Pattern Formation

Another area of interest for both myself and my adviser has been pattern formation processes in nature that are somehow driven by hydrodynamics.

In collaboration with Dr Brueck and Deying Xia at The Center for High-Tech Materials (CHTM), we have been looking at pattern formation in nano-channels of colloidal suspensions which are evaporated out of their suspension onto a patterned substrate.	An example of the final distribution of spherical silica particles (50-80nm) in channels of width similar to the particles.
Through the use of the density evolution PDE (above), we showed that a continuum approach to look at the evolution of large numbers of particles was reasonable. The emphasis of this project was to analyze the local version of the 1D PDE. However, much work has also been done recently (by Dr Putkaradze and D.D.Holm -Los Alamos) to fully understand the non-local higher dimensional version of this equation, which has possible application to a large class of phenomena.	Figure (left) shows an analytic weak solution of the 1D density distribution PDE (density vs channel position). Figure (right) shows a numerical simulation of the collapse of a constant density distribution (plus/minus 10% random deviation) into regions of clumps and regions of voids. Note: density has been normalized such that 1 is closed packed and zero is empty.

In collaboration with Dr Brueck and Deying Xia at The Center for High-Tech Materials (CHTM), we have been looking at pattern formation in nano-channels of colloidal suspensions which are evaporated out of their suspension onto a patterned substrate.

An example of the final distribution of spherical silica particles (50-80nm) in channels of width similar to the particles.

Through the use of the density evolution PDE (above), we showed that a continuum approach to look at the evolution of large numbers of particles was reasonable.

The emphasis of this project was to analyze the local version of the 1D PDE. However, much work has also been done recently (by Dr Putkaradze and D.D.Holm -Los Alamos) to fully understand the non-local higher dimensional version of this equation, which has possible application to a large class of phenomena.

Figure (left) shows an analytic weak solution of the 1D density distribution PDE (density vs channel position). Figure (right) shows a numerical simulation of the collapse of a constant density distribution (plus/minus 10% random deviation) into regions of clumps and regions of voids. Note: density has been normalized such that 1 is closed packed and zero is empty.

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