Quantum dynamics with short-time trajectories and minimal adaptive basis sets

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation

Compositional approach to design of digital circuits

PhD ThesisIn this work we explore compositional methods for design of digital circuits with the aim of improving existing methodoligies for desigh reuse. We address compositionality techniques looking from both structural and behavioural perspectives. First we consider the existing method of handshake circuit optimisation via control path resynthesis using Petri nets, an approach using structural composition. In that approach labelled Petri net parallel composition plays an important role and we introduce an improvement to the parallel composition algorithm, reducing the number of redundant places in the resulting Petri net representations. The proposed algorithm applies to labelled Petri nets in general and can be applied outside of the handshake circuit optimisation use case. Next we look at the conditional partial order graph (CPOG) formalism, an approach that allows for a convenient representation of systems consisting of multiple alternative system behaviours, a phenomenon we call behavioural composition. We generalise the notion of CPOG and identify an algebraic structure on a more general notion of parameterised graph. This allows us to do equivalence-preserving manipulation of graphs in symbolic form, which simplifies specification and reasoning about systems defined in this way, as displayed by two case studies. As a third contribution we build upon the previous work of CPOG synthesis used to generate binary encoding of microcontroller instruction sets and design the corresponding instruction decoder logic. The proposed CPOG synthesis technique solves the optimisation problem for the general case, reducing it to Boolean satisfiability problem and uses existing SAT solving tools to obtain the result.This work was supported by a studentship from Newcastle University EECE school, EPSRC grant EP/G037809/1 (VERDAD) and EPSRC grant EP/K001698/1 (UNCOVER). i

Time dependent decomposition of ammonia borane for the controlled production of 2D hexagonal boron nitride.

Ammonia borane (AB) is among the most promising precursors for the large-scale synthesis of hexagonal boron nitride (h-BN) by chemical vapour deposition (CVD). Its non-toxic and non-flammable properties make AB particularly attractive for industry. AB decomposition under CVD conditions, however, is complex and hence has hindered tailored h-BN production and its exploitation. To overcome this challenge, we report in-depth decomposition studies of AB under industrially safe growth conditions. In situ mass spectrometry revealed a time and temperature-dependent release of a plethora of NxBy-containing species and, as a result, significant changes of the N:B ratio during h-BN synthesis. Such fluctuations strongly influence the formation and morphology of 2D h-BN. By means of in situ gas monitoring and regulating the precursor temperature over time we achieve uniform release of volatile chemical species over many hours for the first time, paving the way towards the controlled, industrially viable production of h-BN

Dynamic task fusion for a block-structured finite volume solver over a dynamically adaptive mesh with local time stepping

Load balancing of generic wave equation solvers over dynamically adaptive meshes with local time stepping is dicult, as the load changes with every time step. Task-based programming promises to mitigate the load balancing problem. We study a Finite Volume code over dynamically adaptive block-structured meshes for two astrophysics simulations, where the patches (blocks) dene tasks. They are classied into urgent and low priority tasks. Urgent tasks are algorithmically latencysensitive. They are processed directly as part of our bulk-synchronous mesh traversals. Non-urgent tasks are held back in an additional task queue on top of the task runtime system. If they lack global side-eects, i.e. do not alter the global solver state, we can generate optimised compute kernels for these tasks. Furthermore, we propose to use the additional queue to merge tasks without side-eects into task assemblies, and to balance out imbalanced bulk synchronous processing phases

