Electronic consumer goods and internet-enabled smart infrastructures require highly integrated miniature electronic systems. One of the main problem with this miniaturisation is that unwanted interactions can arise between different components. Depending on the rate of change of currents within electronic components, these components radiate electromagnetic (EM) waves which can couple into other parts of the structure and can cause interferences. Controlling electromagnetic interferences within electronic devices is becoming an increasingly important challenge. Digital clock speeds are relentlessly increasing already exceeding 10 GHz in high-performance systems and expected to reach 20 GHz by 2020. This is within range of highly sensitive radio frequencies where analogue blocks and chip-sized components become efficient radiators and receivers. In addition, increasing circuit density and decreasing voltage supplies will result in decreased immunity levels. Future design processes of integrated electronic systems will therefore have to include a much more detailed electromagnetic compatibility (EMC) characterisation than is done at present. Carrying out EMC studies for complex multi-signal components within a device in a fast and efficient way will simplify design decisions in industry enormously and will help to bring down costs. The challenges of delivering fast and reliable EMC modelling tools at high frequencies are enormous; determining EM fields in a complex multi-source environment and in the GHz range including multiple-reflections, diffraction and interferences is a hard task already. For realistic electronic devices, the underlying source fields depend in addition on the (a-priori unknown) mode of operation and are thus aperiodic and time dependent; they act in many ways like stochastic, uncorrelated input signals. Indeed, no EMC methodology for modelling transient signals inside and outside of electronic devices originating from decorrelated, noisy sources exists today. This proposal sets out to meet this challenge head-on by developing an efficient numerical method and accompanying measurement techniques for the modelling of radiated transient EM fields inside and outside of multifunction electronic devices. The new numerical method is based on ideas from wave chaos theory using Wigner-Weyl transformation and phase-space propagation techniques. It makes use of the connections between wave correlation functions and phase space densities. Methods for efficiently propagating these densities have been developed recently by members of the project team. In this way, we can work directly in terms of statistical measures such as averages and field correlation functions appropriate for stochastic fields. This innovative approach demands input data from measurements which require a rethink of standard measurement techniques. In particular, correlated two-probe near-field measurements of electronic components become necessary which will be developed and tested as part of the project. The proposed way of approaching EMC issues is completely new and becomes possible only due to the unique mix of expertise available at the University of Nottingham both from the Mathematical Sciences and the Electrical Engineering side Support provided by two industrial partners, inuTech and Computer Simulation Technology (CST), will be vital throughout. This fresh way of thinking will provide the necessary leap within EMC research to satisfy the demands of the electronics industry; it will enhance the applicability of existing EMC protocols and provide the tools to meet the challenges of the future.

Predicting the response of a large, complex mechanical system such as a car or an aeroplane to high frequency vibrations is a remarkably difficult task. Still, obtaining good estimates for the distribution of vibrational energy in such structures, including coupling between sub-components, damping and energy loss in form of acoustic radiation, is of great importance to engineers. An increasing demand for low vibration, low noise products to meet performance specifications and to reduce noise pollution makes any improvement in predicting vibrations response characteristics of immediate interest for industrial applications. Demand for improved virtual prototyping, as opposed to the use of expensive and time-consuming physical prototypes, is another area of application in reducing development costs and time scales. Numerical tools are often based on 'Finite Element Analysis' (FEM). While these methods work well in the low frequency regime, that is, tackling wavelengths of the order of the size of the system, they become too expensive computationally in the mid-to-high frequency regime. In particular, FEM fails to describe accurately so-called mid-frequency problems where sub-components are characterized by a wide variation of wave-lengths. While FEM is suitable for handling 'stiff' elements such as the body frame in a car, it cannot routinely capture energy transport through 'soft' components such as thin, flexible plates coupled to stiff components. A common numerical tool for predicting the vibrational contribution of short wave length components is Statistical Energy Analysis (SEA); it is, however, based on a set of restrictive assumptions which, so far, are often hard to control and generally only fulfilled in the high frequency limit and for low damping. Thus, SEA can not deliver the degree of reliability necessary to make it attractive for a wider end user community in industrial R & D departments. It is suggested here that mathematical tools from wave or quantum chaos can considerably improve the situation sketched above. Recent results by the PI Tanner show that by combining methods ranging from operator theory, dynamical systems theory and small wavelength asymptotics, SEA can be embedded into a more general theory. The new approach is based on semiclassical expansions of the full Green function in terms of rays and describing the nonlinear ray-dynamics in terms of linear operators. The resulting method captures the full correlations in the ray dynamics and has such a much improved range of validity compared to SEA. The method could revolutionise the treatment of vibrations in complex mechanical systems. Not only does it allow (i) to give quantitative bounds for the applicability of SEA (of interest to SEA users); it will also (ii) improve predictive capability in situation where SEA does not apply at a moderate computational overhead; in addition, (iii) it can be easily combined with FEM methods thus making it an ideal candidate for tackling mid-frequency problems. The approximations made are well controlled by starting from a semiclassical approach which makes it possible (iv) to systematically incorporate wave interference effects (absent in standard SEA treatments) into the method.By tackling the issues addressed above we will be able to provide improved and conceptually completely new solution methods to the engineering community based on advanced mathematical methods. The proposed research evolved out of pump-prime EPSRC funding in terms of a Springboard Fellowship. The project is thus by default of interdisciplinary nature and will be tackled jointly by the PI Tanner (Nottingham, Mathematics) and PI Mace (Southampton, ISVR, Engineering) with industrial partners from the FEM/software side (inuTech) and an engineering consulting firm (DS2L) providing input about end-user demands.

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This project will deliver new computational modelling tools that will allow engineers working onsafety critical structures to rationally assess the effects of crack initiation and crack propagation. Suchproblems have to date remained intractable. The research will permit unprecedented understanding of crackpropagation, thereby delivering less conservative designs, and, most importantly avoid unpredictedcatastrophic failures in service. This is possible by building upon the recent success of the extended finite elementmethod (XFEM), which has emerged as a revolutionary simulation tool for modelling discontinuities and has the potential to require an order of magnitude less engineering time than conventional methods.Yet, this new method requires much reliability improvements to invade industry. By leveraging recent theoreticaland numerical developments and working hand-in-hand with future users, this project has the potential toprovide XFEM with the accuracy and robustness it requires to become the new tool of choice for structuralintegrity predictions and reconcile accuracy and computational tractability.Cracks or defects are almost always present in engineering structures. In aerospace engineering for instance, during the life of the aircraft (take offs, flights and landings), these cracks will grow under the influence of the forces applied to the structure. How do engineers ensure that, despite these growing cracks, the aircraft can still be operated safely? The idea is to regularly inspect the aircraft to monitor the major cracks. The next question is to know how often should an aircraft be inspected to prevent catastrophic failure between two inspections. To answer this question, engineers must be able to evaluate the time (number of flights) it takes for the cracks to become fatal to the structure. If it takes 1,000 flights, the maximum inspection interval should be less than 1,000. To estimate the time to failure, engineers use computer methods, where they model the behaviour of the structure using various simplifications: this is known as Damage Tolerance Analysis (DTA).However, today, existing software are still unable to provide engineers with a rational tool to assess the tolerance of a structure to damage. The proposed research has the long-term goal to provide this tool which could provide a paradigm shift in the way engineers think about simulating fracture, whereby sufficient accuracy would not be synonymous with intractable computational time or manpower.