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43,951 results on '"Kumar, V"'

43. A Note on Generalized Locally Toeplitz Operators

Author

Kumar, V. B. Kiran and Sarathkumar, N. S.

Subjects
Mathematics - Numerical Analysis
Abstract

Generalized Locally Toeplitz (GLT) matrix sequences arise from large linear systems that approximate Partial Differential Equations (PDEs), Fractional Differential Equations (FDEs), and Integro-Differential Equations (IDEs). GLT sequences of matrices have been developed to study the spectral/singular value behaviour of the numerical approximations to various PDEs, Fades and IDEs. These approximations can be achieved using any discretization method on appropriate grids through local techniques such as Finite Differences, Finite Elements, Finite Volumes, Isogeometric Analysis, and Discontinuous Galerkin methods. Spectral and singular value symbols are essential for analyzing the eigenvalue and singular value distributions of matrix sequences in the Weyl sense. In this article, we provide a comprehensive overview of the operator-theoretic aspect of GLT sequences. The theory of GLT sequences, along with findings on the asymptotic spectral distribution of perturbed matrix sequences, is a highly effective and successful method for calculating the spectral symbol f. Therefore, developing an automatic procedure to compute the spectral symbols of these matrix sequences would be advantageous, a task that Ahmed Ratnani, N S Sarathkumar, S. Serra-Capizzano have partially undertaken. As an application of the theory developed here, we propose an automatic procedure for computing the symbol of the underlying sequences of matrices, assuming they form a GLT sequence that meets mild conditions.

Published
2024

44. Long-range magnetic order in CePdAl$_3$ enabled by orthorhombic deformation

Author

Stekiel, M., Čermák, P., Franz, C., Meven, M., Legut, D., Simeth, W., Hansen, U. B., Fåk, B., Weber, S., Schönmann, R., Kumar, V., Nemkovski, K., Deng, H., Bauer, A., Pfleiderer, C., and Schneidewind, A.

Subjects
Condensed Matter - Strongly Correlated Electrons, Condensed Matter - Materials Science
Abstract

We investigate the effect of structural deformation on the magnetic properties of orthorhombic CePdAl$_3$ in relation to its tetragonal polymorph. Utilizing x-ray and neutron diffraction we establish that the crystal structure has the $Cmcm$ space group symmetry and exhibits pseudo-tetragonal twinning. According to density-functional calculations the tetragonal-orthorhombic deformation mechanism has its grounds in relatively small free enthalpy difference between the polymorphs, allowing either phase to be quenched and fully accounts for the twinned microstructure of the orthorhombic phase. Neutron diffraction measurements show that orthorhombic CePdAl$_3$ establishes long-range magnetic order below $T_\mathrm{N}$=5.29 (5) K characterized by a collinear, antiferromagnetic arrangement of magnetic moments. Magnetic anisotropies of orthorhombic CePdAl$_3$ arise from strong spin-orbit coupling as evidenced by the crystal-field splitting of the $4f$ multiplet, fully characterised with neutron spectroscopy. We discuss the potential mechanism of frustration posed by antiferromagnetic interactions between nearest neighbours in the tetragonal phase, which hinders the formation of long-range magnetic order in tetragonal CePdAl$_3$. We propose that orthorhombic deformation releases the frustration and allows for long-range magnetic order., Comment: Finalized paper from the splitting of arxiv.org/abs/2106.08194v1

Published
2024
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50. Effect of Conjunctive Use of Inorganic and Organic Sources of Nutrients on Soil Quality Parameters, Key Indicators and Soil Quality Indices (SQIs) under Sorghum + Cowpea Intercropping System in Rainfed Vertisol Soils of Southern India

Author

Sharma, K.L., Chary, G. Ravindra, Reddy, K. Sammi, Lal, Munna, Indoria, A.K., Srinivas, K., Prabhakar, M., Baskar, K., Elamathi, S., Kumar, V. Sanjiv, Anandaraj, N., Chandrika, D. Suma, Gayatri, D. Lakshmi Aruna, Gopinath, K.A., Osman, M., Narsimlu, B., and Sekhar, Ch. Chandra

Published
2019
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