Rough volatility and portfolio optimisation under small transaction costs

The first chapter of the thesis presents the study of the linear-quadratic ergodic control problem of fractional Brownian motion. Ergodic control problems arise naturally in the context of small cost asymptotic expansion of utility maximisation problems with frictions. The optimal solution to the ergodic control problem is derived through the use of an infinite dimensional Markovian representation of fractional Brownian motion as a superposition of Ornstein-Uhlenbeck processes. This solution then allows to compute explicit formulas for the minimised objective value through the variance of the stationary distribution of the Ornstein-Uhlenbeck processes. Building on the first chapter, the second chapter of the thesis presents the main result. This is motivated by the problem an agent faces when trying to minimise her utility loss in the presence of quadratic trading costs in a rough volatility model. Minimising the utility loss amounts to studying a tracking problem of a target that depends on the rough volatility process. This tracking problem is minimised at leading order by an asymptotically optimal strategy that is closely linked to the ergodic control problem of fractional Brownian motion. This asymptotically optimal strategy is explicitly derived. Moreover, the leading order of the small cost expansion is shown to depend only on the roughest part of the considered target. It therefore depends on the Hurst parameter. The third chapter is devoted to a numerical analysis of the utility loss studied in the second chapter. For this, we compare the utility loss in a rough volatility model to a semimartingale stochastic volatility model. The parameter values for both models are fitted to match frictionless utility for realistic values. By applying the result obtained in the second chapter of the thesis, the difference between leading order of utility loss can be explicitly compared

Large-Scale Production and Use of Biomethane

Societal ambitions to create an economy based on renewable resources, require the development of technologies transforming these resources into energy-carrying products and biomaterials. Dual fluidized bed (DFB) gasification represents a key technology for achieving sustainability targets, as it is a scalable and highly efficient route for the conversion of biomass. The development of DFB technology has led to the construction of the GoBiGas (Gothenburg-Biomass-Gasification) demonstration plant, in 2014. The GoBiGas plant is a world-first advancement for large-scale production of biofuels as it represents a substantial scaling up of the gasification technology combined with downstream biomethane synthesis. However, to ensure the desired breakthrough of biomass-based products, it is necessary to improve the profitability of gasification plants, through increasing their size, efficiency and identifying opportunities with high economic feasibility for the transport, energy, and chemical sectors.This thesis presents an exploration of potential improvements for the up-scaling of the biomethane process to a commercial scale. The work summarises and places in context the experience acquired in the research groups at Chalmers and G\uf6teborg Energi AB, including the experience gained from the dedicated experiments in the Chalmers Gasifier and during the commissioning phase of the GoBiGas plant. A method for analysis of the experimental data is introduced, with the goal of improving the quality of the simulations of large-scale gasification processes. The method is applied to the evaluation of the DFB gasifier at the GoBiGas plant, which is presented in the thesis and used as references for further investigations. Some of the measures investigated to increase the profitability of a large-scale plant were proposed in this work, including: an advanced biomass steam dryer integrated with the gasifier, power-to-gas conversion via direct heating of the DFB gasifier and co-production of biomethane with intermediate products for other chemical industries. Furthermore, the utilization of biomethane as fuel for heavy duty vehicles was evaluated within a project in collaboration with Volvo AB. The well-to-wheel approach was applied to calculate the emissions related to three state-of-the-technologies: spark-ignited, dual fuel and high-pressure direct injection.The evaluation of the DFB gasifier at GoBiGas has shown high fuel conversion, with char gasification of ~54%, and the fraction of the volatiles converted to methane of ~34%mass. The cold gas efficiency for GoBiGas was calculate in 71.7%LHVdaf using dried biomass (8% moist). The simulation of the DFB gasifier in a large-scale optimised process showed a cold gas efficiency up to ~85%LHVdaf using fresh biomass (40% moist) and an advanced drying systems. The chemical efficiency of such a plant was calculated in ~72% LHVdaf, which is more than 20pp higher than the current GoBiGas design. Owning to the efficient conversion of the biomass in the gasifier, the co-production of biomethane and other intermediate chemicals represents a feasible opportunity to increase the profitability of the plant. The chemical efficiency of such processes was estimated between 72% and 85% therefore, there is no substantial advantage to produce biomethane, unless biomethane is the desired end-product. \ua0As fuel for heavy-duty vehicles, biomethane reduces the emissions compared to diesel by 30 - 41 gCO2e per MJbiomass, with the biomethane produced at the GoBiGas plant. The emission saving can be increased to 43 - 54 gCO2esaved/MJbiomass if biomethane is produced at large scale. \ua0Following the demonstration at a commercial scale, biomethane is established as a biofuel with a high environmental impact, although the gap between the current status and its potential application is highlighted

