Simulations of particle acceleration beyond the classical synchrotron burnoff limit in magnetic reconnection: An explanation of the Crab flares

It is generally accepted that astrophysical sources cannot emit synchrotron radiation above 160 MeV in their rest frame. This limit is given by the balance between the accelerating electric force and the radiation reaction force acting on the electrons. The discovery of synchrotron gamma-ray flares in the Crab Nebula, well above this limit, challenges this classical picture of particle acceleration. To overcome this limit, particles must accelerate in a region of high electric field and low magnetic field. This is possible only with a non-ideal magnetohydrodynamic process, like magnetic reconnection. We present the first numerical evidence of particle acceleration beyond the synchrotron burnoff limit, using a set of 2D particle-in-cell simulations of ultra-relativistic pair plasma reconnection. We use a new code, Zeltron, that includes self-consistently the radiation reaction force in the equation of motion of the particles. We demonstrate that the most energetic particles move back and forth across the reconnection layer, following relativistic Speiser orbits. These particles then radiate >160 MeV synchrotron radiation rapidly, within a fraction of a full gyration, after they exit the layer. Our analysis shows that the high-energy synchrotron flux is highly variable in time because of the strong anisotropy and inhomogeneity of the energetic particles. We discover a robust positive correlation between the flux and the cut-off energy of the emitted radiation, mimicking the effect of relativistic Doppler amplification. A strong guide field quenches the emission of >160 MeV synchrotron radiation. Our results are consistent with the observed properties of the Crab flares, supporting the reconnection scenario.Comment: 15 pages, 16 figures, Accepted for publication in The Astrophysical Journa

Numerical simulation of the magnetization of high-temperature superconductors: 3D finite element method using a single time-step iteration

We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects associated with currents that are not perpendicular to the local magnetic induction. We consider samples that are subjected to a uniform magnetic field varying linearly with time. Their magnetization is calculated by means of a weak formulation in the magnetostatic approximation of the Maxwell equations (A-phi formulation). An implicit method is used for the temporal resolution (Backward Euler scheme) and is solved in the open source solver GetDP. Picard iterations are used to deal with the power law conductivity of HTS. The finite element formulation is validated for an HTS tube with large pinning strength through the comparison with results obtained with other well-established methods. We show that carrying the calculations with a single time-step (as opposed to many small time-steps) produce results with excellent accuracy in a drastically reduced simulation time. The numerical method is extended to the study of the trapped magnetization of cylinders that are drilled with different arrays of columnar holes arranged parallel to the cylinder axis

Mathematics in Popular Culture: An Analysis of Mathematical Internet Memes

Popular culture has had a great deal of impact on our social, cultural, and political worlds; it is portrayed through different mediums, in different forms, and connects the world to ideas, beliefs, and different perspectives. Though this dissertation is part of a larger body of work that examines the complex relationship between popular culture and mathematical identity, this study takes a different perspective by examining it through the lens of mathematical Internet memes. This study was conducted with 31 secondary school participants and used a two-tiered approach (in-depth focus groups and an individual meme activity) at each of the five school sites visited around New York City. Multiple sources of data were used to reveal that students are receiving messages about mathematics from memes in popular culture. In particular, participants described six core themes from the meme inventory: (1) stereotypical views of mathematics; (2) mathematics is too complicated; (3) no effort should be needed in mathematics; (4) mathematics is useless; (5) mathematics is not fun; and (6) sense of accomplishment from mathematics. Participants were also given free rein to create hypothetical mathematics memes. Findings demonstrate that not only are memes being used to depict mathematical stereotypes, thereby reinforcing negative messages, but also support social media practices (liking, commenting, sharing, and creating) that reify negative messages about mathematics with little to no resistance from opposing perspectives. In general, participants described mathematical memes in a specific manner that demonstrates them having influence over students’ mathematical identity but not entirely on the way one may think. Future research implications include explorations of the “new” online mathematical space students are utilizing; to wit, what makes these specific memes go viral? What are common misconceptions? Are commenters learning from their mistakes and other answer responses? Implications for practice include the creation of formal spaces within classrooms and communities for students to debrief their thoughts and sentiments about mathematics, as well as informal opportunities for educators, students, and community members to engage positively about mathematics: because without these interventions the messages found in memes, whether positive or negative, are potentially legitimized through popular culture’s presentations. Moreover, the results of this study also show that students are unaware of the processes and proficiencies of mathematical learning. More specifically, teachers and others must help students understand knowledge is not transmitted by copying notes or that teaching strategies need to account for students being apprehensive to ask questions in a mathematics classroom. Memes can also be used to explore mathematics content, through error analysis and explanation of concepts

Social Sustainability in Trade and Development Policy: A Life Cycle Approach to Understanding and Managing Social Risk Attributable to Production and Consumption in the EU-27

