scholarly journals Study on Singular Problem of the Generalized Mass Matrix Based on Gauss Principle of Least Constraints

2017 ◽  
Vol 06 (01) ◽  
pp. 56-62
Author(s):  
流松 杨
Keyword(s):  
Mass Matrix ◽  
Singular Problem ◽  
Gauss Principle

scholarly journals Augmented Lagrangian preconditioners for the Oseen–Frank model of nematic and cholesteric liquid crystals

2021 ◽  
Author(s):  
Jingmin Xia ◽  
Patrick E. Farrell ◽  
Florian Wechsung
Keyword(s):  
Liquid Crystals ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Mass Matrix ◽  
Unit Length ◽  
Mesh Size ◽  
Schur Complement ◽  
Cholesteric Liquid Crystals ◽  
Multigrid Algorithm ◽  
The Cost

AbstractWe propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen–Frank model arising in nematic and cholesteric liquid crystals. By applying the augmented Lagrangian method, the Schur complement of the director block can be better approximated by the weighted mass matrix of the Lagrange multiplier, at the cost of making the augmented director block harder to solve. In order to solve the augmented director block, we develop a robust multigrid algorithm which includes an additive Schwarz relaxation that captures a pointwise version of the kernel of the semi-definite term. Furthermore, we prove that the augmented Lagrangian term improves the discrete enforcement of the unit-length constraint. Numerical experiments verify the efficiency of the algorithm and its robustness with respect to problem-related parameters (Frank constants and cholesteric pitch) and the mesh size.

scholarly journals The singly-charged scalar singlet as the origin of neutrino masses

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Tobias Felkl ◽  
Juan Herrero-García ◽  
Michael A. Schmidt
Keyword(s):  
Mass Matrix ◽  
Boson Mass ◽  
Neutrino Masses ◽  
Charged Scalar ◽  
Yukawa Couplings ◽  
Left Handed ◽  
Flavour Violation ◽  
Singly Charged ◽  
Charged Lepton Sector ◽  
Scalar Singlet

Abstract We consider the generation of neutrino masses via a singly-charged scalar singlet. Under general assumptions we identify two distinct structures for the neutrino mass matrix. This yields a constraint for the antisymmetric Yukawa coupling of the singly-charged scalar singlet to two left-handed lepton doublets, irrespective of how the breaking of lepton-number conservation is achieved. The constraint disfavours large hierarchies among the Yukawa couplings. We study the implications for the phenomenology of lepton-flavour universality, measurements of the W-boson mass, flavour violation in the charged-lepton sector and decays of the singly-charged scalar singlet. We also discuss the parameter space that can address the Cabibbo Angle Anomaly.

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

scholarly journals Embedding the texture of the neutrino mass matrix into the MaVaNs scenario

2006 ◽  
Vol 2006 (01) ◽  
pp. 042-042 ◽  
Author(s):  
Mizue Honda ◽  
Ryo Takahashi ◽  
Morimitsu Tanimoto
Keyword(s):  
Neutrino Mass ◽  
Mass Matrix ◽  
Neutrino Mass Matrix

scholarly journals Broken S3 symmetry in the neutrino mass matrix

2011 ◽  
Vol 702 (1) ◽  
pp. 28-33 ◽  
Author(s):  
S. Dev ◽  
Shivani Gupta ◽  
Radha Raman Gautam
Keyword(s):  
Neutrino Mass ◽  
Mass Matrix ◽  
Neutrino Mass Matrix
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