The efficiency of parallel tempering Monte Carlo is studied for a two-dimensional Ising system of length L with N=L^2 spins. An external field is used to introduce a difference in free energy between the two low temperature states. It is found that the number of replicas R_opt that optimizes the parallel tempering algorithm scales as the square root of the system size N. For two symmetric low temperature states, the time needed for equilibration is observed to grow as L^2.18. If a significant difference in free energy is present between the two states, this changes to L^1.02. It is therefore established that parallel tempering is sped up by a factor of roughly L if an asymmetry is introduced between the low temperature states. This confirms previously made predictions for the efficiency of parallel tempering. These findings should be especially relevant when using parallel tempering for systems like spin glasses, where no information about the degeneracy of low temperature states is available prior to the simulation.

The free energy landscape of a protein-like chain is constructed from exhaustive simulation studies using a combination of discontinuous molecular dynamics and parallel tempering methods. The protein model is a repeating sequence of four kinds of monomers, in which hydrogen bond attraction, electrostatic repulsion, and covalent bond vibrations are modeled by step, shoulder and square-well potentials, respectively. These protein-like chains exhibit a helical structure in their folded states. The model allows a natural definition of a configuration by considering which beads are bonded. In the absence of a solvent, the relative free energy of dominant structures is determined from the relative populations, and the probabilities predicted from the calculated free energies are found to be in excellent agreement with the observed probabilities at different temperatures. The free energy landscape of the protein-like chain is analyzed and confirmed to have funnel-like characteristics, confirmed by the fact that the probability of observing the most common configuration approaches unity at low enough temperatures for chains with fewer than 30 beads. The effect on the free energy landscape of an explicit square-well solvent, where the beads that can form intra-chain bonds can also form (weaker) bonds with solvent molecules while other beads are insoluble, is also examined. Simulations for chains of 15, 20 and 25 beads show that at low temperatures, the most likely structures are collapsed helical structures. The temperature at which collapsed helical structures become dominant is higher than in the absence of a solvent. Finally, the dynamics of the protein-like chain immersed in an implicit hard sphere solvent is studied using a simple model in which the implicit solvent interacts on a fast time scale with the chain beads and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. Using a Markovian model of the kinetics of transitions between conformations, the equilibration process from an ensemble of initially extended configurations to mainly folded configurations is investigated at low effective temperatures for a number of different chain lengths. It was observed that folding profiles appear to be single exponentials and independent of temperature at low temperatures.

The free energy landscape of a protein-like chain is constructed from exhaustive simulation studies using a combination of discontinuous molecular dynamics and parallel tempering methods. The protein model is a repeating sequence of four kinds of monomers, in which hydrogen bond attraction, electrostatic repulsion, and covalent bond vibrations are modeled by step, shoulder and square-well potentials, respectively. These protein-like chains exhibit a helical structure in their folded states. The model allows a natural definition of a configuration by considering which beads are bonded. In the absence of a solvent, the relative free energy of dominant structures is determined from the relative populations, and the probabilities predicted from the calculated free energies are found to be in excellent agreement with the observed probabilities at different temperatures. The free energy landscape of the protein-like chain is analyzed and confirmed to have funnel-like characteristics, confirmed by the fact that the probability of observing the most common configuration approaches unity at low enough temperatures for chains with fewer than 30 beads. The effect on the free energy landscape of an explicit square-well solvent, where the beads that can form intra-chain bonds can also form (weaker) bonds with solvent molecules while other beads are insoluble, is also examined. Simulations for chains of 15, 20 and 25 beads show that at low temperatures, the most likely structures are collapsed helical structures. The temperature at which collapsed helical structures become dominant is higher than in the absence of a solvent. Finally, the dynamics of the protein-like chain immersed in an implicit hard sphere solvent is studied using a simple model in which the implicit solvent interacts on a fast time scale with the chain beads and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. Using a Markovian model of the kinetics of transitions between conformations, the equilibration process from an ensemble of initially extended configurations to mainly folded configurations is investigated at low effective temperatures for a number of different chain lengths. It was observed that folding profiles appear to be single exponentials and independent of temperature at low temperatures.

Surface self-assembly, the spontaneous aggregation of molecules into ordered, sta- ble, noncovalently joined structures in the presence of a surface, is of great importance to the bottom-up manufacturing of materials with desired functionality. As a bulk phenomenon informed by molecular-level interactions, surface self-assembly involves coupled processes spanning multiple length scales. Consequently, a computational ap- proach towards investigating surface self-assembled systems requires a combination of quantum-level electronic structure calculations and large-scale multi-body classical simulations. In this work we use a range of simulation approaches from quantum-based methods, to classical atomistic calculations, to mean-field approximations of bulk mixed phases, and explore the self-assembly strategies of simple dipoles and polyaromatic hydrocarbons on symmetric surfaces. / Graduate

A refinement of a minimal model for protein folding originally proposed by Imamura is presented. The representation of the alpha-helix has been improved by adding in explicit modelling of the entire peptide unit. A four-helix bundle consisting of four alpha-helices and three loop regions is generated with the parallel tempering Monte Carlo scheme. Six native states are found for the given sequence, four U-bundle and two Z-bundle states. All six states have energies of E approx -218ε and all appear equally likely to occur in simulation. The highest probability of folding a native state is found to be at a hydrophobic strength of Ch = 0.8 which agrees with the value of Ch = 0.7 used by Imamura in his studies of alpha to beta structural conversions. Two folding stages are observed in the temperature spectrum dependent on the magnitude of the hydrophobic strength parameter. The two stages observed as temperature decreases are 1) the hydrophobic energy causes the random coil to collapse into a compact globule 2) the secondary structure starts forming below a temperature of about T = 0.52ε/kB. The temperature of the first stage, which corresponds to the characteristic collapse temperature Tθ, is highly dependent on the hydrophobic strength. The temperature of the second stage is constant with respect to hydrophobic strength. Attempts to measure the characteristic folding temperature, Tf , from the structural overlap function proved to be difficult due mostly to the presence of six minima and the complications that arose in the parallel tempering Monte Carlo scheme. However, a rough estimate of Tf is obtained at each hydrophobic strength from a native state density analysis. Tf is found to be significantly lower than Tθ.

A refinement of a minimal model for protein folding originally proposed by Imamura is presented. The representation of the alpha-helix has been improved by adding in explicit modelling of the entire peptide unit. A four-helix bundle consisting of four alpha-helices and three loop regions is generated with the parallel tempering Monte Carlo scheme. Six native states are found for the given sequence, four U-bundle and two Z-bundle states. All six states have energies of E approx -218ε and all appear equally likely to occur in simulation. The highest probability of folding a native state is found to be at a hydrophobic strength of Ch = 0.8 which agrees with the value of Ch = 0.7 used by Imamura in his studies of alpha to beta structural conversions. Two folding stages are observed in the temperature spectrum dependent on the magnitude of the hydrophobic strength parameter. The two stages observed as temperature decreases are 1) the hydrophobic energy causes the random coil to collapse into a compact globule 2) the secondary structure starts forming below a temperature of about T = 0.52ε/kB. The temperature of the first stage, which corresponds to the characteristic collapse temperature Tθ, is highly dependent on the hydrophobic strength. The temperature of the second stage is constant with respect to hydrophobic strength. Attempts to measure the characteristic folding temperature, Tf , from the structural overlap function proved to be difficult due mostly to the presence of six minima and the complications that arose in the parallel tempering Monte Carlo scheme. However, a rough estimate of Tf is obtained at each hydrophobic strength from a native state density analysis. Tf is found to be significantly lower than Tθ.

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising.

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising.

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising.

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising.