Ising films with surface defects

The influence of surface defects on the critical properties of magnetic films is studied for Ising models with nearest-neighbour ferromagnetic couplings. The defects include one or two adjacent lines of additional atoms and a step on the surface. For the calculations, both density-matrix renormalization group and Monte Carlo techniques are used. By changing the local couplings at the defects and the film thickness, non-universal features as well as interesting crossover phenomena in the magnetic exponents are observed.Comment: 8 pages, 12 figures included, submitted to European Physical Journal

Surface Defects and Chiral Algebras

We investigate superconformal surface defects in four-dimensional N=2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfeld-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. In each case we find perfect agreement with the predicted characters.Comment: 52 pages, 1 tabl

Surface defects and elliptic quantum groups

A brane construction of an integrable lattice model is proposed. The model is composed of Belavin's R-matrix, Felder's dynamical R-matrix, the Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining operators. This construction implies that a family of surface defects act on supersymmetric indices of four-dimensional $\mathcal{N} = 1$ supersymmetric field theories as transfer matrices related to elliptic quantum groups.Comment: 31 pages. v2: minor changes and corrections; v3: minor improvements, published versio

Bicategories for boundary conditions and for surface defects in 3-d TFT

We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that lift to trivializations in the Witt group of modular tensor categories. The bicategory of boundary conditions can be described through the bicategory of module categories over any such trivialization. A similar description is obtained for topological surface defects. Using string diagrams for bicategories we also establish a precise relation between special symmetric Frobenius algebras and Wilson lines involving special defects. We compare our results with previous work of Kapustin-Saulina and of Kitaev-Kong on boundary conditions and surface defects in abelian Chern-Simons theories and in Turaev-Viro type TFTs, respectively.Comment: 34 pages, some figures. v2: references added. v3: typos corrected and biliography update

Uneven illumination surface defects inspection based on convolutional neural network

Surface defect inspection based on machine vision is often affected by uneven illumination. In order to improve the inspection rate of surface defects inspection under uneven illumination condition, this paper proposes a method for detecting surface image defects based on convolutional neural network, which is based on the adjustment of convolutional neural networks, training parameters, changing the structure of the network, to achieve the purpose of accurately identifying various defects. Experimental on defect inspection of copper strip and steel images shows that the convolutional neural network can automatically learn features without preprocessing the image, and correct identification of various types of image defects affected by uneven illumination, thus overcoming the drawbacks of traditional machine vision inspection methods under uneven illumination

Holographic entanglement entropy of surface defects

We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in ${\cal N}=4$ Super Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussedComment: 41 pages. pdflatex, 3 figures. v2: typos corrected, reference corrected, some comments on CFT interpretation added. v3: references added, some clarification

Theory, Simulation and Nanotechnological Applications of Adsorption on a Surface with Defects

Theory of adsorption on a surface with nanolocal defects is proposed. Two efficacy parameters of surface modification for nanotechnological purposes are introduced, where the modification is a creation of nanolocal artificial defects. The first parameter corresponds to applications where it is necessary to increase the concentration of certain particles on the modified surface. And the second one corresponds to the pattern transfer with the help of particle self-organization on the modified surface. The analytical expressions for both parameters are derived with the help of the thermodynamic and the kinetic approaches for two cases: jump diffusion and free motion of adsorbed particles over the surface. The possibility of selective adsorption of molecules is shown with the help of simulation of the adsorption of acetylene and benzene molecules in the pits on the graphite surface. The process of particle adsorption from the surface into the pit is theoretically studied by molecular dynamic technique. Some possible nanotechnological applications of adsorption on the surface with artificial defects are considered: fabrication of sensors for trace molecule detection, separation of isomers, and pattern transfer.Comment: 12 pages, 2 Postscript figures. Submitted to Surface Science (1998