Abstract We consider a version of Gamow’s liquid drop model with a short range attractive perimeter-penalizing potential and a long-range Coulomb interaction of a uniformly charged mass in three space dimensions. Here we constrain ourselves to minimizing among the class of shapes that are columnar, i.e., constant in one spatial direction. Using the standard perimeter in the energy would lead to non-existence for any prescribed cross-sectional area due to the infinite mass in the constant spatial direction. In order to overcome this issue we use a connected perimeter instead. We prove existence of minimizers for this connected isoperimetric problem with long-range interaction and study the shapes of minimizers in the small and large cross section regimes. For an intermediate regime we use an Ohta–Kawasaki phase field model with connectedness constraint to study the shapes of minimizers numerically. Joint work with Matteo Novaga (Pisa), Steve Wolff-Vorbeck (Freiburg), and Stephan Wojtowytsch (College Station).
Abstract The study of ferromagnetic materials has wide applications not only in theoretical physics but also in engineering and in the development of new technological devices. Due to the different magnetization orientations inside the material, magnetic domain walls (diffuse interfaces between different almost constant magnetization states) appear and evolve in time. The study of this boundary is crucial to understand how this interface evolves and its properties. In this short talk I will discuss the connection between the mean curvature flow and the evolution of this boundary. Using some simplification, it is possible to find heuristically the PDE which governs the evolution of this interface which is related to the mean curvature flow. Then I will show briefly how this interface changes using tecniques related to the viscosity solution theory. This work is done in collaboration of V. Slastikov and G. Di Fratta.
Abstract Tsunamis have a long history of devastation, causing more than 250,000 deaths worldwide during the last two decades. Current warning systems rely on DART-buoys and seismic measurements. DART-buoys measure a tsunami directly once it arrives, which may leave no warning time, whereas seismometers provide a measure on earthquakes but not tsunamis, causing false alarms. Reducing false alarms has been emphasised in recent UNESCO tsunami expert meetings. To this end, we have developed a complementary real-time early tsunami warning system methodology. The methodology is based on analysing acoustic signals under the effects of gravity, known as acoustic-gravity waves (AGWs), that are generated together with the tsunami. The signals travel at the speed of sound in the medium which far exceeds the maximum phase speed of the tsunami. AGWs carry information about the source which is recorded by remote hydrophones (underwater microphones). Analysing these recordings in real-time, requires solving both the inverse and direct problems, which are the main strength behind the proposed warning methodology. In addition, we use machine learning to classify the type of earthquake: horizontal vs vertical. The latter is a necessary condition for the generation of tsunamis. In this talk we shall discuss various acoustic-gravity wave theories and applications, both fundamental and applied, with a particular focus on real-time early tsunami warning. The direct and inverse problem models derived from the linear wave equation will be briefly presented. In addition, the nonlinear resonant triad interaction of acoustic-gravity waves will be discussed and its potential for describing non-point-source tsunamis will be highlighted, focusing on the recent global Tonga tsunami.
Abstract Calcium signaling is an important regulatory mechanism in most body functions, featuring diverse temporal and spatial scales and it is, thus, of great interest to modellers, experimentalists and to the pharmaceutical industry. Several experiments with fertilizing eggs and for later embryogenesis have shown intracellular and intercellular calcium oscillations and waves and that these are coupled to mechanical motions and waves. How these waves are formed and propagate is still largely unknown. I will relay the models we have been developing for two of these biological challenges and the interesting oscillations and waves they yield. Collaboration: Fertilization – T.E. Woolley, K. Swann (Cardiff); Embryogenesis – A. Chakraborty, T.N. Phillips (Cardiff), P. Maini, R. Baker (Oxford), N. Christodoulou, P. Skourides (U. Cyprus).
Abstract Remote sensing currently sits in the heart of many applications studying various environmental problems, such as marine pollution, land use and cover mapping, animal behaviour analysis, air pollution. When it comes to exploiting highly rich remote sensing information, computational imaging approaches play a crucial role to develop important approaches to present solutions for environmental problems. As in everywhere in the real-life scenarios, generally the information is not following a linear characteristic, or simple linear computational imaging approaches fails to proceed successfully. In this talk, we discuss the effect of nonlinearity in remote sensing environmental imaging and support this discussion with various examples from the remote sensing computational imaging area.
Abstract Chemical processes develop over several stages, visiting more or less activated intermediates. The use of molecular dynamics simulations is in principle the perfect choice as configurations are states are already weighted by their probability. However, in the presence of high activation energies, simulations can be fundamentally incomplete, as entire regions of phase space may end up unexplored. The use of advanced molecular dynamics protocols has provided substantial boost to molecular simulations, as well as the possibility not only to learn potential energy surfaces via machine learning, but to focus on distributions rather then reaction mechanisms in the first place.
Abstract High frequency transmitters are key in many aspects of modern technology, from telecom to security; from healthcare to autonomous cars. This talk will show how their non-linear response is essential to achieve high energy efficiency, but also how it leads to issues in terms of signal fidelity and complexity of the systems. A deeper look will be given to the main research challenges that our research group, the Centre for High Frequency Engineering, is trying to solve in this context and how this could lead to collaborations with mathematicians for a paradigm change in the approach to the solutions.