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Erratum: More realistic Hamiltonians for the fractional quantum Hall regime in GaAs and graphene [Phys. Rev. B 87, 245129 (2013)]

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COVID-19 has impacted many institutions and organizations around the world, disrupting the progress of research. Through this difficult time APS and the Physical Review editorial office are fully equipped and actively working to support researchers by continuing to carry out all editorial and peer-review functions and publish research in the journals as well as minimizing disruption to journal access.

We appreciate your continued effort and commitment to helping advance science, and allowing us to publish the best physics journals in the world. And we hope you, and your loved ones, are staying safe and healthy.

Source: http://link.aps.org/doi/10.1103/PhysRevB.92.159902

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Achieving superlubricity with graphene

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Sometimes, experimental results spark enormous curiosity inspiring a myriad of questions and ideas for further experimentation. In 2004, Geim and Novoselov, from The University of Manchester, isolated a single layer of graphene from bulk graphite with the “Scotch Tape Method” for which they were awarded the 2010 Nobel Prize in Physics.  This one experimental result has branched out countless times serving as a source of inspiration in as many different fields.  We are now in the midst of an array of branching-out in graphene research, and one of those branches gaining attention is ultra low friction observed between graphene and other surface materials.  

Much has been learned about graphene in the past 15 years through an immense amount of research, most of which, in non-mechanical realms (e.g., electron transport measurements, thermal conductivity, pseudo magnetic fields in strain engineering).  However, superlubricity, a mechanical phenomenon, has become the focus among many research groups. Mechanical measurements have famously shown graphene’s tensile strength to be hundreds of times that of the strongest steel, indisputably placing it atop the list of construction materials best for a superhero suit.  Superlubricity is a tribological property of graphene and is, arguably, as equally impressive as graphene’s tensile strength.

Tribology is the study of interacting surfaces during relative motion including sources of friction and methods for its reduction.  It’s not a recent discovery that coating a surface with graphite (many layers of graphene) can lower friction between two sliding surfaces.  Current research studies the precise mechanisms and surfaces for which to minimize friction with single or several layers of graphene. 

Research published in Nature Materials in 2018 measures friction between surfaces under constant load and velocity. The experiment includes two groups; one consisting of two graphene surfaces (homogeneous junction), and another consisting of graphene and hexagonal boron nitride (heterogeneous junction).   The research group measures friction using Atomic Force Microscopy (AFM).  The hexagonal boron nitride (or graphene for a homogeneous junction) is fixed to the stage of the AFM while the graphene slides atop.  Loads are held constant at 20 𝜇N and sliding velocity constant at 200 nm/s. Ultra low friction is observed for homogeneous junctions when the underlying crystalline lattice structures of the surfaces are at a relative angle of 30 degrees.  However, this ultra low friction state is very unstable and upon sliding, the surfaces rotate towards a locked-in lattice alignment. Friction varies with respect to the relative angle between the two surface’s crystalline lattice structures. Minimum (ultra low) friction occurs at a relative angle of 30 degrees reaching a maximum when locked-in lattice alignment is realized upon sliding. While in a state of lattice alignment, shearing is rendered impossible with the experimental setup due to the relatively large amount of friction.

Friction varies with respect to the relative angle of the crystalline lattice structures and is, therefore, anisotropic.  For example, the fact it takes less force to split wood when an axe blade is applied parallel to its grains than when applied perpendicularly illustrates the anisotropic nature of wood, as the force to split wood is dependent upon the direction along which the force is applied.  Frictional anisotropy is greater in homogeneous junctions because the tendency to orient into a stuck, maximum friction alignment, is greater than with heterojunctions.  In fact, heterogeneous junctions experience frictional anisotropy three orders of magnitude less than homogeneous junctions. Heterogenous junctions display much less frictional anisotropy due to a lattice misalignment when the angle between the lattice vectors is at a minimum.  In other words, the graphene and hBN crystalline lattice structures are never parallel because the materials differ, therefore, never experience the impact of lattice alignment as do homogenous junctions. Hence, heterogeneous junctions do not become stuck in a high friction state that characterizes homogeneous ones, and experience ultra low friction during sliding at all relative crystalline lattice structure angles.

Presumably, to increase applicability, upscaling to much larger loads will be necessary. A large scale cost effective method to dramatically reduce friction would undoubtedly have an enormous impact on a great number of industries.  Cost efficiency is a key component to the realization of graphene’s potential impact, not only as it applies to superlubricity, but in all areas of application.  As access to large amounts of affordable graphene increases, so will experiments in fabricating devices exploiting the extraordinary characteristics which have placed graphene and graphene based materials on the front lines of material research the past couple decades.

Source: https://quantumfrontiers.com/2020/03/24/achieving-superlubricity-with-graphene/

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Erratum: Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field [Phys. Rev. B 78, 195427 (2008)]

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COVID-19 has impacted many institutions and organizations around the world, disrupting the progress of research. Through this difficult time APS and the Physical Review editorial office are fully equipped and actively working to support researchers by continuing to carry out all editorial and peer-review functions and publish research in the journals as well as minimizing disruption to journal access.

We appreciate your continued effort and commitment to helping advance science, and allowing us to publish the best physics journals in the world. And we hope you, and your loved ones, are staying safe and healthy.

Source: http://link.aps.org/doi/10.1103/PhysRevB.95.039901

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The app I need right now

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The app I need right now

March 19, 2020

tags: math

So I and every other teacher right now are scrambling to get ready to teach school online. Here’s a problem I’m grappling with that I would welcome your advice.

In my Geometry class, we do a lot of group problem solving on wall mounted whiteboards using problems from the Exeter curriculum. It is so helpful for me as a teacher to be able to walk around the room, see students work, ask them questions, give them feedback, and then return later to see how their work has progressed.

I’ve been wondering a lot about what this might look like online. We’re using zoom, and of course there are break rooms, and even a rudimentary “whiteboard” built in where students could finger paint their work. But the reality is, most kids will be doing math work with pencil and paper, and it seems like it will be very hard for me to see that work as it progresses.

My students have all gotten very used to submitting scans of their written math homework using scanbot each night, and this is a great tool for seeing what students have done, but it isn’t seamless enough to really be useful for students to share their math work as they are going.

Here’s what I want—I want an app that allows a student to take a photo of their work. When that student’s work is photographed, it’s added to our class, tagged by student, date and time. Then all of these photographs would be nicely presented to me some way so that I could quickly see a students work, or step through their submissions. It would be extra awesome if I could some how annotate or give feedback to a student’s photo.

This seems like it would be pretty efficient for a student who was working on math and had their phone next to them. They’d just open the app, take a photo, and the work would be there for all to see.

I know students could just hold their notebooks up to a webcam, or take a photo fo their work, air drop it to their laptop, and then screen share. There are also lots of ways to do this saving to Google drive and other such cloud storage tools. But all of these seem to clunky to really foster conversation about math while students are doing it.

Are there any tools out there I’m not aware of that could do this? Is there some other approach that might work?


Source: https://quantumprogress.wordpress.com/2020/03/19/the-app-i-need-right-now/

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