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Michael F. Schatz

Publications and source records attributed to Michael F. Schatz.

34 records · Page 2Linked to original sources
arXiv2013

The Initial State of Students Taking an Introductory Physics MOOC

As part of a larger research project into massively open online courses (MOOCs), we have investigated student background, as well as student participation in a physics MOOC with a laboratory component. Students completed a demographic survey and the Force and Motion Conceptual Evaluation at the beginning of the course. While the course is still actively running, we have tracked student participation over the first five weeks of the eleven-week course.

physics.ed-ph↗
arXiv2013

Velocity Profile in a Two-Layer Kolmogorov-Like Flow

In this article we discuss flows in shallow, stratified horizontal layers of two immiscible fluids. The top layer is an electrolyte which is electromagnetically driven and the bottom layer is a dielectric fluid. Using a quasi-two-dimensional approximation, we derive the depth-averaged two-dimensional (2D) vorticity equation which includes a prefactor to the advection term, previously unaccounted for. In addition, we study how the horizontal components of velocity vary in the vertical direction. For a Kolmogorov-like flow, we evaluate analytical expressions for the coefficients in the generalized 2D vorticity equation, uncovering their dependence on experimental parameters. To test the accuracy of these estimates, we experimentally measure the horizontal velocity fields at the free-surface and at the electrolyte-dielectric interface using particle image velocimetry (PIV). We show that there is excellent agreement between the analytical predictions and the experimental measurements. Our analysis shows that by increasing the viscosity of the electrolyte relative to that of the dielectric, one may significantly improve the uniformity of the flow along the vertical direction.

physics.flu-dyn↗
arXiv2012

Understanding Student Computational Thinking with Computational Modeling

Recently, the National Research Council's framework for next generation science standards highlighted "computational thinking" as one of its "fundamental practices". 9th Grade students taking a physics course that employed the Modeling Instruction curriculum were taught to construct computational models of physical systems. Student computational thinking was assessed using a proctored programming assignment, written essay, and a series of think-aloud interviews, where the students produced and discussed a computational model of a baseball in motion via a high-level programming environment (VPython). Roughly a third of the students in the study were successful in completing the programming assignment. Student success on this assessment was tied to how students synthesized their knowledge of physics and computation. On the essay and interview assessments, students displayed unique views of the relationship between force and motion; those who spoke of this relationship in causal (rather than observational) terms tended to have more success in the programming exercise.

physics.ed-ph↗
arXiv2012

Implementing and assessing computational modeling in introductory mechanics

Students taking introductory physics are rarely exposed to computational modeling. In a one-semester large lecture introductory calculus-based mechanics course at Georgia Tech, students learned to solve physics problems using the VPython programming environment. During the term 1357 students in this course solved a suite of fourteen computational modeling homework questions delivered using an online commercial course management system. Their proficiency with computational modeling was evaluated in a proctored environment using a novel central force problem. The majority of students (60.4%) successfully completed the evaluation. Analysis of erroneous student-submitted programs indicated that a small set of student errors explained why most programs failed. We discuss the design and implementation of the computational modeling homework and evaluation, the results from the evaluation and the implications for instruction in computational modeling in introductory STEM courses.

physics.ed-ph↗
arXiv2012

Comparing large lecture mechanics curricula using the Force Concept Inventory: A five thousand student study

The performance of over 5000 students in introductory calculus-based mechanics courses at the Georgia Institute of Technology was assessed using the Force Concept Inventory (FCI). Results from two different curricula were compared: a traditional mechanics curriculum and the Matter & Interactions (M&I) curriculum. Post-instruction FCI averages were significantly higher for the traditional curriculum than for the M&I curriculum; the differences between curricula persist after accounting for factors such as pre-instruction FCI scores, grade point averages, and SAT scores. FCI performance on categories of items organized by concepts was also compared; traditional averages were significantly higher in each concept. We examined differences in student preparation between the curricula and found that the relative fraction of homework and lecture topics devoted to FCI force and motion concepts correlated with the observed performance differences. Limitations of concept inventories as instruments for evaluating curricular reforms are discussed.

physics.ed-ph↗
arXiv2011

Fostering Computational Thinking

Students taking introductory physics are rarely exposed to computational modeling. In a one-semester large lecture introductory calculus-based mechanics course at Georgia Tech, students learned to solve physics problems using the VPython programming environment. During the term 1357 students in this course solved a suite of fourteen computational modeling homework questions delivered using an online commercial course management system. Their proficiency with computational modeling was evaluated in a proctored environment using a novel central force problem. The majority of students (60.4%) successfully completed the evaluation. Analysis of erroneous student-submitted programs indicated that a small set of student errors explained why most programs failed. We discuss the design and implementation of the computational modeling homework and evaluation, the results from the evaluation and the implications for instruction in computational modeling in introductory STEM courses.

