Rare Events in Reaction-Diffusion Systems Field-theoretical Approximations and Monte Carlo Simulations

Rare events are events that have near-zero probability of occurring. Despite their apparent irrelevance, when they do occur, they can have substantial, and even catastrophic, repercussions. In this thesis, we study rare events in reaction-diffusion systems, a class of mathematical models that finds various applications in physics and life sciences. We employ both theoretical and computational methods to determine the tails of the probability distribution describing the state of system. Firstly, we follow existing literature to derive a quantum-mechanical description for entirely classical reaction-diffusion systems, called the Doi-Peliti formalism. We express the time evolution of the systems as a Feynman path integral, which we then evaluate at the saddle point to obtain a semiclassical approximation for the probability distribution, and a closed-form leading-order expression for the tails. Secondly, we tailor a lesser-known Monte Carlo algorithm for rare probability estimation, called adaptive multilevel splitting, to compute the probability distribution of reaction-diffusion processes. We derive some theoretical results regarding its efficiency, discuss practical implementation choices, and benchmark its performance against well-understood examples. Lastly, we compare the semiclassical approximation to the computational results, determining under which conditions the former succeeds or fails

AI-driven predictions of industrial metal prices on the London metal exchange

The battery manufacturer Northvolt aims to reduce inventory risks. In an increasingly competitive industrial metals market, protecting inventory value by employing hedging strategies is a key component of lowering costs. Using artificial intelligence for reliable predictions of short term prices is an interesting prospect for improving such strategies. This study uses data from the London Metal Exchange, including cash and threemonth futures contracts, along with stock volume, to predict next-day cash prices for six industrial metals. These predictions are compared to a baseline random walk model using the metrics mean squared error (MSE), mean absolute error (MAE), R2 , and directional accuracy. Predictions are made using an Echo State Network (ESN), with optimized parameters chosen by a Genetic Algorithm (GA). The network is trained offline with ridge regression and online with stochastic gradient descent. The performance of the ESNGA setup is validated using chaotic systems (Mackey-Glass and Lorenz equations) before being applied to metals futures data. The data is split into four different sets: a warmup set necessary for ESNs, a training set used for offline training, a validation set to measure GA performance, and a test set of unseen data to ensure the network generalizes well. The GA optimization significantly reduced prediction errors in the Mackey-Glass and Lorenz systems, with MSE values improving from 1.2E-8 to 5.3E-12 and from 3.3E-2 to 8.8E-7, respectively, on the validation set. For metals futures data, the GA enhanced ESN performance, outperforming the random walk across all metrics on the validation set for all six metals. However, slight modifications were necessary to achieve superior performance on the unseen test set. Superior results were achieved for four metals across all metrics, while the results for the remaining two metals were mixed. The GA effectively optimizes ESN parameters for systems with clear, deterministic dynamics but encounters challenges when applied to stochastic futures data, particularly due to the risk of overfitting the validation set. While the ESN-GA method does not consistently outperform the random walk on unseen test data, it demonstrates significant potential. Further exploration with alternative configurations, additional data types, and more robust validation techniques is warranted to enhance its practical applicability

Development and Implementation of test cells to perform DC and LI breakdown testing of materials used in HVDC cable accessories

Abstract The thesis work is to develop,build up and verify a test circuit for measurements of DC breakdown strength and LI testing. The work contains both practical and theoretical elements, focusing on optimizing the design of electrodes as well as the size and shape of samples and to determine the Optimal dielectric properties of the insulation test medium using COMSOL Multiphysics. The aim of the work is to develop methods and design test setups for measuring both DC breakdown strength and Lightning Impulse testing, as a function of electric fields. EPDM insulation and FGM are used in cable accessories considering EPDM rubber has low dielectric loss, making it ideal for high-voltage applications. FGM rubber can be produced by incorporating specific fillers and is designed to control and distribute electric fields within electrical insulation systems. Its main purpose is to prevent high electric field concentration, which can cause insulation breakdown and device failure.Rubber material is being tested using mechanical, chemical, and electrical methods. The dielectric test is one of the electrical testing methods used to determine the dielectric strength of rubber materials. Short-time and long-time tests are being carried out for dielectric testing. AC breakdown testing, DC breakdown testing, and LI breakdown testing on insulation EPDM and FGM samples are conducted using two different insulating liquids with variable permittivities to avoid surface flashover during a short test under international standards. Designing a test cell for a dielectric test with an applied voltage of up to 150kV. Design the test cell (CAD model) and choose the electric field simulation with COMSOL Multiphysics software. To enhance development, the molded electrode test setup has been designed to eliminate the influence of the surrounding medium and facilitate future endurance testing

