Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations

We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $\Gamma_\vartheta$, $\Gamma^0(2)$ and $\Gamma_0(2)$ of $\text{SL}_2(\mathbb Z)$. Each subgroup corresponds to one of the spin structures on the torus. The pole structures of the fermionic MLDEs are investigated by exploiting the valence formula for the level-two congruence subgroups. We focus on the first and second order holomorphic MLDEs without poles and use them to find a large class of `Fermionic Rational Conformal Field Theories', which have non-negative integer coefficients in the $q$-series expansion of their characters. We study the detailed properties of these fermionic RCFTs, some of which are supersymmetric. This work also provides a starting point for the classification of the fermionic Modular Tensor Category.Comment: 63 pages, 4 figures, 19 tables, references added, minor correction

Dual Garside structure and reducibility of braids

Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-theoretical properties. Namely, they showed that if a braid sends a curve to another curve, then the image of this curve after each factor of the left normal form of the braid (with the classical Garside structure) is also standard. We provide a new simple, geometric proof of the result by Benardete-Gutierrez-Nitecki, which can be easily adapted to the case of the dual Garside structure of braid groups, with the appropriate definition of standard curves in the dual setting. This yields a new algorithm for determining the Nielsen-Thurston type of braids

Direct Spectroscopic Observation of Cross-Plane Heat Transfer in a Two-Dimensional Van der Waals Heterostructure

Two-dimensional (2D) transition metal chalcogenides (TMDs) have drawn significant attention in recent years due to their extraordinary optical and electronic properties. As heat transfer plays an important role in device performance, various methods such as optothermal Raman spectroscopy and time-domain thermoreflectance have been developed to measure the thermal conductivity and interfacial thermal conductance in 2D van der Waals (vdW) heterostructures. Here, we employ the vibrational-pump-visible-probe (VPVP) spectroscopy to directly visualize the heat transfer process in a heterostructure of multilayer h-BN and monolayer WS2. Following an impulsive vibrational excitation of h-BN in the mid-infrared, we probe the heat transfer from h-BN through WS2 and finally to the substrate from the subpicosecond to the submicrosecond timescale. The interfacial thermal conductance of the h-BN/WS2 and WS2/SiO2 interfaces is obtained by corroborating the experiments with heat transfer calculations based on the Fourier’s law of heat conduction. Our study demonstrates an alternative, time-resolved optical method to measure cross-plane heat dissipation and opens up a new pathway to investigate the interlayer electron–phonon and phonon–phonon interactions in vdW heterostructures

Steps Before Syntax: Helping Novice Programmers Solve Problems using the PCDIT Framework

Novice programmers often struggle with problem solving due to the high cognitive loads they face. Furthermore, many introductory programming courses do not explicitly teach it, assuming that problem solving skills are acquired along the way. In this paper, we present 'PCDIT', a non-linear problem solving framework that provides scaffolding to guide novice programmers through the process of transforming a problem specification into an implemented and tested solution for an imperative programming language. A key distinction of PCDIT is its focus on developing concrete cases for the problem early without actually writing test code: students are instead encouraged to think about the abstract steps from inputs to outputs before mapping anything down to syntax. We reflect on our experience of teaching an introductory programming course using PCDIT, and report the results of a survey that suggests it helped students to break down challenging problems, organise their thoughts, and reach working solutions

Interpretation of two SINBAD photon-leakage benchmarks with nuclear library ENDF/B-VIII.0 and Monte Carlo code MCS

A review of the documentation and an interpretation of the NEA-1517/74 and NEA-1517/80 shielding benchmarks (measurements of photon leakage flux from a hollow sphere with a central 14 MeV neutron source) from the SINBAD database with the Monte Carlo code MCS and the most up-to-date ENDF/B-VIII.0 neutron data library are conducted. The two analyzed benchmarks describe satisfactorily the energy resolution of the photon detector and the geometry of the spherical samples with inner beam tube, tritium target and cooling water circuit, but lack information regarding the detector geometry and the distances of shields and collimators relatively to the neutron source and the detector. Calculations are therefore conducted for a sphere model only. A preliminary verification of MCS neutron-photon calculations against MCNP6.2 is first conducted, then the impact of modelling the inner beam tube, tritium target and cooling water circuit is assessed. Finally, a comparison of calculated results with the libraries ENDF/B-VII.1 and ENDF/B-VIII.0 against the measurements is conducted and shows reasonable agreement. The MCS and MCNP inputs used for the interpretation are available as supplementary material of this article. (C) 2019 Korean Nuclear Society, Published by Elsevier Korea LLC

Supernova Propagation And Cloud Enrichment: A new model for the origin of 60^{60}Fe in the early solar system

The radioactive isotope $^{60}$Fe ($T_{1/2} = 1.5$ Myr) was present in the early solar system. It is unlikely that it was injected directly into the nascent solar system by a single, nearby supernova. It is proposed instead that it was inherited during the molecular cloud stage from several supernovae belonging to previous episodes of star formation. The expected abundance of $^{60}$Fe in star forming regions is estimated taking into account the stochasticity of the star-forming process, and it is showed that many molecular clouds are expected to contain $^{60}$Fe (and possibly $^{26}$Al [$T_{1/2} = 0.74$ Myr]) at a level compatible with that of the nascent solar system. Therefore, no special explanation is needed to account for our solar system's formation.Comment: 15 pages, 3 figure