physics.ed-ph↗
arXiv2011

Non-equilibrium Pattern Modes Extracted from Experimental Data

We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an experimental ensemble of Rayleigh-Bénard convection patterns with nearby initial conditions close to the onset of secondary instability. An analysis of the ensemble evolution reveals the spatial structure of the dominant modes of the system as well as the corresponding growth rates. The extracted modes are related to localized versions of instabilities found in the ideal unbounded system. The approach may prove useful in describing instability in experimental systems as a step toward prediction and control.

physics.flu-dyn↗
arXiv2009

Transient Turbulence in Taylor-Couette Flow

Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present the first direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes spanning five orders of magnitude. We also show that there is a regime where Taylor-Couette flow shares many of the decay characteristics observed in other shear flows, including Poisson statistics and the coexistence of laminar and turbulent patches. Our data suggest that characteristic decay times increase super-exponentially with increasing Reynolds number but remain bounded in agreement with the most recent data from pipe flow and with a recent theoretical model. This suggests that, contrary to the prevailing view, turbulence in linearly stable shear flows may be generically transient.

physics.flu-dyn↗
arXiv2009

A Tale of Two Curricula: The performance of two thousand students in introductory electromagnetism

The performance of over 2000 students in introductory calculus-based electromagnetism (E&M) courses at four large research universities was measured using the Brief Electricity and Magnetism Assessment (BEMA). Two different curricula were used at these universities: a traditional E&M curriculum and the Matter & Interactions (M&I) curriculum. At each university, post-instruction BEMA test averages were significantly higher for the M&I curriculum than for the traditional curriculum. The differences in post-test averages cannot be explained by differences in variables such as pre-instruction BEMA scores, grade point average, or SAT scores. BEMA performance on categories of items organized by subtopic was also compared at one of the universities; M&I averages were significantly higher in each topic. The results suggest that the M&I curriculum is more effective than the traditional curriculum at teaching E&M concepts to students, possibly because the learning progression in M&I reorganizes and augments the traditional sequence of topics, for example, by increasing early emphasis on the vector field concept and by emphasizing the effects of fields on matter at the microscopic level.

physics.ed-ph↗
arXiv2009

Homological Characterizations of Spiral Defect Chaos in Rayleigh-Benard Convection

We use a quantitative topological characterization of complex dynamics to measure geometric structures. This approach is used to analyze the weakly turbulent state of spiral defect chaos in experiments on Rayleigh-Benard convection. Different attractors of spiral defect chaos are distinguished by their homology. The technique reveals pattern asymmetries that are not revealed using statistical measures. In addition we observe global stochastic ergodicity for system parameter values where locally chaotic dynamics has been observed previously.

nlin.PS↗
arXiv2007

Estimating the State of Large Spatiotemporally Chaotic Systems

Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the high dimensionality of large spatiotemporally chaotic systems prevents the use of classical data assimilation techniques. Here, via numerical computations on the paradigmatic example of large aspect ratio Rayleigh-Benard convection, we demonstrate the applicability of a recently developed data assimilation method designed to circumvent this difficulty. In addition, we describe extensions of the algorithm for estimating unknown system parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of situations in which there is spatiotemporally chaotic behavior.

nlin.CD↗
arXiv2007

Modal Extraction in Spatially Extended Systems

We describe a practical procedure for extracting the spatial structure and the growth rates of slow eigenmodes of a spatially extended system, using a unique experimental capability both to impose and to perturb desired initial states. The procedure is used to construct experimentally the spectrum of linear modes near the secondary instability boundary in Rayleigh-Bénard convection. This technique suggests an approach to experimental characterization of more complex dynamical states such as periodic orbits or spatiotemporal chaos.

physics.flu-dyn↗
arXiv2000

Convective instability on a crystal surface

The distinction between absolute and convective instabilities is well known in the context of hydrodynamics and plasma physics. In this Letter, we examine an epitaxial crystal growth model from this point of view and show that a strain-induced step bunching instability can be convective. Using analytic stability theory and numerical simulations, we study the response of the crystal surface to an inhomogeneous deposition flux that launches impulsive and time-periodic perturbations to a uniform array of steps. The results suggest a new approach to morphological patterning.

cond-mat.mtrl-sci↗
arXiv1995

Onset of Surface-Tension-Driven Benard Convection

Experiments with shadowgraph visualization reveal a subcritical transition to a hexagonal convection pattern in thin liquid layers that have a free upper surface and are heated from below. The measured critical Marangoni number (84) and observation of hysteresis (3%) agree with theory. In some experiments, imperfect bifurcation is observed and is attributed to deterministic forcing caused in part by the lateral boundaries in the experiment.

patt-sol↗
arXiv1995

Long-Wavelength Instability in Surface-Tension-Driven Benard Convection

Laboratory studies reveal a deformational instability that leads to a drained region (dry spot) in an initially flat liquid layer (with a free upper surface) heated uniformly from below. This long-wavelength instability supplants hexagonal convection cells as the primary instability in viscous liquid layers that are sufficiently thin or are in microgravity. The instability occurs at a temperature gradient 34% smaller than predicted by linear stability theory. Numerical simulations show a drained region qualitatively similar to that seen in the experiment.

patt-sol↗