Synthesis and Characterization of Simulated Corium Materials

One part, of the massive undertaking that is risk management and accident prevention regarding nuclear power, is the study of corium. Corium, being the resulting material created during a nuclear meltdown, is an amalgamation of molten nuclear fuel combined with anything and everything it comes into contact with. Corium is not only dangerous during a meltdown when it risks causing further damage to the reactor and surrounding equipment. Due to it’s high radioactivity, it stays dangerous for a significant amount of time after the accident as well. It is therefore important to study this material in order to better understand how to minimize any potential further damage, further contamination of surroundings and to find ways to safely carry out cleanup efforts. These studies however, are quite limited due to the hazardous nature of the corium. This project is therefore focused on exploring a way to safely synthesize small batches of low-activity corium, without requiring specialized equipment, to be used for smaller scale studies. This proof of conept was achieved by first synthesizing spent nuclear fuel consisting of UO2 in the form of 238 U, as a lower activity replacement of enriched uranium, doped with several inactive elements for the purpose of simulating fission products. This powdered SIMfuel was then ground together with a selection of materials commonly found on the inside of a nuclear reactor and then fired in a reducing atmosphere at temperatures up to 1750℃ to create a clump of material similar to corium. Analysis of this corium using powder-XRD and ICP-MS showed that the structure and properties of the synthesized corium varies significantly based on the composition and temperature it was created in. A leaching study was also carried out using the samples, but the results were inconclusive. The (justifiable) lack of real-world corium samples available for analysis means very little to compare these samples to, but this shows that a method of creating low activity samples it possible

Testing of Field Grading Materials For HVDC Cable Joints

Abstract HVDC cable systems are designed to transmit large amounts of electricity over long distances with minimal losses. Most failures in these systems happen because of issues with cable accessories like joints and terminations. They are caused by strong electric fields appearing in such components due to geometrical features of the designs and inhomogeneities in the structure of the insulation system incorporating various materials. To enhance the performance of cable accessories, electric field control in the insulation is crucial. To address this, so-called field grading materials (FGMs) can be used to even out the electric field distributions. Thanks to their non-linear properties, these materials secure normal operations of the cable system and also are capable of handling events like lightning overvoltage and switching impulses. This thesis focuses on exploring electrical and mechanical properties of FGMs by testing samples of materials with different types and concentration of fillers at various temperatures and electric field strength. The focus is on a comparative analysis, where the properties of EPDM (Ethylene Propylene Diene Monomer) are taken as a reference. New materials with good electrical and mechanical properties are selected based on specific criteria, followed by measurements of their non-linear conductivity. Experimental results show that three selected materials met the criteria for nonlinear conductivity. To further evaluate their performance as a base for building a large scale component, electrothermal simulations of a 525 kV DC cable joint made of those materials have been conducted for different voltage levels including nominal, type test and lightning impulse voltages. The simulation results show minimal differences in the field grading effects caused by the selected FGMs applied in different locations of the cable joint, likely because of similar non-linear behavior of their properties in the studied ranges of temperatures and electric stresses

Design of smart orthosis for rehabilitation of Achilles tendon ruptures

Abstract This thesis presents a compact system for measuring forces under the foot, designed for rehabilitation after an Achilles tendon rupture. The aim is that this system could provide patients and care providers with critical data about the recovery process, for a more personalized and effective treatment. The core component of this system is a newly developed flexible insole that senses forces under the foot. The force is measured in three dimensions (i.e., normal and shear forces) using magnetic-based sensors, placed in a grid of 73 nodes. The large area covered by the sensor, and the flexibility, are improvements over previous magnetic-based force measurement systems. The insole and additional support electronics were mounted on a standard ankle orthosis (also known as Walker). In addition, two IMUs were used to estimate the orientation of the insole. Software was also developed to process and visualize the data. The measurements from the insole are sent to a signal processing chain to calculate relevant biomechanics parameters such as the center of pressure and joint torques. The signal processing chain was implemented within ROS2, together with micro-ros for the low-level communication with hardware. ROS2 is also used for visualization purposes. The results are promising, showing that magnetic-based sensors are feasible for measuring 3D forces under the foot. The sensors display a nearly linear response to vertical pressure, although there is considerable hysteresis that introduces errors in the measurements. Future work to improve calibration, verify reliability, and improve ease of use is needed before the system can be used in a clinical setting

