Fluid Dynamics Commons^™

Nonlinear Physics Of Parity-Broken Fluids, Sudheesh Srivastava

Dissertations, Theses, and Capstone Projects

This thesis explores parity-breaking mechanisms, nonlinear wave phenomena, and localization transitions across different physical contexts. First, we examine modulation instability in parity-breaking systems, deriving modified nonlinear Schr¨odinger equations that reveal direction dependent instabilities. Next, we investigate wave turbulence, demonstrating numerically that parity-breaking dispersion significantly alters turbulent cascades and modifies their statistical properties. Lastly, we analyze localization in quasiperiodic tight- binding model based on polariton condensate lattice. Collectively, these studies illustrate the universal role of symmetries and nonlinear interactions in shaping macroscopic behaviors, facilitating interdisciplinary insights.

Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas

Dissertations, Theses, and Capstone Projects

This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …

Aspects Of Parity Breaking In Classical And Quantum Fluids, Dylan J. Reynolds

Dissertations, Theses, and Capstone Projects

Parity-breaking is ubiquitous across many scales of physics, from the rotation of galaxies at the largest of scales, to the cyclotron orbits of electrons at the microscopic scale. In describing the collective dynamics of many particle systems, parity breaking effects typically originate from some form of chirality, such as angular momentum, at the level of the constituent particles. External forces can also induce chiral motion, with the primary examples being the Lorentz and Coriolis forces.

The effects of parity breaking are perhaps most strikingly seen in active matter, systems of complex particles that tend to convert energy into some directed …

Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg

Dissertations, Theses, and Capstone Projects

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled.

Here we delve into the world of active matter by studying colloidal-sized (100 …

Connections Between Atmospheric Blocking, General Circulation, And Weather Extremes In A Hierarchy Of Models And Various Climates, Veeshan Narinesingh

Dissertations, Theses, and Capstone Projects

The field of geophysical fluid dynamics (GFD) includes the study of both the motion and thermodynamic aspects of the atmosphere. These properties are of particular importance because they directly influence both local and large-scale weather and climate and are associated with various phenomena. One phenomena that is particularly influential is atmospheric blocking. Atmospheric blocks are persistent, quasi-stationary anticyclones (a.k.a. high-pressure systems) that occur in the atmosphere and disrupt the flow. Blocks are known to induce heat extremes and cold spells, as well as steer storms and cause numerous types of hazards. Yet despite the hazards associated with blocks, our current …

Frozen In Time: A Numerical Modeling Approach To The Study Of Ice Bearing Planetesimals Through Carbonaceous Chondrites, Jasmine M. Bayron

Dissertations, Theses, and Capstone Projects

Icy planetesimals are significant objects of study for meteoritics, planetary science, and astrobiology due to their connections to the origins of life and liquid water on Earth. An existing closed system aqueous alteration model was adapted to simulate several scenarios involving early Solar System geologic processes occurring in an icy planetesimal interior. The model described in this work has been developed not only to test the validity of constraints currently thought to apply to CM1 parent bodies, but to directly compare the implications of these constraints for the isotopic composition and the modal mineralogy of carbonaceous chondrites. Isotopic ratios of …

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …

The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, Michael Kumaresan

Dissertations, Theses, and Capstone Projects

We study the Cauchy problem for the advection-diffusion equation when the diffusive parameter is vanishingly small. We consider two cases - when the underlying flow is a shear flow, and when the underlying flow is generated by a Hamiltonian. For the former, we examine the problem on a bounded domain in two spatial variables with Dirichlet boundary conditions. After quantizing the system via the Fourier transform in the first spatial variable, we establish the enhanced-dissipation effect for each mode. For the latter, we allow for non-degenerate critical points and represent the orbits by points on a Reeb graph, with vertices …