QUANTIFICATION OF RANDOM PROCESSES: FROM DIFFUSION TO RHEOLOGY

Quantifying random processes has many practical applications, from drug delivery and pharmaceutical research to fertility analysis. Quantification of random displacement of objects in a fluid domain can lead to measuring several important physical properties. For example, from the Brownian motion of passive particles, the diffusion coefficient of the particles can be measured. Randomness can also be used to report uncertainty in particle image velocimetry (PIV) measurements. Rheological properties of the environment can be found from random displacements of probing particles.

This dissertation provides novel and advanced methods for quantifying randomness and methods to extract physical information from that. As examples of random processes, we studied diffusion particles and subdiffraction objects, and actively swimming bacteria in various environmental conditions.

First, we developed image-based Probability Estimation of Displacement (iPED), a method for estimating the probability density function of displacement from images of randomly moving objects. We then used iPED to measure the diffusion coefficient of particle.

We also used the PDF of random displacement to estimate uncertainty in PIV measurements called Moment of Probability of Displacements (MPD). In order to extract the environmental effect on random displacements, we used iPED to study the evolution of the PDF as a function of time lag and introduced a novel approach called Particle Image Rheometry (PIR).

For objects smaller than diffraction limit of the optical system, such as proteins or quantum dots, we introduce another framework to measure the diffusion coefficient by studying the overall changes in the concentration in the image domain. We termed this approach Concentration Image Diffusimetry (CID). CID enables measurement of concentration-dependent diffusion coefficient which is a tool needed for drug development and pharmaceutical industry.

Overall this dissertation provides image analysis algorithms that are superior to existing methods and provide a fertile ground for research and discovery in academic and industrial settings.