Absolute continuity of measures corresponding to the Ito processes and processes of the diffusion type

1977 ◽  
pp. 236-296
Author(s):  
R. S. Liptser ◽  
A. N. Shiryayev
Keyword(s):  
Absolute Continuity ◽  
Diffusion Type

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.

scholarly journals Electrokinetic and in situ spectroscopic investigations of CO electrochemical reduction on copper

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jing Li ◽  
Xiaoxia Chang ◽  
Haochen Zhang ◽  
Arnav S. Malkani ◽  
Mu-jeng Cheng ◽  
...  
Keyword(s):  
Mass Transport ◽  
Active Sites ◽  
Gas Diffusion ◽  
Reduction Reaction ◽  
Adsorbed Hydrogen ◽  
Diffusion Type ◽  
Proton Coupled Electron Transfer ◽  
Alkaline Electrolytes ◽  
Reaction Orders

AbstractRigorous electrokinetic results are key to understanding the reaction mechanisms in the electrochemical CO reduction reaction (CORR), however, most reported results are compromised by the CO mass transport limitation. In this work, we determined mass transport-free CORR kinetics by employing a gas-diffusion type electrode and identified dependence of catalyst surface speciation on the electrolyte pH using in-situ surface enhanced vibrational spectroscopies. Based on the measured Tafel slopes and reaction orders, we demonstrate that the formation rates of C2+ products are most likely limited by the dimerization of CO adsorbate. CH4 production is limited by the CO hydrogenation step via a proton coupled electron transfer and a chemical hydrogenation step of CO by adsorbed hydrogen atom in weakly (7 < pH < 11) and strongly (pH > 11) alkaline electrolytes, respectively. Further, CH4 and C2+ products are likely formed on distinct types of active sites.

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