Substrate-supported triplet superconductivity in Dirac semimetals

Stimulated by the success of graphene and its emerging Dirac physics, the quest for versatile and tunable electronic properties in atomically thin systems has led to the discovery of various chemical classes of 2D compounds. In particular, honeycomb lattices of group-IV elements, such as silicene and germanene, have been found experimentally. Whether it is a necessity of synthesis or a desired feature for application purposes, most 2D materials demand a supporting substrate. In this work, we highlight the constructive impact of substrates to enable the realization of exotic electronic quantum states of matter, where the buckling emerges as the decisive material parameter adjustable by the substrate. At the example of germanene deposited on MoS$_2$, we find that the coupling between the monolayer and the substrate, together with the buckled hexagonal geometry, conspire to provide a highly suited scenario for unconventional triplet superconductivity upon adatom-assisted doping.Comment: 11 pages, 8 figure

Computerized Design of Low-noise Face-milled Spiral Bevel Gears

An advanced design methodology is proposed for the face-milled spiral bevel gears with modified tooth surface geometry that provides a reduced level of noise and has a stabilized bearing contact. The approach is based on the local synthesis of the gear drive that provides the 'best' machine-tool settings. The theoretical aspects of the local synthesis approach are based on the application of a predesigned parabolic function for absorption of undesirable transmission errors caused by misalignment and the direct relations between principal curvatures and directions for mating surfaces. The meshing and contact of the gear drive is synthesized and analyzed by a computer program. The generation of gears with the proposed geometry design can be accomplished by application of existing equipment. A numerical example that illustrates the proposed theory is presented

Learning Compositional Visual Concepts with Mutual Consistency

Compositionality of semantic concepts in image synthesis and analysis is appealing as it can help in decomposing known and generatively recomposing unknown data. For instance, we may learn concepts of changing illumination, geometry or albedo of a scene, and try to recombine them to generate physically meaningful, but unseen data for training and testing. In practice however we often do not have samples from the joint concept space available: We may have data on illumination change in one data set and on geometric change in another one without complete overlap. We pose the following question: How can we learn two or more concepts jointly from different data sets with mutual consistency where we do not have samples from the full joint space? We present a novel answer in this paper based on cyclic consistency over multiple concepts, represented individually by generative adversarial networks (GANs). Our method, ConceptGAN, can be understood as a drop in for data augmentation to improve resilience for real world applications. Qualitative and quantitative evaluations demonstrate its efficacy in generating semantically meaningful images, as well as one shot face verification as an example application.Comment: 10 pages, 8 figures, 4 tables, CVPR 201

Ising Model on the Affine Plane

We demonstrate that the Ising model on a general triangular graph with 3 distinct couplings $K_1,K_2,K_3$ corresponds to an affine transformed conformal field theory (CFT). Full conformal invariance of the $c= 1/2$ minimal CFT is restored by introducing a metric on the lattice through the map $\sinh(2K_i) = \ell^*_i/ \ell_i$ which relates critical couplings to the ratio of the dual hexagonal and triangular edge lengths. Applied to a 2d toroidal lattice, this provides an exact lattice formulation in the continuum limit to the Ising CFT as a function of the modular parameter. This example can be viewed as a quantum generalization of the finite element method (FEM) applied to the strong coupling CFT at a Wilson-Fisher IR fixed point and suggests a new approach to conformal field theory on curved manifolds based on a synthesis of simplicial geometry and projective geometry on the tangent planes

The Euclidean Mousetrap: Schopenhauer’s Criticism of the Synthetic Method in Geometry

In his doctoral dissertation On the Principle of Sufficient Reason, Arthur Schopenhauer there outlines a critique of Euclidean geometry on the basis of the changing nature of mathematics, and hence of demonstration, as a result of Kantian idealism. According to Schopenhauer, Euclid treats geometry synthetically, proceeding from the simple to the complex, from the known to the unknown, “synthesizing” later proofs on the basis of earlier ones. Such a method, although proving the case logically, nevertheless fails to attain the raison d’être of the entity. In order to obtain this, a separate method is required, which Schopenhauer refers to as “analysis,” thus echoing a method already in practice among the early Greek geometers, with however some significant differences. In this essay, I here discuss Schopenhauer’s criticism of synthesis in Euclid’s Elements, and the nature and relevance of his own method of analysis

Learning to Synthesize a 4D RGBD Light Field from a Single Image

We present a machine learning algorithm that takes as input a 2D RGB image and synthesizes a 4D RGBD light field (color and depth of the scene in each ray direction). For training, we introduce the largest public light field dataset, consisting of over 3300 plenoptic camera light fields of scenes containing flowers and plants. Our synthesis pipeline consists of a convolutional neural network (CNN) that estimates scene geometry, a stage that renders a Lambertian light field using that geometry, and a second CNN that predicts occluded rays and non-Lambertian effects. Our algorithm builds on recent view synthesis methods, but is unique in predicting RGBD for each light field ray and improving unsupervised single image depth estimation by enforcing consistency of ray depths that should intersect the same scene point. Please see our supplementary video at https://youtu.be/yLCvWoQLnmsComment: International Conference on Computer Vision (ICCV) 201

A Shape-Aware Model for Discrete Texture Synthesis

International audienceWe present a novel shape-aware method for synthesizing 2D and 3D discrete element textures consisting of collections of distinct vector graphics objects. Extending the long-proven point process framework, we propose a shape process, a novel stochastic model based on spatial measurements that fully take into account the geometry of the elements. We demonstrate that our approach is well-suited for discrete texture synthesis by example. Our modelenables for both robust statistical parameter estimation and reliable output generation by Monte Carlo sampling. Our numerous experiments show that contrary to current state-of-the-art techniques, our algorithm manages to capture anisotropic element distributions and systematically prevents undesirable collisions between objects