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Q-operators for open quantum spin chains
Get PDFIt has long been known that the one-dimensional, quantum mechanical, Heisenberg
XXX and XXZ models are closely related to the two-dimensional, statistical mechanical six-vertex model. This connection is elucidated through the quantum group
perspective. In particular, representations of a universal R matrix, an element of
the quantum group, provide solutions to the Yang-Baxter equation, which under-pins the integrable structure of these models in the bulk. By understanding how to
construct these representations, we can derive a wide family of integrable models,
by applying this procedure to a different choice of quantum group.
Recently, interest has turned to extending this process in order to consider quantum integrable modles with a boundary. In particular, the structure which underpins
these models is that of the boundary Yang-Baxter equation, also known as the reflection relation. The complicating factor here is the introduction of another universal
element of the algebra, the K-matrix, which requires us to understand the interplay
between the Borel and co-ideal subalgebras of the quantum group.
Working with the representation theory of the quantum affine algebra Uqp
ˆsl2q,
we present some recent results for the six-vertex model with diagonal boundary
conditions. We recall boundary fusion identities and boundary factorisation relations
for the Heisenberg XXZ spin chain, both of which have been published in recent
work. These are juxtaposed with their counterparts for the XXZ chain with quasi-periodic boundary conditions.
By taking the isotropic limit of these relations, we extend these results to the
open XXX chain with diagonal boundary conditions. Furthermore, we construct
new Q-operators for the open XXZ and XXX models, alongside a Verma module
transfer matrix, and consider their analytic properties. We derive new T Q-relations
for the open XXX chain, and outline the route towards the factorisation of the
spin-l{2 transfer matrices of the models.EPSRC fundin
Effect of wax on the rheology of oil
Get PDFThe presence of wax in crude oil presents significant challenges in the oil and gas industry,
affecting production and transportation due to its impact on fluid rheology. This study
addresses the limited understanding of solid-liquid and solid-liquid-vapour equilibria in wax-related issues and investigates the effect of wax on crude oil rheology.
Experimental investigations were conducted using a high-pressure, high-temperature visual
rig and Quartz Crystal Microbalance (QCM) techniques to generate wax disappearance
temperature data for synthetic and real oil systems. Additionally, an autoclave cell equipped
with impellers was employed to examine the influence of temperature, shear rate, and
composition on oil viscosity. Measurements were performed at temperatures ranging from
277-294K and pressures up to 37 MPa.
The obtained viscosity and density data, along with existing research, were utilized to refine
compositional viscosity models. Novel black oil models were developed by adjusting the
coefficients of the Beggs and Robinson dead oil model. Furthermore, a new dead oil model
based on the work of Bennison was introduced, incorporating a broader range of data points.
The live oil model, derived from the work of Chew and Connally, outperformed existing
models, exhibiting an average absolute error of 30.1% compared to 69.7% for the best-performing Beggs and Robinson model. Additionally, a non-Newtonian viscosity model was
developed based on the correlation between wax content, shear rate, temperature, and
viscosity, demonstrating an average absolute error of 36%.
This study contributes to filling the gaps in the literature regarding wax-related issues in
crude oil production and transportation. The findings improve our understanding of the
impact of wax on crude oil rheology and facilitate the development of more accurate viscosity
models. By enhancing our knowledge of wax-related challenges, this research aimed to
optimize the management of CO2 reach oil production and transportation processes in the oil
and gas industry
Robust high dynamic range transducers for surface form and finish
No full textAbstract and full text unavailable. Restricted access until 01.04.2025. Please refer to PDF
Advancing knowledge on fugitive gas migration from integrity compromised energy wells
Get PDFDecommissioned oil and gas wells can suffer integrity failure and release fugitive gases
into the environment. This typically occurs unnoticed since post-abandonment
monitoring is uncommon. To reach NetZero, methane emissions from fugitive sources
such as decommissioned wells, must be mitigated increasing the need for research on this
emerging issue. This research aimed to advance knowledge on this topic through three
main thrusts. First, by evaluating the integrity of decommissioned wells in the field,
finding no signs of integrity failure and highlighting a need for standardised assessment
methods. Next, by identifying sedimentary rock properties controlling fugitive gas
migration in the shallow subsurface of an area of extensive hydrocarbon development,
finding flow will occur through units with low total displacement pressure, or through
preferential pathways. Finally, by evaluating data from an airborne methane survey to
better understand the incidence rate of well integrity failure and identify well attributes
related to its occurrence, finding a 5% failure rate and that well operator, well type,
abandonment years, completion type, surface casing vent flow and remedial treatments
reported may be linked to integrity failure. Overall, this study will aid in developing
effective fugitive gas monitoring and detection strategies, establishing emission targets
and identifying parameters involved in development of well integrity failure.James Watt ScholarshipGeoscience BC’s grant (Project 2017-002
Use of generative learning to improve realism in fluvial facies modelling
No full textThis thesis investigates using generative adversarial networks (GANs) to fast-build geologically plausible 3D facies models of fluvial systems by learning simulated facies patterns
and their uncertainty from a process-based model with different avulsion parameters. Fluvial systems, e.g. meandering rivers, can create complicated facies distributions composed
of multiple facies with varied shapes and transitions due to the complex sedimentary processes and the partiality of the resulting record. Conventional simulation tools, such as
process-based models and geostatistical approaches, use a stochastic process to simulate
fluvial facies models based on physic-based or rule-based processes, parametric geometries or spatial correlation models. The stochastic nature allows those conventional tools
to produce an ensemble of different realisations. However, those realisations often can’t
be directly sampled when integrated into a model updating loop, requiring external geological parametrisation, e.g. PCA. Deep generative models, e.g. GANs, showed powerful
learning capability that allows using a small number of latent parameters obeying a simple
distribution, e.g. Gaussian or Uniform distribution, to sample random realisations, which
can be regarded as a geological parameterisation itself. GANs have successfully reproduced realisations from object-based models. This triggers the interest in exploiting the
learning capacity for data complexity, capturing geological processes more closely. As
GANs can learn geological patterns from object-based models, how about process-based
models?
