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In this work, a numerical development for the supercontinuum (SC) generation is demonstrated by developing a fractional calculus model for a photonic crystal fibre of hexagonal design. The solutions are presented in the temporal and spectral way of the Nonlinear Schrödinger Equation (NLSE). The results show that, for a spectral development of the NLSE, great computational savings are obtained and the analysis of the phenomena that intervene in the generation of this non-linear effect is feasible.

AAPT SM 21

Fractional Calculus Approach in Supercontinuum Generation in Photonic Crystal Fibers

nonlinear effect.

photonic crystal fiber

supercontinuum generation

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Building on my presentations in the past, I argue that students can become more grounded in physics by the realization of that multitude of physics equations which can be regarded in terms of the Law of Conservation of Energy or Conservation of Mass. Examples of this are in Kirchhoff's two Laws of Electricity in terms of, respectively, voltage loops which is scaled per charge and current splitting scaled per time. Another set of complementary examples is in fluid dynamics regarding, respectively, Bernoulli's Equation which is scaled per volume and the Continuity Equation scaled per time (see also Poster Session for details). Revisiting these Conservation Laws also underscores their broad importance and aids in student recall and additional application into the future. Examples of potential confusions and pitfalls for teachers to be aware of are given.

Spiraling Conservation of Energy/Mass in Introductory Physics: Kirchhoff to Bernoulli

Parallel Pedagogy Introductory Mechanics, at Cal Poly since 2014 [P.Schwartz, TPT, 55, 280 (2017)]:
• We simultaneously introduce momentum, energy, dynamics, kinematics on the first day;
• build complexity while repeating the process in the following order: rotation, systems, components, trigonometry, the two quadratic kinematics equations;
• require full conceptual support, rather than correct answer, for credit;
• engage students at home with interactive videos and textbook, reserving class time for group work, demonstrations, discussion;
• while learning assistants model learning process, stimulate conversation.
After 16 classes, >900 students.
• Most students prefer this method.
• CLASS (Colorado Learning Attitudes about Science Survey, http://www.colorado.edu/ sei/class/) results indicate improvement – especially applied conceptual understanding.
• Students demonstrate superior concept application (Pedagogy Changes Can Improve Concept Application, O.Staveland, P.Schwartz, TPT, submitted)
• Using publicly-available text and interactive videos, a first-time mechanics instructor seamlessly and successfully adopted parallel pedagogy.
Support: http://sharedcurriculum.peteschwartz.net/parallel-pedagogy/ 
As soon as it publishes, please see:
"Pedagogy Changes Can Improve Concept Application" O. Staveland, P. Schwartz, The Physics Teacher, in press


Parallel Pedagogy: Seven Years, and 1000 Students Later

I will speak briefly about why I like the approach of parallel pedagogy, then provide a link to a Perusall(R) course that I have set up just for the meeting, populated with some or all of the OER textbook I’m using for my introductory physics classes. I’ll highlight the format of the book and explain the motivation behind the formatting. Then I will share examples of student work that follow the pattern of analysis used in the book. I will also show how I use Perusall(R) for asynchronous interactions and myOpenMath for immediate feedback to students.

Using OER materials, Perusall(R), and myOpenMath with Parallel Pedagogy

Computer simulations have been used to support student learning in physics, not only to boost conceptual understanding but to make labs more widely accessible to different populations. However, their impact on student learning has shown mixed results. To better understand this impact, HTML5-based computer simulations for topics in mechanics were investigated in a large, algebra-based, studio physics course for life science students at a private, research-intensive institution. Over a period of three years, we compared learning outcomes of students using traditional hands-on equipment only, a simulation only, or a hybrid combination of both for activities on energy, momentum, simple harmonic motion, and rotational dynamics. We will present our findings of this study through an equity lens, both from the experience of online learning due to the global pandemic and from consideration of the limited access to lab equipment for many students.

