likelihood and involves the calculation of a Radon–Nikodym derivative. This methodology is often not available when minor changes are made to the model. However, these complications can usually be avoided and results obtained under more general conditions using quasi-likelihood methods. The basic ideas are explained in this paper and are illustrated through discussion of the Cox–Ingersoll–Ross model and a modification of the Langevin model.

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