This thesis deeply exploited applying GANs to learn facies models from a process-based
simulator, FLUMY, which is a step forward in deep generative model applications from
the research to real-world challenges. This work tackled several identified problems in
GAN learning 2D and 3D meandering fluvial patterns by proposing a set of unique model
structures, learning frameworks and training strategies.
The ultimate product of this PhD project is a GAN-based 3D facies modelling tool for
low net-to-gross meandering fluvial systems called FluvialGAN3D simulator. This project
used a low NTG ratio meandering fluvial dataset as an example to develop the configuration
of GANs. Extending FluvialGAN3D to other sedimentary settings requires corresponding training datasets and may need to tune GANs’ hyperparameters. The FluvialGAN3D
simulator consists of two pre-trained generators and a reconstruction program, achieved
by solving the problems below in the thesis:
1 creating a benchmark meandering fluvial dataset available for reproduction.
2 comparison of different GAN setups.
3 generating complex multi-facies distributions that represent the features and the variability of the process-based simulations.
4 efficient GAN training on 2D patterns to reconstruct 3D facies models.
5 geological consistent 3D reconstruction of the deposited succession of arbitrary
thickness.
6 investigating different extensions, including soft conditioning to well and seismic
data
Convergence rates of the numerical approximation of stochastic Navier-Stokes equations in 2D and 3D
Get PDFFinite-element algorithms for the space-time discretisation of the stochastic Navier-Stokes equations with periodic boundary conditions are considered, in two and three
dimensions. The stochastic forcing is represented by an operator on a Hilbert space,
growing linearly with respect to the velocity, acting on the differential of a cylindrical
Wiener process. Convergence rates for the error between the exact and approximate
solutions are proved in terms of the L
∞
t L
2
x ∩ L
2
tW1,2
x
-norm, with respect to convergence in probability. For the two-dimensional space-time algorithm, convergence
rates from Carelli and Prohl (SIAM J Numer Anal 50(5):2467–2496, 2012) are improved from linear in space and (almost) 1
4
in time to linear in space and (almost)
1
2
in time. This improvement is due to a decomposition of the pressure function
into deterministic and stochastic parts; the resulting stochastic term is a martingale which allows the use of the Burkholder-Davis-Gundy inequality to obtain an
improved error estimate of the convergence rates. Similar convergence rates are
proved for the three-dimensional space-time algorithm although holding only up to
some stopping time, providing the first result regarding convergence rates for local
strong solutions for the stochastic Navier-Stokes equations in three dimensions
Advances in Multi-Agent Reinforcement Learning : experience sharing, parameter sharing, equilibrium selection
Get PDFMulti-Agent Reinforcement Learning (MARL) has recently gained significant attention due to its potential to train decision-making policies in complex environments
involving multiple agents. This thesis presents four contributions to the field of
MARL, addressing challenges such as sample efficiency, scaling to large numbers of
agents, and improving solution quality. The first contribution is a benchmark of
nine state-of-the-art MARL algorithms across 25 tasks, providing a comprehensive
overview of the current capabilities of MARL methods. The results of the benchmark
study not only provide a thorough evaluation of existing methods, but also identify
several areas for potential improvement. The second contribution is the Shared Experience Actor-critic (SEAC) algorithm, which improves sample efficiency by allowing
agents to share their experiences in an actor critic framework. SEAC addresses the
limitation of existing algorithms in learning from sparse rewards environments and
is shown to consistently outperform two baselines and two state-of-the-art methods
in those settings. The third contribution is the Selective Parameter Sharing (SePS)
algorithm, which groups agents that would benefit from sharing parameters, leading
to improved sample efficiency and faster convergence. Experiments show that SePS
combines the benefits of other parameter sharing baselines, and can scale to hundreds
of agents, even if the agents are not homogeneous. The fourth contribution is the
Pareto Actor-critic (Pareto-AC) algorithm, an algorithm that aims to converge to
Pareto optimal equilibria. Many state-of-the-art MARL algorithms, as identified
by the benchmarking study, tend to converge to suboptimal equilibria. Instead,
PAC is shown to converge to the Pareto equilibria in a range of tasks, even if
multiple suboptimal equilibria exist. Through these contributions, this thesis makes
significant progress towards addressing key challenges of MARL
Reward crowdfunding : an empirical investigation of trends and success factors
No full textAbstract and full text unavailable. Restricted access until 01.09.2026
The impact of entrepreneurship education in developing entrepreneurial intentions in TVET institutions in Trinidad and Tobago
Get PDFThe Trinidad and Tobago government has recognised entrepreneurial development as a
central pillar for achieving sustainable growth in the national economy and reducing
unemployment. Hence, the government has made a strategic decision to invest in
entrepreneurship by implementing and expanding several initiatives to support the
development of entrepreneurs. A significant part of this investment goes into
entrepreneurship education programmes. Over the years, there has been an ongoing
public debate on the government’s returns on investment into entrepreneurship
programmes.
