Computational approaches to stochastic systems in physics and biology

In this dissertation, I devise computational approaches to model and understand two very different systems which exhibit stochastic behavior: quantum fluids with topological defects arising during quenches and forcing, and complex microbial communities living and evolving with the gastrointestinal tracts of vertebrates. As such, this dissertation is organized into two parts.;In Part I, I create a model for quantum fluids, which incorporates a conservative and dissipative part, and I also allow the fluid to be externally forced by a normal fluid. I use then this model to calculate scaling laws arising from the stochastic interactions of the topological defects exhibited by the modeled fluid while undergoing a quench.;In Chapter 2 I give a detailed description of this model of quantum fluids. Unlike more traditional approaches, this model is based on Cell Dynamical Systems (CDS), an approach that captures relevant physical features of the system and allows for long time steps during its evolution. I devise a two step CDS model, implementing both conservative and dissipative dynamics present in quantum fluids. I also couple the model with an external normal fluid field that drives the system. I then validate the results of the model by measuring different scaling laws predicted for quantum fluids. I also propose an extension of the model that also incorporates the excitations of the fluid and couples its dynamics with the dynamics of the condensate.;In Chapter 3 I use the above model to calculate scaling laws predicted for the velocity of topological defects undergoing a critical quench. To accomplish this, I numerically implement an algorithm that extracts from the order parameter field the velocity components of the defects as they move during the quench process. This algorithm is robust and extensible to any system where defects are located by the zeros of the order parameter. The algorithm is also applied to a sheared stripe-forming system, allowing the calculation of the corresponding scaling laws.;In Part II, I investigate the evolutionary dynamics of communities of microbes living in the gastrointestinal tracts of vertebrates, and ask to what degree their evolution is niche-driven, where organisms fitter to their environment become dominant, or if it is neutral, where the organisms evolve stochastically and are otherwise functionally equivalent within their communities. To that end, a series of computational tools were developed to pre-process, curate and reduce the data sets.;In Chapter 4, I analyze the raw data for this research, namely short reads of 16S ribosomal RNA, and quantify how much of phylogenetic information is lost by using these short reads instead of full-length reads, and show that for lengths spanning 300 to 400 base pairs, we can recover some meaningful phylogenetic information.;In Chapter 5, I introduce a pipeline for pre-processing, alignment and curation of libraries of short reads of rRNA. We show that this pipeline significantly reduces the artifacts usually associated with these sequences, resulting in better clustering of the sequences, and better phylogenetic trees representing their organismal relationships.;In Chapter 6 I use the data processed with the above tools to analyze communities of microbes living in gastrointestinal tracts of vertebrates, and we ask to what extent the evolutionary dynamics of these communities is dominated by niche-based evolution, or if the communities behave neutrally, where evolution is random and all organisms are functionally equivalent. We conclude that there is evidence for strong niche-based dynamics, though we cannot fully discard some degree of neutral evolution.;Finally, in Chapter 7 I propose a method to quantify the balance present in phylogenetic trees to compare a large-scale molecular phylogeny to full organismal taxonomies. I show that there is considerable structure in all of them, but direct comparison of both types of trees is difficult at the moment due to their different intrinsic structure.