About optimal loss function for training physics-informed neural networks under respecting causality

A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for physics-informed neural networks (PINNs) methodology is that it becomes possible to represent the loss function in the form of a single term associated with differential equations, thus eliminating the need to tune the scaling coefficients for the terms related to boundary and initial conditions. The weighted loss functions respecting causality were modified and new weighted loss functions based on generalized functions are derived. Numerical experiments have been carried out for a number of problems, demonstrating the accuracy of the proposed methods.Comment: 25 pages, 7 figures, 6 table

Dangling bonds and magnetism of grain boundaries in graphene

Grain boundaries with dangling bonds (DBGB) in graphene are studied by atomistic Monte Carlo and molecular dynamics simulations in combination with density functional (SIESTA) calculations. The most stable configurations are selected and their structure is analyzed in terms of grain boundary dislocations. It is shown that the grain boundary dislocation with the core consisting of pentagon, octagon and heptagon (5-8-7 defect) is a typical structural element of DBGB with relatively low energies. Electron energy spectrum and magnetic properties of the obtained DBGB are studied by density functional calculations. It is shown that the 5-8-7 defect is magnetic and that its magnetic moment survives after hydrogenation. The effects of hydrogenation and of out of plane deformations on the magnetic properties of DBGB are studied.Comment: 10 pages, 11 figures, 4 tables, the final version accepted in pr

Electronic states of disordered grain boundaries in graphene prepared by chemical vapor deposition

Perturbations of the two dimensional carbon lattice of graphene, such as grain boundaries, have significant influence on the charge transport and mechanical properties of this material. Scanning tunneling microscopy measurements presented here show that localized states near the Dirac point dominate the local density of states of grain boundaries in graphene grown by chemical vapor deposition. Such low energy states are not reproduced by theoretical models which treat the grain boundaries as periodic dislocation-cores composed of pentagonal-heptagonal carbon rings. Using ab initio calculations, we have extended this model to include disorder, by introducing vacancies into a grain boundary consisting of periodic dislocation-cores. Within the framework of this model we were able to reproduce the measured density of states features. We present evidence that grain boundaries in graphene grown on copper incorporate a significant amount of disorder in the form of two-coordinated carbon atoms. © 2013 Elsevier Ltd. All rights reserved

Visualizing chemical states and defects induced magnetism of graphene oxide by spatially-resolved-X-ray microscopy and spectroscopy

[[abstract]]This investigation studies the various magnetic behaviors of graphene oxide (GO) and reduced graphene oxides (rGOs) and elucidates the relationship between the chemical states that involve defects therein and their magnetic behaviors in GO sheets. Magnetic hysteresis loop reveals that the GO is ferromagnetic whereas photo-thermal moderately reduced graphene oxide (M-rGO) and heavily reduced graphene oxide (H-rGO) gradually become paramagnetic behavior at room temperature. Scanning transmission X-ray microscopy and corresponding X-ray absorption near-edge structure spectroscopy were utilized to investigate thoroughly the variation of the C 2p(π*) states that are bound with oxygen-containing and hydroxyl groups, as well as the C 2p(σ*)-derived states in flat and wrinkle regions to clarify the relationship between the spatially-resolved chemical states and the magnetism of GO, M-rGO and H-rGO. The results of X-ray magnetic circular dichroism further support the finding that C 2p(σ*)-derived states are the main origin of the magnetism of GO. Based on experimental results and first-principles calculations, the variation in magnetic behavior from GO to M-rGO and to H-rGO is interpreted, and the origin of ferromagnetism is identified as the C 2p(σ*)- derived states that involve defects/vacancies rather than the C 2p(π*) states that are bound with oxygen-containing and hydroxyl groups on GO sheets.[[notice]]補正完

Structure and magnetism of defected carbon materials

Contains fulltext : 101516.pdf (publisher's version ) (Open Access)Radboud Universiteit Nijmegen, 25 februari 2013Promotores : Fasolino, A., Katsnelson, M.I.106 p

Structure and magnetism of disordered carbon

Contains fulltext : 111434.pdf (preprint version ) (Open Access

Mechanism and free-energy barrier of the type-57 reconstruction of the zigzag edge of graphene

Contains fulltext : 92060.pdf (publisher's version ) (Open Access

Data on generation of Kekulé structures for graphenes, graphynes, nanotubes and fullerenes and their aza-analogs

Two new features are added to existing algorithms for kekulization of chemical structures, i.e., handling of triple and cumulene bonds in cycles and use of random atom sorting to remove unmatched atoms. Handling of triple and cumulene bonds enables kekulization of graphynes and graphdiynes. Random sorting speeds up the calculation time, i.e., kekulization of large chemical structures containing about 107 atoms takes ≤1 min on a typical PC. Source codes (Pascal, GNU GPL license) are included as a compiled application (Windows 64). Calculation times and unmatched atom statistics are provided for graphenes, graphynes, nanotubes, graphyne nanotubes and fullerenes. Benchmark comparisons are made for some data

Electronic, magnetic and transport properties of graphene ribbons terminated by nanotubes

Contains fulltext : 103336.pdf (author's version ) (Open Access