Improving social sustainability within Europe and abroad is among the founding premises of the European Union. European Commission external policy documents – in particular, those associated with trade and development - explicitly call for the use of policy instruments as a means of improving social conditions in third countries. Unclear, however, is the extent to which progress in social sustainability as a result of Commission policy measures is being assessed, or measures to further leverage improved social sustainability implemented. Life cycle thinking (LCT) refers to a management philosophy predicated on holistic consideration of management alternatives for the purpose of preventing unintentional burden shifting – whether between supply chain activities or issue areas. Significant strides have already been made in the environmental domain to operationalize life cycle thinking in European Commission policies, with supporting methodological norms, frameworks, tools and data. To date, comparable approaches and instruments are lacking in support of life cycle-based social sustainability policy initiatives. Such information and tools are critical in support of improved policy design, implementation, monitoring and/or reformulation. Social risk refers to the potential for one or more parties to be exposed to negative social conditions that, in turn, undermine social sustainability. We conducted a macro-scale analysis of the social risk profile of EU-27 trade by combining trade statistics regarding imports from intra- and extra-territorial trading partners in 2010 with country and sector-specific social risk indicator data. These data cover 17 social themes in five thematic areas: Labour Rights and Decent Work; Health and Safety; Human Rights; Governance; and Community Infrastructure. We assessed the apparent social risk profiles of EU-27 imports based on consideration of country-of-origin social risk data only, compared to a life cycle-based social risk assessment which took into account the distribution of social risk along product supply chains. Our intention was to better understand how and to what extent current trade-based consumption in the EU-27 may be associated with socially unsustainable conditions, and the value of applying a life cycle perspective for sustainability management in this context. Our analysis underscores the importance of a life cycle-based approach to understanding and managing social risk in support of policies for socially sustainable development. Moreover, the methods and information presented herein offer a potentially powerful decision-support tool for policy makers wishing to better understand the magnitude and distribution of social risk associated with EU production and consumption patterns, the mitigation of which will contribute to socially sustainable development within Europe and abroad. A novel opportunity hence presents itself for decision makers and those who provide scientific and technical support to policy making to collaborate closely in moving forward the agenda for socially sustainable development. This will require the identification of strategic policy directions and supporting research projects, building upon existing, complementary environmental and economic sustainability assessment tools within the European Commission, which will continue to strengthen the elaboration, implementation, and impact assessment of science-based policy for sustainable development.JRC.H.8 - Sustainability Assessmen

Periodic squeezing in a polariton Josephson junction

The use of a Kerr nonlinearity to generate squeezed light is a well-known way to surpass the quantum noise limit along a given field quadrature. Nevertheless, in the most common regime of weak nonlinearity, a single Kerr resonator is unable to provide the proper interrelation between the field amplitude and squeezing required to induce a sizable deviation from Poissonian statistics. We demonstrate experimentally that weakly coupled bosonic modes allow exploration of the interplay between squeezing and displacement, which can give rise to strong deviations from the Poissonian statistics. In particular, we report on the periodic bunching in a Josephson junction formed by two coupled exciton-polariton modes. Quantum modeling traces the bunching back to the presence of quadrature squeezing. Our results, linking the light statistics to squeezing, are a precursor to the study of nonclassical features in semiconductor microcavities and other weakly nonlinear bosonic systems.Comment: 6 pages, 4 figure

Meme-ingful mathematics: crafting critical conversations about mathematics through student meme analysis

Published versionOur view of self is built upon our understanding of the world and its history, much of which is crafted by interactions beyond the classroom, including “the Internet, films, newspapers, television programs, novels, and strip cartoons” (Joseph, 2011, p.1). Through these interactions, society crafts conceptions about those who enjoy the study of mathematics. Hersh and John- Steiner (2011) outline four common myths about mathematics; mathematicians “lack emotional complexity” (p. 2), the study of mathematics “is a solitary pursuit” (p. 4), the great mathematicians are young and male, and that “mathematics is an effective filter for higher education” (p. 6). More generally, our society tends to view those who do well in mathematics as gifted, smart, nerdy, or crazy (Boaler, 2022; Hall & Surrtamm, 2020; Epstein et al., 2010). These same messages about mathematics are replicated throughout social media by way of the creation and distribution of memes - “small cultural units of transmission that flow from person to person by copying or imitation” (Gal et al., 2016, p. 1700). The more popular or relatable the message, the more swiftly it is copied within each online echo chamber or ecosystem (Gleeson et al., 2014). Through their study, Bini et al. (2020) established that mathematical memes elicit ideas about mathematics and create openings for the collective meaning-making of the mathematical idea encoded in the meme.https://www.pmena.org/pmenaproceedings/PMENA%2045%202023%20Proceedings%20Vol%202.pdfPublished versio

Pre-service teachers' interrogation of mathematics education following a digital clinical simulation

This preliminary study explores how digital clinical simulations can reveal pre-service teachers’ understanding of equity and mathematical instructional decisions. Pre-service teachers engaged in a digital clinical simulation where their responses to scripted mathematical small group scenarios led them to different simulated outcomes. The analysis of the full class debrief conversation following the simulation experience surfaced how pre-service teachers interrogated the boundaries of mathematics education. This revealed how they felt tension about certain conceptualizations of mathematics teaching and equitable pedagogies. This study suggests that digital clinical simulations could support pre-service teachers’ sensemaking of the inherent relationship between mathematical pedagogy and equitable orientations through moments of tension within the simulation, and interrogation of that norm during the debrief.Massachusetts Institute of Technologyhttps://www.pmena.org/pmenaproceedings/PMENA%2045%202023%20Proceedings%20Vol%201.pdfPublished versio