Building correct communicating systems (i.e. concurrent and distributed systems) is a hard task. Such systems often present non-deterministic behaviours that are hard to reproduce. This means that, whenever there is a bug in one of such systems, fixing it is a time consuming and costly task. Furthermore, distributed systems are nowadays widespread in our society, including key sectors such as banking or E-healthcare. Thus, bugs in communicating systems can be very damaging, threatening large economic costs, and the safety and security of the industries that rely on them. To guarantee the correctness of communicating systems, many tools and theories have been developed. Session types are among the most influential theories for verifying the absence of concurrency bugs in communicating systems. Session types can guarantee that process implementations only follow the specified structured sequence of actions (send/receive). These specifications effectively represent communication protocols, and session type theories provide techniques to verify that they are absent of concurrency bugs. Among the most influential extensions of session types is the theory of Multiparty Session Types (MPST), which enables the modelling of protocols among an arbitrary number of participants, and has been integrated with many mainstream languages. However, most of the tools based on session types are not following the exact theories that are presented in the scientific publications, since they also need to take into account engineering issues. Furthermore, most of the session type theories are proven correct using complex pen-and-paper soundness proofs. Such proofs can contain errors, and the literature shows examples of these cases. This is a big threat to the validity of large bodies of work. Proof assistants are tools that can guarantee the correctness of these soundness arguments. Encoding languages, tools, and theories in a proof assistant is called mechanisation, and it has led to large influential developments in computer science, such as CompCert, a certified C compiler that has proven to present significantly less bugs than other comparable compilers, and that is currently being used in the context of critical systems. But proof mechanisation is significantly hard, and not much work exists on mechanising MPST. One of the main hurdles in mechanising MPST is the notion of process equivalence, or bisimilarity. Informally, two processes are bisimilar if they match each others actions, according to their Labelled-state Transition System (LTS) semantics. One main techniques for proving bisimilarity is known as the bisimulation proof method, which relies on finding a relation between two processes that guarantees that they will match each other's moves according to their LTS. These proofs are widespread in concurrency theory, and are key to successful mechanisations of MPST. We need a way to simplify the mechanisation of LTS semantics, and bisimilarity proofs. We will study common bisimulation proof techniques and algorithms, and find and implement a suitable candidate for mechanisation. Our main goal is to automate as much as possible of the mechanisation of the LTS semantics. One of the key challenges is to find the suitable definitions: pen-and-paper proofs can often overlook details that are important in a mechanisation. For example, termination is often informally justified in pen-and-paper proofs, but the specific details are key to a successful mechanisation. We will mechanise a generic framework for LTS semantics and bisimilarity in the Coq proof assistant, and use it in two case studies from the project partners. These case studies will serve both as a way to evaluate success, and as main driving elements of this project. Finally, we will study the extraction of certified implementations within our framework, thus contributing to increase the safety and reliability of distributed systems.

Our understanding of the Earth's core, its formation and the geodynamo on geological timescales is derived from palaeomagnetic studies. Similarly, palaeomagnetic data plays a key role in the fields of palaeogeography, palaeoclimatology, tectonics, volcanology and many other geological areas. These studies rely on the ability of a rock's constituent magnetic minerals to record a meaningful and decipherable magnetic remanence. To reliably interpret palaeomagnetic data we need to understand the mechanisms that induce magnetic remanence and can subsequently alter it. Whilst some mechanisms, e.g., thermoremanent magnetisation (TRM) acquisition, are well understood, there is a broad class of remanence acquiring or altering mechanisms termed chemical (or crystallisation) remanent magnetisation (CRM) or chemical alteration, that are poorly understand yet are frequent in nature and so commonly contribute to palaeomagnetic observations. CRM refers to any process that physically or chemically alters the magnetic minerals of a rock. It can take many forms, for example: (1) it can be a remanence induced and retained in magnetic grains as they grow at ambient temperature, i.e. a growth CRM, or (2) it can be the resultant change in a mineral's magnetic remanence as it chemically alters through oxidation or reduction, where the new phase can be either magnetically stronger or weaker. The problem is further complicated in that it is often difficult to distinguish between say a TRM and CRM, yet the origin and interpretation of the two remanence signals is completely different. For example, if the ancient geomagnetic field intensity (palaeointensity) is a growth CRM yet wrongly assumed to be a TRM in origin, this will lead to an over-estimate of the ancient geomagnetic field strength. Theoretical treatment of CRM and chemical alteration has been limited due to the broadness and complexity of the problem, and the difficulty in quantifying these processes experimentally. Theoretical models only exist for the smallest magnetic grains, termed single domain (SD) as their magnetisation is uniform. Larger grains have complex domain patterns and are termed multidomain (MD); small MD grains just above the SD threshold size tend display some SD characteristics and are termed pseudo-SD (PSD). Such PSD grains tend to dominate the signal of rocks, yet no rigorous theoretical understanding exists for PSD CRM. The aim of this proposal is to apply state-of-the-art experimental and numerical techniques to the understanding and quantification of the CRM and chemical alteration processes in SD and PSD samples. We will employ the latest advanced transmission electron microscopy (TEM) techniques including electron holography that allows us to image magnetisation on atomic scales in real-time as the minerals alter under controlled oxidising/reducing atmospheres. To link the TEM images to the bulk magnetic properties we will use our recently developed multiphase micromagnetic models, allowing us to relate nanometre sized chemical changes to the magnetic mineralogy to the measured bulk magnetic properties. We will quantify how different types of chemical alteration affect both palaeo-directional and palaeointensity information. In particular we will examine experimentally and numerically: (1) grain growth/dissolution and (2) low-temperature oxidation, e.g., the oxidation of titanomagnetite to titanomaghemite at temperatures < 150 C.

