# Phase Reconstruction using the Hybrid Input – Output Algorithm, and Multi-scale modelling of droplet coalescence

*Applied Mathematics Student Seminar*

*by (1) Chu Wu and (2) Lachlan Mason*

*Institution:*The University of Melbourne

*Date: Tue 18th September 2012*

*Time: 1:00 PM*

*Location: Old Geology Theatre 2*

*Abstract*: (1) The phase problem is a phenomenon that arises in various fields of science and engineering, like electron microscopy, astronomy and x-ray crystallography. These disciplines usually capture images which can be expressed as a complex number but sometimes, the modern day detection equipment can only measure the Fourier Transform magnitude but not the phase. Thus the original object cannot be reconstructed. For this seminar, I would like to discuss briefly, the hybrid input – output algorithm which is one of the techniques used to overcome the phase problem. In particular I will be discussing the method’s effectiveness in the presence of sinusoidal overlay and random noise.

(2) Droplet coalescence is a throughput-limiting factor in industrial solvent extraction. In this short talk I will introduce a numerical model for symmetric binary droplet collisions. I will give a brief overview of volume of fluid (VOF) and level set (LS) simulation techniques.