相关论文: A tool for teaching General Relativity
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
The teaching of general relativity at the secondary school and lower undergraduate university levels is necessarily based on approaches with a restricted use of mathematics. An important aspect of teaching general relativity at this level…
This paper is on customization of computer models using the Easy Java Simulation authoring toolkit for the Singapore syllabus, based on real astronomical data, supported with literature reviewed researched pedagogical features. These 4 new…
From the first approach to General Relativity we learn about the Christoffel symbols, and it is easy to notice that their coordinated components do not transform as a tensor. It is then confusing to find renowned books on the subject that…
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This…
We develop an Easy Java Simulation (EJS) model for students to visualize geostationary orbits near Earth, modeled using Java 3D implementation of the EJS 3D library. The simplified physics model is described and simulated using simple…
Creating software dedicated to simulation is essential for teaching and research in Science, Technology, Engineering, and Mathematics (STEM). Physics lecturing can be more effective when digital twins are used to accompany theory classes.…
We present the basic concepts of tensor products of vector spaces, emphasizing linear algebraic and combinatorial techniques as needed for applied areas of research. The topics include (1) Introduction; (2) Basic multilinear algebra; (3)…
Numerical tensor calculus comprise basic tensor operations such as the entrywise addition and contraction of higher-order tensors. We present, TLib, flexible tensor framework with generic tensor functions and tensor classes that assists…
Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of…
Within the efforts to bring frontline interactive astrophysics and astronomy to the classroom, the Hands on Universe (HOU) developed a set of exercises and platform using real data obtained by some of the most advanced ground and space…
Sequential data such as time series, video, or text can be challenging to analyse as the ordered structure gives rise to complex dependencies. At the heart of this is non-commutativity, in the sense that reordering the elements of a…
We introduce a new OpenMath content dictionary, named tensor1, containing symbols for the expression of tensor formulas. These symbols support the expression of non-Cartesian coordinates and invariant, multilinear expressions in the context…
This paper is devoted to present the Mathematics Grammar Library, a system for multilingual mathematical text processing. We explain the context in which it originated, its current design and functionality and the current development goals.…
This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…
As generative AI becomes increasingly embedded in everyday life, the thoughtful and intentional integration of AI-based tools into statistics education has become essential. We address this need with a focus on homework assignments and we…
We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…
The scalar-tensor theory of gravitation has been and still is one of the most widely discussed "alternative theories" to General Relativity (GR). Despite nearly half a century of its age, it continues to attract renewed interests of not…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the…