Landau levels in wrinkled and rippled graphene sheets

We study the discrete energy spectrum of curved graphene sheets in the presence of a magnetic field. The shifting of the Landau levels is determined for complex and realistic geometries of curved graphene sheets. The energy levels follow a similar square root dependence on the energy quantum number as for rippled and flat graphene sheets. The Landau levels are shifted towards lower energies proportionally to the average deformation and the effect is larger compared to a simple uni-axially rippled geometry. Furthermore, the resistivity of wrinkled graphene sheets is calculated for different average space curvatures and shown to obey a linear relation. The study is carried out with a quantum lattice Boltzmann method, solving the Dirac equation on curved manifolds.Comment: 6 pages, 4 figures, 27th International Conference on Discrete Simulation of Fluid Dynamic

Quantum spin-Hall effect on the M\"obius graphene ribbon

Topological phases of matter have revolutionized quantum engineering. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we study the topological and geometrical transport properties of a M\"obius graphene ribbon. In the absence of a magnetic field, we measure a quantum spin-Hall current on the graphene strip, originating from topology and curvature, whereas a quantum Hall current is not observed. In the torus geometry a Hall current is measured. Additionally, a specific illustration of the equivalence between the Berry and Ricci curvature is presented through a travelling wave-packet around the M\"obius band.Comment: arXiv admin note: substantial text overlap with arXiv:1810.0210

Canonical normalizing flows for manifold learning

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable invertible transformations. Therefore, once the manifold is properly aligned via a reconstruction loss, the probability density is tractable on the manifold and maximum likelihood can be used to optimize the network parameters. Naturally, the lower-dimensional representation of the data requires an injective-mapping. Recent approaches were able to enforce that the density aligns with the modelled manifold, while efficiently calculating the density volume-change term when embedding to the higher-dimensional space. However, unless the injective-mapping is analytically predefined, the learned manifold is not necessarily an efficient representation of the data. Namely, the latent dimensions of such models frequently learn an entangled intrinsic basis, with degenerate information being stored in each dimension. Alternatively, if a locally orthogonal and/or sparse basis is to be learned, here coined canonical intrinsic basis, it can serve in learning a more compact latent space representation. Toward this end, we propose a canonical manifold learning flow method, where a novel optimization objective enforces the transformation matrix to have few prominent and non-degenerate basis functions. We demonstrate that by minimizing the off-diagonal manifold metric elements $\ell_1$-norm, we can achieve such a basis, which is simultaneously sparse and/or orthogonal. Canonical manifold flow yields a more efficient use of the latent space, automatically generating fewer prominent and distinct dimensions to represent data, and a better approximation of target distributions than other manifold flow methods in most experiments we conducted, resulting in lower FID scores.Comment: NeurIPS 202

Confining massless Dirac particles in two-dimensional curved space

Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fermion wave-packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved space region. We propose a general power law expression for the probability of confinement with respect to average spatial curvature for the studied geometry.Comment: 10 pages 8 figure

Flow and Dirac particles on curved and topological manifolds

A compelling challenge for simulations is the situation when fluid flows threw confining surfaces strongly deform. Here we present a novel method for fluid structure interaction (FSI) simulations where an original 2$^{nd}$-order curved space lattice Boltzmann fluid solver (LBM) is coupled to a finite element method (FEM) for thin shells. The LBM can work independently on a standard lattice in curved coordinates without the need for interpolation, re-meshing or an immersed boundary. The LBM distribution functions are transformed dynamically under coordinate change. In addition, force and momentum can be calculated on the nodes exactly in any geometry. Furthermore, the FEM shell is a complete numerical tool with implementations such as growth, self-contact and strong external forces. We show resolution convergent error for standard tests under metric deformation. Mass and volume conservation, momentum transfer, boundary-slip and pressure maintenance are verified through specific examples. Additionally, a brief deformation stability analysis is carried out. Next, we study the interaction of a square fluid flow channel to a deformable shell. Finally, we simulate a flag at moderate Reynolds number, air flow channel. The scheme is limited to small deformations of $\mathcal{O}(10\%)$ relative to domain size, by improving its stability the method can be naturally extended to multiple applications without further implementations. Furthermore, it is common knowledge that Dirac particles have been notoriously difficult to confine, an important property in the context of quantum computing and waveguides. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fermion wave-packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved space region. We propose a general power law expression for the probability of confinement with respect to average spatial curvature for the studied geometry. Additionally, the characteristic 2D honeycomb carbon atom lattice of graphene makes it a perfect flat electronic material which can be stacked and reshaped resulting in spectacular electronic properties. Here we study the discrete energy spectrum of curved graphene sheets in the presence of a magnetic field. The shifting of the Landau levels is determined for complex and realistic geometries of curved graphene sheets. The energy levels follow a similar square root dependence on the energy quantum number as for rippled and flat graphene sheets. The Landau levels are shifted towards lower energies proportionally to the average deformation and the effect is larger compared to a simple uni-axially rippled geometry. The resistivity of wrinkled graphene sheets is calculated for different average space curvatures and shown to obey a linear relation. Moreover, we propose a periodic quantized alternating current device with a curved graphene sheet. The study is carried out with a quantum lattice Boltzmann method, solving the Dirac equation on curved manifolds. Finally, it is currently evident that topological phases of matter have revolutionized quantum engineering. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we study the topological and geometrical transport properties of a M\"obius graphene ribbon. We measure a quantum Spin-Hall current on the graphene strip, in the absence of a magnetic field, originating from topology and curvature, whereas a quantum Hall current is not observed. In the torus geometry a Hall current is measured. Additionally, a specific illustration of the equivalence between the Berry and Ricci curvature is presented through a travelling wave-packet around the M\"obius band

