An investigation of molecular dynamics for simple liquids
<p>This thesis contains work expanding the theoretical understanding of molecular dynamics used to aid the study of simple liquids. It does so by focusing on investigating forces, which govern the dynamics of manybody systems. We loosely address three questions: <em>How can we categorise...
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
2023
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| _version_ | 1797111862415851520 |
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| author | Utterson, JNFW |
| author2 | Erban, R |
| author_facet | Erban, R Utterson, JNFW |
| author_sort | Utterson, JNFW |
| collection | OXFORD |
| description | <p>This thesis contains work expanding the theoretical understanding of molecular dynamics used to aid the study of simple liquids. It does so by focusing on investigating forces, which govern the dynamics of manybody systems. We loosely address three questions: <em>How can we categorise force distributions? What can we gauge from force data? When do forces obey Newton’s third law?</em></p>
<p>The first of these questions is addressed using statistical mechanics to derive standardised moments of the force distribution for a simple LennardJones liquid in both 1d and 3d with the aid of molecular dynamics.</p>
<p>To answer the second question, we introduce the notions of force spaces and configurations spaces, and look at equivalence of these. We begin the investigation using the harmonic potential, and develop homotopy continuation methods for non-linear forces like Lennard-Jones. Convergent behaviour and limitations are explored for many-body systems, and a general two-body direct inversion is developed and implemented.</p>
<p>The final question is entrenched in classical potential theory, and approached through work focusing on understanding the functional dependence of the interatomic potential. We develop theorems and provide corresponding constructive proofs concluding that potentials which obey certain symmetries can be described by distances, as opposed to positions. This enables us to understand when forces display reciprocity.</p> |
| first_indexed | 2024-03-07T08:16:22Z |
| format | Thesis |
| id | oxford-uuid:edb3605d-c09b-40ff-a9b9-853785212bfe |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:16:22Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | oxford-uuid:edb3605d-c09b-40ff-a9b9-853785212bfe2024-01-03T12:30:58ZAn investigation of molecular dynamics for simple liquidsThesishttp://purl.org/coar/resource_type/c_db06uuid:edb3605d-c09b-40ff-a9b9-853785212bfeEnglishHyrax Deposit2023Utterson, JNFWErban, R<p>This thesis contains work expanding the theoretical understanding of molecular dynamics used to aid the study of simple liquids. It does so by focusing on investigating forces, which govern the dynamics of manybody systems. We loosely address three questions: <em>How can we categorise force distributions? What can we gauge from force data? When do forces obey Newton’s third law?</em></p> <p>The first of these questions is addressed using statistical mechanics to derive standardised moments of the force distribution for a simple LennardJones liquid in both 1d and 3d with the aid of molecular dynamics.</p> <p>To answer the second question, we introduce the notions of force spaces and configurations spaces, and look at equivalence of these. We begin the investigation using the harmonic potential, and develop homotopy continuation methods for non-linear forces like Lennard-Jones. Convergent behaviour and limitations are explored for many-body systems, and a general two-body direct inversion is developed and implemented.</p> <p>The final question is entrenched in classical potential theory, and approached through work focusing on understanding the functional dependence of the interatomic potential. We develop theorems and provide corresponding constructive proofs concluding that potentials which obey certain symmetries can be described by distances, as opposed to positions. This enables us to understand when forces display reciprocity.</p> |
| spellingShingle | Utterson, JNFW An investigation of molecular dynamics for simple liquids |
| title | An investigation of molecular dynamics for simple liquids |
| title_full | An investigation of molecular dynamics for simple liquids |
| title_fullStr | An investigation of molecular dynamics for simple liquids |
| title_full_unstemmed | An investigation of molecular dynamics for simple liquids |
| title_short | An investigation of molecular dynamics for simple liquids |
| title_sort | investigation of molecular dynamics for simple liquids |
| work_keys_str_mv | AT uttersonjnfw aninvestigationofmoleculardynamicsforsimpleliquids AT uttersonjnfw investigationofmoleculardynamicsforsimpleliquids |