Stiff piano string modeling: Computational comparison between finite differences and digital waveguide

2004 ◽  
Vol 116 (4) ◽  
pp. 2561-2561
Author(s):  
Julien Bensa ◽  
Stefan Bilbao ◽  
Richard Kronland‐Martinet ◽  
Thierry Voinier ◽  
Julius O. Smith
Keyword(s):  
Finite Differences ◽  
Digital Waveguide ◽  
Computational Comparison

A First-Principles Computational Comparison of the Aqueous Anatase TiO2 (001) Interface and the Disordered, Fluorinated TiO2 Interface

2018 ◽  
Author(s):  
Kyle Reeves ◽  
Damien Dambournet ◽  
Christel Laberty-Robert ◽  
Rodolphe Vuilleumier ◽  
Mathieu Salanne
Keyword(s):  
Density Of States ◽  
Density Functional ◽  
Water Dissociation ◽  
Water Molecules ◽  
Chemical Doping ◽  
Charge Balance ◽  
Functional Theory ◽  
Adsorption Of Water ◽  
Properties Of Materials ◽  
Computational Comparison

Chemical doping and other surface modifications have been used to engineer the bulk properties of materials, but their influence on the surface structure and consequently the surface chemistry are often unknown. Previous work has been successful in fluorinating anatase TiO<sub>2</sub> with charge balance achieved via the introduction of Ti vacancies rather than the reduction of Ti. Our work here investigates the interface between this fluorinated titanate with cationic vacancies and a<br>monolayer of water via density functional theory based molecular dynamics. We compute the projected density of states for only those atoms at the interface and for those states that fall within 1eV of the Fermi energy for various steps throughout the simulation, and we determine that the<br>variation in this representation of the density of states serves as a reasonable tool to anticipate where surfaces are most likely to be reactive. In particular, we conclude that water dissociation at the surface is the main mechanism that influences the anatase (001) surface whereas the change in<br>the density of states at the surface of the fluorinated structure is influenced primarily through the adsorption of water molecules at the surface.

A First-Principles Computational Comparison of the Aqueous Anatase TiO2 (001) Interface and the Disordered, Fluorinated TiO2 Interface

2018 ◽  
Author(s):  
Kyle Reeves ◽  
Damien Dambournet ◽  
Christel Laberty-Robert ◽  
Rodolphe Vuilleumier ◽  
Mathieu Salanne
Keyword(s):  
Density Of States ◽  
Density Functional ◽  
Water Dissociation ◽  
Water Molecules ◽  
Chemical Doping ◽  
Charge Balance ◽  
Functional Theory ◽  
Adsorption Of Water ◽  
Properties Of Materials ◽  
Computational Comparison

Chemical doping and other surface modifications have been used to engineer the bulk properties of materials, but their influence on the surface structure and consequently the surface chemistry are often unknown. Previous work has been successful in fluorinating anatase TiO<sub>2</sub> with charge balance achieved via the introduction of Ti vacancies rather than the reduction of Ti. Our work here investigates the interface between this fluorinated titanate with cationic vacancies and a<br>monolayer of water via density functional theory based molecular dynamics. We compute the projected density of states for only those atoms at the interface and for those states that fall within 1eV of the Fermi energy for various steps throughout the simulation, and we determine that the<br>variation in this representation of the density of states serves as a reasonable tool to anticipate where surfaces are most likely to be reactive. In particular, we conclude that water dissociation at the surface is the main mechanism that influences the anatase (001) surface whereas the change in<br>the density of states at the surface of the fluorinated structure is influenced primarily through the adsorption of water molecules at the surface.

THE METHOD OF FINITE DIFFERENCES APPLIED TO DESCRIPITION OF A METALIC COMPONENT

2017 ◽  
Author(s):  
Lisiane Trevisan ◽  
Juliane Donadel ◽  
Bianca de Castro
Keyword(s):  
Finite Differences

Finite differences with exponential filtering in the calculation of reactivity

Kerntechnik ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. 210-213 ◽  
Author(s):  
D. Suescún Díaz ◽  
A. Senra Martinez
Keyword(s):  
Finite Differences

Umbral Calculus

10.37236/24 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
A. Di Bucchianico ◽  
D. Loeb
Keyword(s):  
19Th Century ◽  
Finite Differences ◽  
State Of The Art ◽  
Umbral Calculus ◽  
Current State ◽  
Logical Foundation ◽  
Complete Bibliography ◽  
The 19Th Century ◽  
Mathematical Literature

We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 500 references) which we expect to update regularly.

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