Large-Scale Production and Use of Biomethane

Societal ambitions to create an economy based on renewable resources, require the development of technologies transforming these resources into energy-carrying products and biomaterials. Dual fluidized bed (DFB) gasification represents a key technology for achieving sustainability targets, as it is a scalable and highly efficient route for the conversion of biomass. The development of DFB technology has led to the construction of the GoBiGas (Gothenburg-Biomass-Gasification) demonstration plant, in 2014. The GoBiGas plant is a world-first advancement for large-scale production of biofuels as it represents a substantial scaling up of the gasification technology combined with downstream biomethane synthesis. However, to ensure the desired breakthrough of biomass-based products, it is necessary to improve the profitability of gasification plants, through increasing their size, efficiency and identifying opportunities with high economic feasibility for the transport, energy, and chemical sectors.This thesis presents an exploration of potential improvements for the up-scaling of the biomethane process to a commercial scale. The work summarises and places in context the experience acquired in the research groups at Chalmers and G\uf6teborg Energi AB, including the experience gained from the dedicated experiments in the Chalmers Gasifier and during the commissioning phase of the GoBiGas plant. A method for analysis of the experimental data is introduced, with the goal of improving the quality of the simulations of large-scale gasification processes. The method is applied to the evaluation of the DFB gasifier at the GoBiGas plant, which is presented in the thesis and used as references for further investigations. Some of the measures investigated to increase the profitability of a large-scale plant were proposed in this work, including: an advanced biomass steam dryer integrated with the gasifier, power-to-gas conversion via direct heating of the DFB gasifier and co-production of biomethane with intermediate products for other chemical industries. Furthermore, the utilization of biomethane as fuel for heavy duty vehicles was evaluated within a project in collaboration with Volvo AB. The well-to-wheel approach was applied to calculate the emissions related to three state-of-the-technologies: spark-ignited, dual fuel and high-pressure direct injection.The evaluation of the DFB gasifier at GoBiGas has shown high fuel conversion, with char gasification of ~54%, and the fraction of the volatiles converted to methane of ~34%mass. The cold gas efficiency for GoBiGas was calculate in 71.7%LHVdaf using dried biomass (8% moist). The simulation of the DFB gasifier in a large-scale optimised process showed a cold gas efficiency up to ~85%LHVdaf using fresh biomass (40% moist) and an advanced drying systems. The chemical efficiency of such a plant was calculated in ~72% LHVdaf, which is more than 20pp higher than the current GoBiGas design. Owning to the efficient conversion of the biomass in the gasifier, the co-production of biomethane and other intermediate chemicals represents a feasible opportunity to increase the profitability of the plant. The chemical efficiency of such processes was estimated between 72% and 85% therefore, there is no substantial advantage to produce biomethane, unless biomethane is the desired end-product. \ua0As fuel for heavy-duty vehicles, biomethane reduces the emissions compared to diesel by 30 - 41 gCO2e per MJbiomass, with the biomethane produced at the GoBiGas plant. The emission saving can be increased to 43 - 54 gCO2esaved/MJbiomass if biomethane is produced at large scale. \ua0Following the demonstration at a commercial scale, biomethane is established as a biofuel with a high environmental impact, although the gap between the current status and its potential application is highlighted