An examination of the existing literature revealed that some research had been conducted
exploring the impact of entrepreneurship education on university students. However,
further exploration of the literature uncovered that there remains a scarcity of research
focusing on the impact of entrepreneurship education in Technical and Vocational
Education and Training (TVET) Institutions. This gap is significant since many
entrepreneurship education programmes are offered at TVET institutions in Trinidad and
Tobago. The study seeks to close that gap by researching the impact of entrepreneurship
education in developing entrepreneurial intentions in Technical Vocation Education and
Training Institutions in Trinidad and Tobago.
This study looks to address the following research question: What is the impact of
entrepreneurship education in developing entrepreneurial intentions among students in
TVET institutions in Trinidad and Tobago? As part of the research, a new model called
the Integrated Entrepreneurial Intentions Model (IEIM) which will be used to help better
understand how to improve the effectiveness of entrepreneurship education in TVET
institutions. This model combined the components of The Theory of Planned Behaviour
(attitude, subjective norm, and perceived behavioural control) and the Cultural
Dimensions of Entrepreneurship Education Ecosystem Model (EEE-Model) to gain a
more holistic understanding of entrepreneurial intentions.
This research adopted a phenomenology paradigm using a mixed methodology
(qualitative and quantitative) to examine the research questions. After a pilot study, data
were collected using a questionnaire survey and focus group. Five hypotheses were
developed to investigate the key variables identified: entrepreneurship education as an
independent variable emphasising the programmes offered, teaching methodologies,
TVET institutions’ responsibilities and cultural influences. While entrepreneurial
intentions focused on attitude and support as dependent variables. Using random
selection, the survey was distributed to 1,130 with a response rate of 30.5% (345
participants) usable surveys for data analysis.
The data was analysed using the IBM SPSS software, which focuses on descriptive
statistics. Subsequently, using Smart PLS-SEM, the research analysed the Common
Method Bias (CMV), Cronbach’s alpha, discriminant and convergent validity, construct
reliability, composite reliability and causal model, path coefficient, f square, average
extracted variance and q square values. Furthermore, the research employed the PLS
(SEM) structure equation modelling techniques to measure and analyse the relationships
between the observed and latent variables while testing the five hypotheses. After this,
the NVivo software was used to help sort, code, and analyse the responses collated during
the focus groups.
The results revealed that three hypotheses were accepted, while the other two were
rejected. It was also revealed that the newly proposed Integrated Entrepreneurial
Intentions Model (IEIM) is acceptable for analysing entrepreneurial intentions. The
finding of this research made a valuable contribution to the body of knowledge in the
field of entrepreneurship education and entrepreneurial intentions, to practice and policy,
particularly in a Trinidad and Tobago context
Hierarchical and adaptive methods for accurate and efficient risk estimation
Get PDFPractical systems that depend on unknown factors are frequently well-represented
through a stochastic model. By estimating statistics of the underlying model, critical features of the system can be inferred. When such inferences assist decision-making, accurate uncertainty quantification is crucial, meaning that robust error
estimates or confidence intervals accompany the estimated parameters. Sufficiently
accurate estimates can require several samples from the underlying model. When
exact samples of the model are computationally infeasible or unavailable, one must
carefully balance statistical errors with approximation bias to retain accurate uncertainty quantification. The multilevel Monte Carlo (MLMC) approach provides
an efficient framework for accurately approximating expectations of quantities of
interest given a hierarchy of increasingly accurate model approximations. Motivated by problems arising in financial credit risk management and option pricing,
this thesis considers the development and analysis of novel MLMC estimators
within two frameworks: Firstly, we develop a hierarchy of nested MLMC estimators to estimate systems of repeatedly nested expectations given approximate
samples of the model conditioned an underlying filtration at a discrete progression
of time points. Secondly, we consider an adaptive MLMC scheme to approximate
point evaluations of the distribution of underlying quantities of interest. Both
methods are combined to compute the probability of significant financial losses
arising from credit risk factors. The method attains a specified error tolerance ε
with an asymptotic cost of order ε
−2
|log ε|
2
, reduced from order ε
−5 using standard
Monte Carlo estimationEngineering and Physical Sciences Research Council (EPSRC) Centre for Doctoral Training in Mathematical Modelling, Analysis and Computation (MAC-MIGS), grant EP/S02329/
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