Trajectory ensemble methods for understanding complex stochastic systems
This thesis investigates the equilibrium and dynamic properties of stochastic systems of varying complexity. The dynamic properties of lattice models -- the 1-d Ising model and a 3-d protein model -- and equilibrium properties of continuous models -- particles in various potentials -- are presented....
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2013
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| Online Access: | https://eprints.nottingham.ac.uk/13368/ |
| _version_ | 1848791717279432704 |
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| author | Mey, Antonia S.J.S. |
| author_facet | Mey, Antonia S.J.S. |
| author_sort | Mey, Antonia S.J.S. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This thesis investigates the equilibrium and dynamic properties of stochastic systems of varying complexity. The dynamic properties of lattice models -- the 1-d Ising model and a 3-d protein model -- and equilibrium properties of continuous models -- particles in various potentials -- are presented. Dynamics are studied according to a large deviation formalism, by looking at non-equilibrium ensembles of trajectories, classified according to a dynamical order parameter. The phase structure of the ensembles of trajectories is deduced from the properties of large-deviation functions, representing dynamical free-energies.
The 1-d Ising model is studied with Glauber dynamics uncovering the dynamical second-order transition at critical values of the counting field 's', confirming the analytical predictions by Jack and Solich. Next, the dynamics in an external magnetic field are studied, allowing the construction of a dynamic phase diagram in the space of temperature, s-field and magnetic field. The dynamic phase diagram is reminiscent of that of the 2-d Ising model. In contrast, Kawasaki dynamics give rise to a dynamical phase structure similar to the one observed in kinetically constrained models.
The dynamics of a lattice protein model, represented by a self avoiding walk with three different Hamiltonians, are studied. For the uniform Go Hamiltonian all dynamics occurs between non-native and native trajectories, whereas for heterogeneous Hamiltonians and Full interaction Hamiltonians a first-order dynamical transition to sets of trapping trajectories is observed in the s-ensemble. The model is studied exhaustively for a particular sequence, constructing a qualitative phase diagram, from which a more general dynamic behaviour is extrapolated.
Lastly, an estimator for equilibrium expectations, represented by a transition matrix in an extended space between temperatures and a set of discrete states obtained through the discretisation of a continuous space, is proposed. It is then demonstrated that this estimator outperforms conventional multi-temperature ensemble estimates by up to three orders of magnitude, by considering three models of increasing complexity: diffusive particles in a double-well potential, a multidimensional folding potential and a molecular dynamics simulations of alanine dipeptide. |
| first_indexed | 2025-11-14T18:32:57Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-13368 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:32:57Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-133682025-02-28T11:24:44Z https://eprints.nottingham.ac.uk/13368/ Trajectory ensemble methods for understanding complex stochastic systems Mey, Antonia S.J.S. This thesis investigates the equilibrium and dynamic properties of stochastic systems of varying complexity. The dynamic properties of lattice models -- the 1-d Ising model and a 3-d protein model -- and equilibrium properties of continuous models -- particles in various potentials -- are presented. Dynamics are studied according to a large deviation formalism, by looking at non-equilibrium ensembles of trajectories, classified according to a dynamical order parameter. The phase structure of the ensembles of trajectories is deduced from the properties of large-deviation functions, representing dynamical free-energies. The 1-d Ising model is studied with Glauber dynamics uncovering the dynamical second-order transition at critical values of the counting field 's', confirming the analytical predictions by Jack and Solich. Next, the dynamics in an external magnetic field are studied, allowing the construction of a dynamic phase diagram in the space of temperature, s-field and magnetic field. The dynamic phase diagram is reminiscent of that of the 2-d Ising model. In contrast, Kawasaki dynamics give rise to a dynamical phase structure similar to the one observed in kinetically constrained models. The dynamics of a lattice protein model, represented by a self avoiding walk with three different Hamiltonians, are studied. For the uniform Go Hamiltonian all dynamics occurs between non-native and native trajectories, whereas for heterogeneous Hamiltonians and Full interaction Hamiltonians a first-order dynamical transition to sets of trapping trajectories is observed in the s-ensemble. The model is studied exhaustively for a particular sequence, constructing a qualitative phase diagram, from which a more general dynamic behaviour is extrapolated. Lastly, an estimator for equilibrium expectations, represented by a transition matrix in an extended space between temperatures and a set of discrete states obtained through the discretisation of a continuous space, is proposed. It is then demonstrated that this estimator outperforms conventional multi-temperature ensemble estimates by up to three orders of magnitude, by considering three models of increasing complexity: diffusive particles in a double-well potential, a multidimensional folding potential and a molecular dynamics simulations of alanine dipeptide. 2013-07-15 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/13368/1/ClassicThesis.pdf Mey, Antonia S.J.S. (2013) Trajectory ensemble methods for understanding complex stochastic systems. PhD thesis, University of Nottingham. |
| spellingShingle | Mey, Antonia S.J.S. Trajectory ensemble methods for understanding complex stochastic systems |
| title | Trajectory ensemble methods for understanding complex stochastic systems |
| title_full | Trajectory ensemble methods for understanding complex stochastic systems |
| title_fullStr | Trajectory ensemble methods for understanding complex stochastic systems |
| title_full_unstemmed | Trajectory ensemble methods for understanding complex stochastic systems |
| title_short | Trajectory ensemble methods for understanding complex stochastic systems |
| title_sort | trajectory ensemble methods for understanding complex stochastic systems |
| url | https://eprints.nottingham.ac.uk/13368/ |