There are three types of breakup: wavy sheet, perforation, and rim. In wavy sheet breakup, increasing viscosity or surface tension increases droplet size. To investigate further, we carry out direct numerical simulations of jet breakup, which show that suface tension has little effect, but increasing viscosity leads to fewer droplets. Decreasing the jet velocity also results in fewer droplets, with a wider size distribution.

Each type of breakup involves primary breakup into cylinders of fluid, then secondary breakup into droplets. We thus consider the breakup of a cylinder of fluid. Direct numerical simulations suggest that within the tested parameter range viscosity has little impact on droplet size, however it does influence the timescale on which the instability evolves considerably. Linear stability analysis suggests that increasing viscosity increases the wavelength of the most unstable mode, which we expect leads to larger droplets, and that it reduces the rate of breakup.

Perforations - holes in the sheet - also lead to breakup. We find how the length fraction of the sheet that is void changes with time.

After breakup, the droplets continue to evolve. We develop a model, based on a transport equation, for this process. A key parameter is the breakup rate constant - larger values lead to more breakup, fewer large droplets, and a narrower size distribution.

Together, these mathematical approaches improve our understanding of how droplets form, and can be used to guide experimental work.

The purpose of this study group was to investigate whether this tech- nique could be used in practice, with emphasis on the recovery of intel- ligible speech from a video feed of a room. During the week, the group investigated several aspects of the problem, including:

• how much an object vibrates due to sound;

• what can be done to maximize the vibration;

• how the MIT technique detects minute vibrations in videos; • what affects the quality of the resulting recording; and

• how good a recording is needed for intelligible speech.

It was discovered the MIT experiments would not have recovered intel- ligible speech from an ordinary conversation; their success depended on loud sounds and prior knowledge of “Mary had a little lamb”. Camera vibrations were also ignored by MIT; these are expected to be signifi- cant, but the technique could be adapted to be resilient to them. Other possibilities for enhancing their technique, by exploiting resonances or reflections, are discussed in the report. A high-speed low-noise cam- era is essential, and any existing video footage (such as from CCTV) is unlikely to be of sufficient quality. Further experiments with high-end high-speed cameras are needed to assess the feasibility of the technique in practice.

In this report, the problem at hand and important information are compiled before 3 approaches to model a terrorist attack in a public space are considered - a Particle Model, a Discrete Network Model, and a Game Simulation model. Whilst this is by no means a complete list of possible models of a terrorist attack, these were believed to be models that could be developed the most in a week at the ESGI130 at the University of Warwick. For each model type, we first consider their assumptions and suitability to the problem, then model the scenario. Finally, we consider possible extensions to each model, and also how they may be used to evaluate the most effective strategies of the Public and Responders given the information available to them at any one time.