Metals are essential in our daily lives and have a finite supply. For example, smartphones are pocket-sized vaults of critical metals, as they contain several rare earth elements (REE) that produce the colours in the liquid crystal display, and others give the screen its glow. The magnets in the speaker, microphone and vibration units also contain REE. The current CO2 emissions and environmental impact of mining those metals are untenable. The supply chain of these metals is also dependent on geopolitical conditions, and currently, China is the world's largest producer. To decrease our reliance on critical metal mining, we need new efficient, low-cost, low-energy and environmentally friendly solutions to recover metals from waste. This project will start a new collaboration between UK and Denmark, joining teams that complement each other in their expertise. Exchange visits and a workshop will facilitate this collaborative research that aims to develop an environmentally friendly method to recover critical metals from wastes. We will be using metal-tolerant bacteria isolated from different environments and exploiting their capability to solubilise metals in a reactor with a low-level electric current. This new approach will combine two different technologies - bioleaching and electrodialysis. Bioleaching uses acid-producing bacteria to solubilise metals from various ores and wastes. However, the process can be very slow, and further separation processes are needed, so it will be combined with electrodialysis. Electrodialysis uses a low-level electric current to transport ions through a membrane. The metals that bacteria solubilise from waste can be transported and separated by the electric current and more easily recovered. This project will demonstrate how we can combine these technologies, providing a direct route for scaling up and applying to different wastes, contributing to more efficient and sustainable resource use, recovering value from waste and minimising pollution.

Denmark

For centuries people have used magnetic compasses to guide them on their way and explore new territories. This has led scientists to embark on their own journeys of discovery about Earth's magnetism, and to the discovery of electromagnetism that is at the heart of modern technology - phones, TVs, computers, etc. Now, in the age of GPS, you might think that compasses are obsolete, but guidance by the Earth's magnetic field is still vital to explore for oil and minerals below ground (where GPS can't reach) and as a safety backup for planes etc. And ironically, GPS is affected by natural hazards caused by the Earth's magnetic field. So the scientific study of Earth's magnetism continues to be important in many ways, so much so that in 2012 the European Space Agency will launch a mission called Swarm in which three satellites will orbit the Earth to survey its magnetic field in unprecedented detail. These measurements will be used to improve mathematical models of the geomagnetic field that provide a standard reference for various applications. One target area is a better understanding and description of the relatively rapid and complex magnetic fluctuations caused by electrical currents flowing in the upper atmosphere and in Space, ultimately driven by disturbances happening on the Sun that wax and wane with an 11-year solar cycle. This so-called external magnetic field also induces currents to flow in oceans and under the Earth's surface which in turn creates additional magnetic fluctuations. Together, the external and induced magnetic field (EIMF) limits the accuracy of geomagnetic field models such that they aren't useful for surveys and navigation at places and times when the EIMF fluctuations are large, such as in the polar regions and during so-called magnetic storms that may happen once a month and last several days. The EIMF also creates a natural hazard for large-scale electrically conducting systems such as power outages in electricity grids, corrosion in oil pipelines, and even phantom railway signals. In this project we will study the EIMF using a solar cycle's worth of measurements made at over 300 different locations around the world, recently collected together for the first time by an international project called SuperMAG. Our idea is to borrow mathematical techniques usually used by meteorologists for studying the weather and climate to identify the natural cycles and patterns of the EIMF. In conjunction with the Swarm mission, the resulting new descriptions and understanding of the EIMF "weather" and "climate" should help to improve the next generation of computer models of Earth's magnetic field. It can also be used to as a basis to assess and predict the risk of power outages in UK's National Grid caused by extreme EIMF fluctuations.