Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Explicita symplektiska integratorer för icke-separabla Hamiltonianer i molekyldynamik.
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Explicit Symplectic Integrators for Non-Separable Hamiltonians in Molecular Dynamics (English)
Abstract [sv]

Inom molekyldynamik bör modeller av metalliska system i allmänhet ha systemets temperatur som en beroende variabel \cite{acklandTemperatureDependenceInteratomic2012}. I synnerhet bör termen i systemets Hamiltonian som representerar potentiell energi utöver det interpartikulära avståndet även vara beroende av temperatur. Detta temperaturberoende gör i allmänhet Hamiltonianen icke-separabel. Konventionella explicita numeriska metoder som är symplektiska då de används på system med separabel Hamiltonian är i allmänhet inte symplektiska då de används i system med icke-separabel Hamiltonian. På grund av detta eftersöks en integrator som behåller symplekticitet då den används i system med en icke-separabel Hamiltonian. En samling integratorer som är symplektiska även då de används på system med icke-separabel Hamiltonian visas prestera lika bra eller bättre än de konventionella Velocity Verlet- och fjärde ordningens Runge Kutta-integratorerna, med nackdelen att de undersökta integratorerna uppvisar numerisk instabilitet då de tillämpas på system där de interpartikulära krafterna beror exponentiellt på inverterade interpartikulära avstånd. Till författarnas kännedom är denna studie den första tillämpningen av de undersökta integratorerna inom molekyldynamik. Resultaten i denna studie ger en fingervisning om att de undersökta integratorerna inte ger en övergripande lösning på problemet att integrera rörelseekvationerna hos ett system med icke-separabel Hamiltonian. Emellertid behövs vidare undersökningar som använder den undersökta samlingen av integratorer i andra system i molekyldynamik än de som undersöks i denna studie för att ge en mer definitiv slutsats.

Abstract [en]

In molecular dynamics, mathematical models of metallic systems should in general have the temperature of the system as a dependent variable \cite{acklandTemperatureDependenceInteratomic2012}. In particular, the potential energy term of the Hamiltonian function of the interaction model should be dependent on temperature in addition to interparticular distances. This puts the Hamiltonian function on a form which is generally non-separable. Conventional explicit numerical methods which are symplectic when used to integrate the equations of motion of systems with separable Hamiltonians are not in general symplectic when used to integrate the equations of motion of systems with a non-separable Hamiltonian. Hence, an integrator which sustains symplecticity when used in a system with non-separable Hamiltonian is sought. A family of explicit integrators which are symplectic when integrating systems with a non-separable Hamiltonian are shown to exhibit similar or superior performance to the Velocity Verlet and fourth-order Runge-Kutta schemes, albeit with the drawback of numerical instability when used on a system where forces depend exponentially on the inverted interparticular distances. To the knowledge of the authors, this study is the first time this family of integrators is applied in the context of molecular dynamics. The results of this study provide a first indication that a comprehensive solution to the problem of integrating the equations of motion of a system with a non-separable Hamiltonian explicitly and symplectically is not provided by the considered family of integrators. However, further investigations into using this family of integrators in other molecular dynamics systems than those investigated here are needed to provide a more definitive conclusion.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:203
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-255696OAI: oai:DiVA.org:kth-255696DiVA, id: diva2:1341307
Supervisors
Examiners
Available from: 2019-08-08 Created: 2019-08-08 Last updated: 2019-08-08Bibliographically approved

Open Access in DiVA

fulltext(2030 kB)10 downloads
File information
File name FULLTEXT01.pdfFile size 2030 kBChecksum SHA-512
c65eadb7b721a1bf589709c828770c4566ee18f9f8ec8c4c130b6390dfa79983707a49f6869ec825605cb15eb9a25c047a72e00fa348865e57ebd377afcb625e
Type fulltextMimetype application/pdf

By organisation
School of Engineering Sciences (SCI)
Engineering and Technology

Search outside of DiVA

GoogleGoogle Scholar
Total: 10 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 45 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf