arXiv subjects

Michael F. Schatz

Publications and source records attributed to Michael F. Schatz.

At least 19 recordsLinked to original sources

arXiv2024

Hysteresis and ribbons in Taylor-Couette flow of a semidilute non-colloidal suspension

In this study, we numerically investigate hysteretic behaviors of secondary bifurcations in the Taylor-Couette flow of a semidilute, neutrally buoyant, and noncolloidal suspension. We consider a suspension with a bulk particle volume fraction of 0.1, a radius ratio of 0.877, and a particle size of 60. The suspension balance model (SBM) is introduced for numerical simulations to model the dynamics of particles undergoing shear-induced particle migration with rheological constitutive laws. The suspension flow transitions from circular Couette flow (CCF) via ribbons (RIB), spiral vortex flow (SVF), and wavy spiral vortex flow (WSVF) to wavy vortex flow (WVF) with the increase of suspension Reynolds number. The primary transition arises very slowly with an oscillatory critical mode and appears through a supercritical (or non-hysteretic) bifurcation. However, we find hysteretic behaviors in subsequent bifurcations (spiral vortex flow (SVF) to wavy spiral vortex flow (WSVF) and WSVF to wavy vortex flow (WVF)) during increasing-Re and decreasing-Re procedures with a rapid-step change near the transition boundaries. The WSVF and WVF states are more sustained below the transition boundaries when the Reynolds number is rapidly decreased in stages. However, the SVF and WSVF become WSVF and WVF more sharply with increasing Re, respectively. To conclude this study, we also examine in detail, a standing wave of weak counter-rotating vortices that occurs as the primary instability and analyze the wave that oscillates in time but is stationary in space in the RIB state.

physics.flu-dyn↗

arXiv2022

Observing a Dynamical Skeleton of Turbulence in Taylor-Couette Flow Experiments

Recent work suggests unstable recurrent solutions of the equations governing fluid flow can play an important role in structuring the dynamics of turbulence. Here we present a method for detecting intervals of time where turbulence "shadows" (spatially and temporally mimics) recurrent solutions. We find that shadowing occurs frequently and repeatedly in both numerical and experimental observations of counter-rotating Taylor-Couette flow, despite the relatively small number of known recurrent solutions in this system. Our results set the stage for experimentally-grounded dynamical descriptions of turbulence in a variety of wall-bounded shear flows, enabling applications to forecasting and control.

physics.flu-dyn↗

arXiv2021

Data-driven detection of drifting system parameters

Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global parameters from variations in an identified model using only observational data. This capability, when paired with first principles analysis, can effectively distinguish the effects of these changing parameters from the intrinsic complexity of the system. Here we illustrate this by identifying a set of governing equations for an experiment generating a weakly turbulent fluid flow, then analyzing variation in the coefficients of these equations to unravel the drift in its physical parameters.

physics.flu-dyn↗

arXiv2021

Transforming the Preparation of Physics GTAs: Curriculum Development

Graduate Teaching Assistants (GTAs) are key partners in the education of undergraduates. Given the potentially large impact GTAs can have on undergraduate student learning, it is important to provide them with appropriate preparation for teaching. But GTAs are students themselves, and not all of them desire to pursue an academic career. Fully integrating GTA preparation into the professional development of graduate students lowers the barrier to engagement so that all graduate students may benefit from the opportunity to explore teaching and its applications to many potential career paths. In this paper we describe the design and implementation of a GTA Preparation course for first-year Ph.D. students at the Georgia Tech School of Physics. Through a yearly cycle of implementation and revision, guided by the 3P Framework we developed (Pedagogy, Physics, Professional Development), the course has evolved into a robust and comprehensive professional development program that is well-received by physics graduate students.

physics.ed-ph↗

arXiv2021

Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression

Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws describing simple, low-dimensional systems with low levels of noise. Here we demonstrate that combining a data-driven methodology with some general physical principles enables discovery of a quantitatively accurate model of a non-equilibrium spatially-extended system from high-dimensional data that is both noisy and incomplete. We illustrate this using an experimental weakly turbulent fluid flow where only the velocity field is accessible. We also show that this hybrid approach allows reconstruction of the inaccessible variables -- the pressure and forcing field driving the flow.

physics.flu-dyn↗

arXiv2020

Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow

Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion-symmetric subspace. In particular, we find numerous isolated heteroclinic connections between different types of solutions -- equilibria, periodic, and quasi-periodic orbits -- as well as continua of connections forming higher-dimensional connecting manifolds. We also compute a homoclinic connection of a periodic orbit and provide strong evidence that the associated homoclinic tangle forms the chaotic repeller that underpins transient turbulence in the symmetric subspace.

physics.flu-dyn↗

arXiv2020

Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits

In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating that turbulent flows in both experiment and numerics transiently display time-periodic dynamics when they shadow unstable periodic orbits (UPOs). We show that UPOs we computed are also statistically significant, with turbulent flows spending a sizable fraction of the total time near these solutions. As a result, the average rates of energy input and dissipation for the turbulent flow and frequently visited UPOs differ only by a few percent.

physics.flu-dyn↗

arXiv2019

A novel subcritical transition to turbulence in Taylor-Couette flow with counter-rotating cylinders

The transition to turbulence in Taylor-Couette flow often occurs via a sequence of supercritical bifurcations to progressively more complex, yet stable, flows. We describe a subcritical laminar-turbulent transition in the counter-rotating regime mediated by an unstable intermediate state in a system with an axial aspect ratio of $Γ=5.26$ and a radius ratio of $η=0.905$. In this regime, flow visualization experiments and numerical simulations indicate the intermediate state corresponds to an aperiodic flow featuring interpenetrating spirals. Furthermore, the reverse transition out of turbulence leads first to the same intermediate state, which is now stable, before returning to an azimuthally-symmetric laminar flow. Time-resolved tomographic particle image velocimetry is used to characterize the experimental flows; these measurements compare favorably to direct numerical simulations with axial boundary conditions matching those of the experiments.

physics.flu-dyn↗

arXiv2018

Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow

Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.

physics.flu-dyn↗

arXiv2018

Assessing a GTA professional development program

For the last four years, the School of Physics at Georgia Tech have been preparing new Graduate Teaching Assistants (GTAs) through a program that integrates pedagogy, physics content, and professional development strategies. Here we discuss various assessments we have used to evaluate the program, among them surveys, GTA self-reporting, and end-of-semester student evaluations. Our results indicate that GTAs who participate in the program find its practical activities useful, feel better prepared for teaching, make use of learner-centered teaching strategies, and receive higher scores in teaching evaluations.

physics.ed-ph↗

arXiv2017

Bifurcations in a Quasi-Two-Dimensional Kolmogorov-Like Flow

We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a 2D model (Suri ${\it et al.}$ 2014), derived from first principles by depth-averaging the full three-dimensional Navier-Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions.

physics.flu-dyn↗

arXiv2016

Forecasting Fluid Flows Using the Geometry of Turbulence

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully-resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.

nlin.CD↗

arXiv2016

Exploring University Students' Engagement with Online Video Lectures in a Blended Introductory Mechanics Course

The advent of MOOCs has stimulated interest in using online videos to deliver content in university courses. We examined student engagement with 78 online videos that we created and were incorporated into a one-semester blended introductory mechanics course at the Georgia Institute of Technology. We found that students were more engaged with videos that supported laboratory activities than with videos that presented lecture content. In particular, the percentage of students accessing laboratory videos was consistently greater than 80 percent throughout the semester while the percentage of students accessing lecture videos dropped to less than 40 percent by the end of the term. Moreover, students were more likely to access the entirety of a laboratory video than a lecture video. Our results suggest that students may access videos based on perceived value: students appear to consider the laboratory videos as essential for successfully completing the laboratories while students appear to consider the lecture videos as something more akin to supplementary material. We found there was little correlation between student engagement with the videos and the performance in the course. In addition, an examination of the in-video content suggests that students focus more on concrete information that is explicitly required for assignment completion (e.g., actions required to complete laboratory work, or formulas/mathematical expressions needed to solve particular problems) and less on content that is considered more conceptual in nature. The results of the study suggest ways in which instructors may revise courses to better support student learning.

physics.ed-ph↗

arXiv2015

Analysis of Kolmogorov Flow and Rayleigh-Bénard Convection using Persistent Homology

We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow field patterns from numerical simulations of two important problems in fluid dynamics: Kolmogorov flow and Rayleigh-Bénard convection. For each image we compute a persistence diagram to yield a reduced description of the flow field; by applying different metrics to the space of persistence diagrams, we relate characteristic features in persistence diagrams to the geometry of the corresponding flow patterns. We also examine the dynamics of the flow patterns by a second application of persistent homology to the time series of persistence diagrams. We demonstrate that persistent homology provides an effective method both for quotienting out symmetries in families of solutions and for identifying multiscale recurrent dynamics. Our approach is quite general and it is anticipated to be applicable to a broad range of open problems exhibiting complex spatio-temporal behavior.

math.AT↗

arXiv2014

Peer Evaluation of Video Lab Reports in an Introductory Physics MOOC

Assessing student performance becomes challenging when course enrollment becomes very large (~10^4 students). As part of a Massive Open Online Course (MOOC) in introductory physics offered by Georgia Tech in 2013, students submitted video reports on mechanics labs. Peer evaluation of these reports provided the primary method for evaluating student laboratory work. This paper describes the methods developed and used to guide students in evaluating each other's video lab reports. We also discuss how students' peer evaluation behavior changed with different interventions provided in the course.

physics.ed-ph↗

arXiv2014

Peer Evaluation of Video Lab Reports in a Blended Introductory Physics Course

The Georgia Tech blended introductory calculus-based mechanics course emphasizes scientific communication as one of its learning goals, and to that end, we gave our students a series of four peer-evaluation assignments intended to develop their abilities to present and evaluate scientific arguments. Within these assignments, we also assessed students' evaluation abilities by comparing their evaluations to a set of expert evaluations. We summarize our development efforts and describe the changes we observed in student evaluation behavior.

physics.ed-ph↗

arXiv2014

Student Use of a Single Lecture Video in a Flipped Introductory Mechanics Course

In the Fall of 2013, Georgia Tech offered a 'flipped' calculus-based introductory mechanics class as an alternative to the traditional large-enrollment lecture class. This class flipped instruction by introducing new material outside of the classroom through pre-recorded, lecture videos. Video lectures constituted students' initial introduction to course material. We analyze how students engaged with online lecture videos via 'clickstream' data, consisting of time-stamped interactions (plays, pauses, seeks, etc.) with the online video player. Analysis of these events has shown that students may be focusing on elements of the video that facilitate a 'correct' solution.

physics.ed-ph↗

arXiv2013

Integrating Numerical Computation into the Modeling Instruction Curriculum

We describe a way to introduce physics high school students with no background in programming to computational problem-solving experiences. Our approach builds on the great strides made by the Modeling Instruction reform curriculum. This approach emphasizes the practices of "Developing and using models" and "Computational thinking" highlighted by the NRC K-12 science standards framework. We taught 9th-grade students in a Modeling-Instruction-based physics course to construct computational models using the VPython programming environment. Numerical computation within the Modeling Instruction curriculum provides coherence among the curriculum's different force and motion models, links the various representations which the curriculum employs, and extends the curriculum to include real-world problems that are inaccessible to a purely analytic approach.

physics.ed-ph↗