Privacy Risks in Text Masking Models for Anonymization

Large Language Models (LLMs) are increasingly employed to anonymize texts containing Personal Identifiable Information (PII), often relying on Named Entity Recognition (NER) to identify and remove sensitive data. This thesis explores the privacy risks associated with such text masking models by evaluating their vulnerability to Membership Inference Attacks (MIAs) and extraction attacks. MIAs are attempting to identify whether or not a data point was part of the training dataset, knowledge of the membership can in certain scenarios be a breach of privacy. Two state-of-theart MIAs have been used to conduct attacks on text masking models. This study also proposes a framework based on multi-armed bandits for performing extraction attacks and evaluates two different strategies within this framework. The results from the MIAs indicate that there is some risk of revealing information regarding the training data. The extraction attacks did not yield great results in terms of performance but indicate that the concept could possibly be useful if developed further

Evaluation of Neural-Network and Large-Language Model Approaches for Generating Instructions for Animations

Conversational agents are used more and more in customer service, health care, for educational purposes. The fundamental problems of conversational agents are many, including limitations in interpretation of complex queries and lack of emotional intelligence. Despite this, there are distinct advantages of conversational agents, such as efficient data analysis, reduction of operational costs and aid in interactive learning for personalized teaching. The most significant challenge this project aims to undertake is to generate realistic and complex animations in the context of interactive learning with a real-time constraint. The investigation includes how to select machine learning tools and models to aid in the advancement of animation generation, by using both Large-Language Models and purposely constructed Neural Networks. While Large-Language Models are convenient when used in straightforward conditions, Neural Networks are more dependable in an operative application thanks to their consistent format, adaptability and specifically developed purpose

Electrical machine initial design and computational tool

Electric and hybrid electric vehicles widely use Interior Permanent Magnet Synchronous Machines (IPMSM) due to their high torque and power densities. The initial design phase of these electrical machines are critical as they affect the performance, efficiency and costeffectiveness. This thesis explores the development and application of a Python-based computational tool for the initial design of IPMSMs, aiming to achieve optimal machine performance while reducing dependency on iterative Finite Element Method (FEM) solutions. The scope of the research was to develop a robust framework that bridges theoretical design principles with practical computational methods, aiding innovation in electrical machine engineering. An analytical approach was adopted for the preliminary design, focusing on the relationship between machine sizing and performance parameters. Preliminary designs were derived using geometrical constraints and mathematical equations. These designs were validated through Magnetic Equivalent Circuit (MEC) models and sensitivity analysis, with results further corroborated by FEM simulations. The study is centered on two case studies: a MotorCAD template and a journal model. The Python tool demonstrated high accuracy, with sizing parameters closely matching those from MotorCAD and the journal model. Sensitivity analysis was conducted to evaluate the impact of variations in air-gap thickness, magnet width, pole-arc to pole-pitch ratio, and magnet strength on machine performance. The results showcased consistent trends between the Python tool and MotorCAD, emphasizing the tool’s reliability and robustness. The computational tool made it computationally efficient by enabling rapid prototyping and reduced iteration time. This work highlights how the tool can efficiently and accurately design IPMSM, providing a solid foundation for future advancements in electrical machine engineering

Numerical Methods for mapping band-type resonance in insect flight

Insect flight is a highly complex and energy-intensive process. Flapping-wing insects employ a unique muscle contraction mechanism that enables high-frequency wing beats, with metabolic rates reaching several times those at rest. Their remarkable endurance during flight highlights the importance of understanding the energy optimization involved. This thesis focuses on developing numerical methods to map band-type resonance, which serves as a benchmark for assessing whether a system achieves an energy-optimal state. We describe the mapping of band-type resonance as an optimization problem and propose two primary numerical methods: particle swarm optimization and numerical continuation. We evaluate the accuracy of the numerical solutions via the solution work loops and power waveforms and compare them with analytical approximations to the space of band-type resonant states. Our findings reveal that while the standalone particle swarm method can provide a relatively complete set of estimated solutions, the solution space lacks continuity. The numerical continuation method sacrifices some completeness in finding solution sets to ensure better continuity in the corresponding domain of the output solution set. After comparing these methods' performance in identifying potential solutions for simple cases, we improve them and propose a compound numerical method for solving more complex problems, such as higher harmonic and nonlinear oscillators. Notably, this compound algorithm performs well not only on simple linear cases with known analytical solutions but also on complex problems lacking analytical solutions, offering a valuable numerical tool for estimating the mapping zone of band-type resonance when analytical methods are not feasible. Comparing the results of mapping zones of band-type resonance with wingbeat frequency modulation behaviour observed in actual insect species suggests that such behaviour may be consistent with sustained resonant energy savings by exploiting band-type resonance. This report is written in English