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Register a new userComputer Algebra calculation of XRMS polarisation dependence in the non spherical case
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Simple analytical formulae, directly relating the experimental geometry and sample orientation to the measured R(M)XS scattered intensity are very useful to design experiments and analyse data. Such formulae can be obtained by the contraction of an expression containing the polarisations and crystal field tensors, and where the magnetisation vector acts as a rotation derivativecite{mirone}. The result of a contraction contains a scalar product of (rotated) polarisation vectors and the crystal field axis. The contraction rules give rise to combinatorial algorithms which can be efficiently treated by computers. In this work we provide and discuss a concise Mathematica code along with a few example applications to non-centrosymmetric magnetic systems.
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We develop a simple tensorial contraction method to obtain analytical formula for X-ray resonant magnetic scattering. We apply the method considering first electric dipole-dipole and electric quadrupole-quadrupole scattering in the isolated atom approximation and compare the results with previous works. Then we apply the method to derive phenomenological original formulas which account also for non-spherical systems and for dipole-quadrupole mixing.
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python framework. There are libraries for Julia that cover the majority of scientific and engineering computations demands. The aim of this paper is to combine the usage of the Julia framework for numerical computations and for symbolic computations in mathematical modeling problems. The main functional domains determining various variants of the application of computer algebra systems are described. In each of these domains, generic representatives of computer algebra systems in Julia are distinguished. The conclusion is that it is possible (and even convenient) to use computer algebra systems within the Julia framework.
We have developed a detector which records the full polarisation state of a terahertz (THz) pulse propagating in free space. The three-electrode photoconductive receiver simultaneously records the electric field of an electromagnetic pulse in two orthogonal directions as a function of time. A prototype device fabricated on Fe+ ion implanted InP exhibited a cross polarised extinction ratio better than 390:1. The design and optimisation of this device are discussed along with its significance for the development of new forms of polarisation sensitive time domain spectroscopy, including THz circular dichroism spectroscopy.
We determine the Hall algebra, in the sense of Toen, of the algebraic triangulated category generated by a spherical object.
The paper presents a method for calculation of non-spherical particle T-matrices based on the volume integral equation and the spherical vector wave function basis, and relies on the Generalized Source Method rationale. The developed method appears to be close to the invariant imbedding approach, and the derivations aims at intuitive demonstration of the calculation scheme. In parallel calculation of single columns of T-matrix is considered in detail, and it is shown that this way not only has a promising potential of parallelization but also yields an almost zero power balance for purely dielectric particles.
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