Techno-economic evaluation of battery storage systems in industry

In the context of a changing energy system towards one dominated by renewable energy sources, the demand for flexible energy generation and consumption will increase. Battery storage systems can provide a significant share of this energy flexibility, especially when combined with an industrial manufacturing plant to shift the industrial electricity demand over time. This paper contributes to a better understanding of the business decision when investing in a battery storage system and when marketing energy flexibility. For this purpose, the work considers the techno-economic and regulatory framework for flexibility measures and examines the optimal investment and dispatch planning for a battery storage system in an industrial company. The studies in this thesis focus on three central aspects. As a first aspect, the various revenue streams for the stored electricity are analysed and how these influence the profitability of a battery storage system. In particular, the provision of frequency containment reserve power, peak load shifting or peak shaving, arbitrage trading on the energy markets and the increase in self-consumption through photovoltaic self-generation are addressed. For this purpose, an optimisation model is formulated as a discrete, linear programme that maps the economic framework of the flexibility markets and integrates the technological constraints of the battery storage system. As a second aspect, uncertainties about market prices, load and generation behaviour are integrated into the optimisation model and the influence on the investment decision is investigated. This is done on the one hand by a two-stage robust optimisation model, which represents the uncertainty about the market success on the intraday market. On the other hand, the significance of the sequence of uncertain market decisions is illuminated through a multi-stage stochastic optimisation model. As a third aspect, the trade-off between the economic and ecological use of a battery storage system is analysed. For this purpose, an ecological, CO₂-minimal dispatch is calculated by deriving national CO₂-emission factors and compared with an economically optimal dispatch. The case studies are analysed based on real industrial load data from small, medium and large enterprises. The thesis discusses the technical and economic framework conditions, with the main focus on Germany. However, a comparison between the countries Germany, Denmark, and Croatia is also presented. The results show that peak shaving and the provision of frequency containment reserve are complementary and make the investment in a battery storage system economically viable. Self-generation through a photovoltaic system can reduce the risk arising from uncertain energy market prices. However, the sequence of uncertain decisions has a significant impact on the design of the battery storage system. Economically feasible operation through arbitrage trading, on the other hand, is not possible due to the small price differences in the markets and limitations due to battery ageing and efficiency. These battery characteristics also influence the use of a battery storage system for CO₂-reduction. Due to the limited number of cycles and relatively high charging losses, battery technology is currently unsuitable for CO₂-minimal storage use. Nevertheless, the economic and ecological potential of battery storage systems strongly depends on individual factors such as local grid charges, the selected battery technology and the individual industrial load profile. Advances in battery technology, such as increased lifetime, and possible new flexibility markets, such as dynamic grid charges, offer new application and marketing opportunities that could increase the economic viability of a battery storage system

A Bayesian approach to single-particle electron cryo-tomography in RELION-4.0

We present a new approach for macromolecular structure determination from multiple particles in electron cryo-tomography (cryo-ET) data sets. Whereas existing subtomogram averaging approaches are based on 3D data models, we propose to optimise a regularised likelihood target that approximates a function of the 2D experimental images. In addition, analogous to Bayesian polishing and contrast transfer function (CTF) refinement in single-particle analysis, we describe the approaches that exploit the increased signal-to-noise ratio in the averaged structure to optimise tilt-series alignments, beam-induced motions of the particles throughout the tilt-series acquisition, defoci of the individual particles, as well as higher-order optical aberrations of the microscope. Implementation of our approaches in the open-source software package RELION aims to facilitate their general use, particularly for those researchers who are already familiar with its single-particle analysis tools. We illustrate for three applications that our approaches allow structure determination from cryo-ET data to resolutions sufficient for de novo atomic modelling.This work was funded by the UK Research and Innovation (UKRI) Medical Research Council (MC_UP_A025_1013 to SHWS; and MC_UP_1201/16 to JAGB), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC-CoG-2014, grant 648432, MEMBRANEFUSION to JAGB and ERC StG-2019, grant 852915 CRYTOCOP to GZ); the Swiss National Science Foundation (grant 205321_179041/1 to DC-D), the Max Planck Society (to JAGB) and the UKRI Biotechnology and Biological Sciences Research Council (grant BB/T002670/1 to GZ). TAMB is a recipient of a Sir Henry Dale Fellowship, jointly funded by the Wellcome Trust and the Royal Society (202231/Z/16/Z). JZ was partially funded by the European Union’s Horizon 2020 research and innovation program (ERC-ADG-2015, grant 692726, GlobalBioIm to Michael Unser)