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An example is the Stone Wales defect in nanotubes, which consists of two adjacent 5-membered and two 7-membered atom rings. Schematic illustration of defects in a compound solid, using GaAs as an example. Amorphous solids may contain defects. These are naturally somewhat hard to define, but sometimes their nature can be quite easily understood.
The relationship is defined by a symmetry operation called a twin operation. [1] [2] The twin operation is not one of the normal symmetry operations of the untwinned crystal structure. For example, the twin operation may be reflection across a plane that is not a symmetry plane of the single crystal. [1] [2]
Theo Pavlidis' Algorithm is a well-known method for contour tracing in binary images proposed, designed to methodically detect and follow the boundaries of related components. The technique starts by locating an initial boundary pixel, which is usually the first black pixel seen while scanning the image from top to bottom and left to right.
PyOD is an open-source Python library developed specifically for anomaly detection. [56] scikit-learn is an open-source Python library that contains some algorithms for unsupervised anomaly detection. Wolfram Mathematica provides functionality for unsupervised anomaly detection across multiple data types [57]
The method of images (or method of mirror images) is a mathematical tool for solving differential equations, in which boundary conditions are satisfied by combining a solution not restricted by the boundary conditions with its possibly weighted mirror image. Generally, original singularities are inside the domain of interest but the function is ...
The striped borders correspond to perfectly matched layers, which are used to simulate open boundaries by absorbing the outgoing waves. A perfectly matched layer ( PML ) is an artificial absorbing layer for wave equations , commonly used to truncate computational regions in numerical methods to simulate problems with open boundaries, especially ...
Physics-informed neural networks for solving Navier–Stokes equations. Physics-informed neural networks (PINNs), [1] also referred to as Theory-Trained Neural Networks (TTNs), [2] are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs).
An electron backscatter diffraction pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source. Electron backscatter diffraction (EBSD) is a scanning electron microscopy (SEM) technique used to study the crystallographic structure of materials.