Related papers: Ultra-large-scale electronic structure theory and …
Advantages of introducing the electron structure function in electron induced processes are demonstrated. At present energies the same experiment gives more precise description of the electron than photon structure. The momentum scales…
Numerical aspects of large-scale electronic state calculation are explored on flexible organic device materials. Physical theory, numerical method and real application studies are discussed in the context of…
Efficient methods are proposed, for computing integrals appeaing in electronic structure calculations. The methods consist of two parts: the first part is to represent the integrals as contour integrals and the second one is to evaluate the…
Some key notions of line geometry are recalled, along with their application to mechanics. It is then shown that most of the basic structures that one introduces in the pre-metric formulation of electromagnetism can be interpreted directly…
For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…
We describe the fundamental equations for description of electron-photon interactions in insulating nanostructures. Since the theory for the nanostructures are based on the theory for the bulk crystals, we shall describe elements of the…
We discuss our new implementation of the Real-space Electronic Structure method for studying the atomic and electronic structure of infinite periodic as well as finite systems, based on density functional theory. This improved version which…
Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of…
Most elementary numerical schemes found useful for solving classical trajectory problems are {\it canonical transformations}. This fact should be make more widely known among teachers of computational physics and Hamiltonian mechanics. From…
The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic scale structure of matter and its properties, involves transforming the Cartesian…
An efficient low-order scaling method is presented for large-scale electronic structure calculations based on the density functional theory using localized basis functions, which directly computes selected elements of the density matrix by…
Networks of silicon nanowires possess intriguing electronic properties surpassing the predictions based on quantum confinement of individual nanowires. Employing large-scale atomistic pseudopotential computations, as yet unexplored branched…
Machine learning has now become an integral part of research and innovation. The field of machine learning density functional theory has continuously expanded over the years while making several noticeable advances. We briefly discuss the…
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may…
Electronic structure calculations for solids based on many-electron wavefunctions have been hampered by the argument that for large electron numbers wavefunctions are not a legitimate scientific concept, because they face an exponential…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
We review a recent proposal of a first principles approach to the electronic structure of materials with strong electronic correlations. The scheme combines the GW method with dynamical mean field theory, which enables one to treat strong…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…