Quantized Alternate Current on Curved Graphene

Based on the numerical solution of the Quantum Lattice Boltzmann Method in curved space, we predicted the onset of a quantized alternating current on curved graphene sheets. This numerical prediction was verified analytically via a set of semi-classical equations that related the Berry curvature to real space curvature. The proposed quantized oscillating current on curved graphene could form the basis for the implementation of quantum information-processing algorithms

Explicitly Minimizing the Blur Error of Variational Autoencoders

Variational autoencoders (VAEs) are powerful generative modelling methods, however they suffer from blurry generated samples and reconstructions compared to the images they have been trained on. Significant research effort has been spent to increase the generative capabilities by creating more flexible models but often flexibility comes at the cost of higher complexity and computational cost. Several works have focused on altering the reconstruction term of the evidence lower bound (ELBO), however, often at the expense of losing the mathematical link to maximizing the likelihood of the samples under the modeled distribution. Here we propose a new formulation of the reconstruction term for the VAE that specifically penalizes the generation of blurry images while at the same time still maximizing the ELBO under the modeled distribution. We show the potential of the proposed loss on three different data sets, where it outperforms several recently proposed reconstruction losses for VAEs

3D-printed iodine-ink CT phantom for radiomics feature extraction - advantages and challenges

Background To test and validate novel CT techniques, such as texture analysis in radiomics, repeat measurements are required. Current anthropomorphic phantoms lack fine texture and true anatomic representation. 3D-printing of iodinated ink on paper is a promising phantom manufacturing technique. Previously acquired or artificially created CT data can be used to generate realistic phantoms. Purpose: To present the design process of an anthropomorphic 3D-printed iodine ink phantom, highlighting the different advantages and pitfalls in its use. To analyze the phantom's X-ray attenuation properties, and the influences of the printing process on the imaging characteristics, by comparing it to the original input dataset. Methods Two patient CT scans and artificially generated test patterns were combined in a single dataset for phantom printing and cropped to a size of 26 × 19 × 30 cm3. This DICOM dataset was printed on paper using iodinated ink. The phantom was CT-scanned and compared to the original image dataset used for printing the phantom. The water-equivalent diameter of the phantom was compared to that of a patient cohort (N = 104). Iodine concentrations in the phantom were measured using dual-energy CT. 86 radiomics features were extracted from 10 repeat phantom scans and the input dataset. Features were compared using a histogram analysis and a PCA individually and overall, respectively. The frequency content was compared using the normalized spectrum modulus. Results Low density structures are depicted incorrectly, while soft tissue structures show excellent visual accordance with the input dataset. Maximum deviations of around 30 HU between the original dataset and phantom HU values were observed. The phantom has X-ray attenuation properties comparable to a lightweight adult patient (∼54 kg, BMI 19 kg/m2). Iodine concentrations in the phantom varied between 0 and 50 mg/ml. PCA of radiomics features shows different tissue types separate in similar areas of PCA representation in the phantom scans as in the input dataset. Individual feature analysis revealed systematic shift of first order radiomics features compared to the original dataset, while some higher order radiomics features did not. The normalized frequency modulus |f(ω)| of the phantom data agrees well with the original data. However, all frequencies systematically occur more frequently in the phantom compared to the maximum of the spectrum modulus than in the original data set, especially for mid-frequencies (e.g., for ω = 0.3942 mm−1, |f(ω)|original = 0.09 * |fmax|original and |f(ω)|phantom = 0.12 * |fmax|phantom). Conclusions 3D-iodine-ink-printing technology can be used to print anthropomorphic phantoms with a water-equivalent diameter of a lightweight adult patient. Challenges include small residual air enclosures and the fidelity of HU values. For soft tissue, there is a good agreement between the HU values of the phantom and input data set. Radiomics texture features of the phantom scans are similar to the input data set, but systematic shifts of radiomics features in first order features, due to differences in HU values, need to be considered. The paper substrate influences the spatial frequency distribution of the phantom scans. This phantom type is of very limited use for dual-energy CT analyses.ISSN:0094-2405ISSN:2473-4209ISSN:1522-854