Use of physics simulations in supporting equity and student learning

The sudden transition to remote instruction left many students struggling to fully engage with courses which had fewer opportunities for meaningful interpersonal interactions. In response, we formed “Learning Pods – online learning communities of small student groups connected through Slack and mentored in collaboration skills. Subsequently, Learning Pods became an organizing structure of the introductory calculus-based mechanics course. Features of the Learning Pod Intervention varied as we scaled up from courses with ~100 students to those with 300-500 students. Based on analysis of student survey questions, we present preliminary indicators of increased student self-efficacy and improved engagement with instructors and peers. Improved self-efficacy and engagement have been correlated with improved success and persistence, especially for students from groups underrepresented in physics. We observe that different implementations increased student self-efficacy to different degrees, and that instructor and TA engagement in mentoring effective collaboration lowered barriers for students’ engagement with TAs.

Facilitating Online Learning Communities in Large-Enrollment Introductory Physics Courses

We developed a number of digital tools to support teaching quantum mechanics. The idea behind that is main concepts of quantum mechanics are non-intuitive to an uninitiated student due to the lack of daily experience with quantum mechanics: The basis of intuition is experience. Therefore, teaching quantum mechanics with a support of numerical experiments for all main topics of quantum mechanics appears to be essential for an efficient and quick learning process. The numerical experiments are prepared using PYTHON computer codes and a graphical interface. Students and instructors can use the graphical interface to change parameters of the suggested numerical experiments or they can download, modify and run the codes on their personal computers. Finally, a website, gathering overall numerical experiments, was designed. It can be used by universities and institutions in their different educations.

Teaching quantum mechanics in an experiential learning and engaging environment

Computation has delivered many benefits to the teaching and learning of quantum mechanics. It increases students' engagement with the subject matter, enabling them to be doers as opposed to just thinkers or traditional problem solvers. In many cases, practices, tools and methods previously used only in research have been brought to the classroom, significantly enriching the class. In this presentation we will discuss multimodal techniques, some successfully used in atomic physics, to computation in quantum mechanics, including visual, numerical, and symbolic computation. We will present select activities and projects on large eigenvalue problems, scattering, and time-dependent dynamic evolution. Working examples will be given in Python but the templates should be adaptable to other platforms.

Multimodal computation in quantum mechanics

Many of us remember passively wading through a lengthy and esoteric derivation of the energy eigenstates of the harmonic oscillator, which we likely revisit only when teaching the topic. In contrast, a computational introduction engages students in a dynamic investigation that immediately produces visualizations in a process they can repeat ad infinitum for any number of potential energy functions. In this talk, I share my recent iteration of a junior-level Modern Physics course, for which I created a sequence of computational assignments based on published PICUP Exercise Sets, developed a new Exercise Set about x-ray crystallography, and implemented a revise-and-resubmit structure for assignment grading. I conclude with a discussion of assessment interviews I conducted after the course to examine the ways in which computation helped the students learn challenging quantum concepts, and discuss needs to address in future semesters.

Implementation and Assessment of Computation in a Modern Physics Course

I will describe a first attempt to build computation into the undergraduate quantum mechanics course at High Point University. In a spin first approach, students uncover the postulates of quantum mechanics entirely in the context of spin-1/2 degrees of freedom before developing position-space wave function technology needed to study the standard array of potential wells. This non-standard approach to teaching quantum mechanics is particularly well suited for the integration of computation. In addition to presenting several examples of how integrated computational exercises can aid in student understanding of key ideas in quantum mechanics, I will share some possible independent projects involving advanced topics which are accessible to students well versed in the basic computational methods used to investigate spin.

Integrating Computation into a Spin First Undergraduate Quantum Mechanics Course

This presentation will provide an overview of presentations that are available to those attending for use with their classes. The presentations are designed for students in grades 6-8, 9 – 12, and college introductory physics courses. Climate science challenges are presented in terms of thermodynamics/entropy changes that occur due to procuring and burning fossil fuels to produce electricity. Information about the Climate Reality Project will also be included.

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Fractional Calculus Approach in Supercontinuum Generation in Photonic Crystal Fibers

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Spiraling Conservation of Energy/Mass in Introductory Physics: Kirchhoff to Bernoulli

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