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**Reference Number:** 2017-HW-AMS-38

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**Reference Number:** 2017-HW-Maths-09

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**Reference Number:** 2017-HW-Maths-17

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**Reference Number:** 2017-HW-Maths-15

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Some directions: At high frequencies naive numerical methods require a very fine mesh to capture the rapidly oscillating sound pressure. Tools from harmonic analysis and PDE give rise to new regularity estimates and efficient adaptive mesh refinements. Detailed models of instruments (or other sound sources like tires or high-speed trains) give rise to realistic simulations of sound, based on mathematically challenging multi-physics problems.

**Reference Number:** 2017-HW-Maths-32

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Equipped with these tools, we will look into a quantum-like description for photosynthesis. Here, quantum-like means that the mathematical structure is different from conventional quantum mechanics. We will investigate a quantum network formulation for electron transport in organic molecules and describe the photosynthesis by a quantum channel representation. A question of general interest then is whether and how we can transfer these ideas to solar cells to ultimately improve the performance.

**Reference Number:** 2017-HW-Maths-33

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Edinburgh Earth and Environment Doctoral Training Partnership

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**Reference Number:** 2017-HW-Maths-28

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At the other end of the scale, with colleagues in biology we have the opportunity to take a large amount of cell movement data and to develop models for molecular movement and interactions. The project would apply new techniques for estimating parameters and could be used to inform new biological theories and experiments.

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**Reference Number:** 2017-HW-Maths-34

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**Reference Number:** 2017-HW-Maths-29

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**Reference Number:** 2017-HW-Maths-35

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