Related papers: Computer Algebra and Material Design
Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We introduce the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than…
A routine crystallography technique, crystal structure analysis, is rarely performed in computational condensed matter research. The lack of methods to identify and characterize crystal structures reliably in particle simulation data…
We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.
Information technologies for studying physical-mathematical disciplines on base of mathematical modeling in the computer algebra system Maple are described.
We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric…
The properties of soft electronic materials depend on the coupling of electronic and conformational degrees of freedom over a wide range of spatiotemporal scales. Description of such properties requires multiscale approaches capable of, at…
This paper describes REAP, a software-hardware approach that enables high performance sparse linear algebra computations on a cooperative CPU-FPGA platform. REAP carefully separates the task of organizing the matrix elements from the…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of…
With the advent of high-level programming languages capable of quickly rendering three-dimensional simulations, the inclusion of computers as a learning tool in the classroom has become more prevalent. Although work has begun to study the…
The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
Crystalline materials, with symmetrical and periodic structures, exhibit a wide spectrum of properties and have been widely used in numerous applications across electronics, energy, and beyond. For crystalline materials discovery,…