The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory for...

Accurate numerical calculations of electronic structure are often dominated in cost by tensor contractions. These tensors are typically symmetric under interchange of modes, enabling reduced-size representations as well as a reduced computation cost. Direct evaluation algorithms for such contractions use matrix and vector unfoldings of the tensors, computing and accumulating products of input e...

Abstract. The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a new general method for any rank of CKT. This method can also be applied to other types of Killing equations, as well as to overdetermined systems c...

The {\em tensor power method} generalizes the matrix method to higher order arrays, or tensors. Like in case, fixed points of are eigenvectors tensor. While every real symmetric has an eigendecomposition, vectors generating a decomposition not always In this paper we show that whenever eigenvector is} generator tensor, then (if is sufficiently high) robust} , i.e., it attracting point method....

The energy equation for turbulent flow of fiber suspensions was derived in terms of second order correlation tensors. Fiber motion of turbulent energy including the correlation between pressure fluctuations and velocity fluctuations was discussed at two points of flow field, at which the correlation tensors were the functions of space coordinates, distance between two points, and time.

Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we propose Blocked Compact Symmetric Storage wherein we consider the tensor by blocks and store only the unique blocks of a symmetric tensor. We propose an algo...

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations dualities, which is not immediately obvious. A prime example Scherk-Schwarz reductions double theory, have been shown to be one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation only the tip of iceberg. Currently, most general known...

Visualization of fourth-order tensors from solid mechanics has not been explored in depth previously. Challenges include the large number of components (3x3x3x3 for 3D), loss of major symmetry and loss of positive definiteness (with possibly zero or negative eigenvalues). This paper presents a decomposition of fourth-order tensors that facilitates their visualization and understanding. Fourth-o...