Subjects: Mathematics >> Mathematical Physics submitted time 2022-12-07
Abstract： In this article we employ classical tricks to give local and global well-posedness to MagnetoElasticity System. Different from many cases, we consider the equation which the magnetic field satisfies is Landau-Lifshitz system without viscidity, i.e. the Schrodinger flow. As is well known, people can not obtain ¨ global existence of Schrodinger flow at general cases. However, the reason why we do what others can not ¨ do is the Schrodinger flow with non-zero convection term.
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Subjects: Mathematics >> Mathematical Physics submitted time 2021-06-16
Abstract： In this paper, we mainly discuss the copositivity of 4th order symmetric tensor defined by scalar dark matter stable under a $\mathbb{Z}_{3}$ discrete group, and obtain an analytically necessary and sufficient condition of the copositivity of such a class of tensors. Furthermore, this analytic expression may be used to verify the vacuum stability for $\mathbb{Z}_{3}$ scalar dark matter. "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematical Physics submitted time 2020-11-23
Abstract： In this paper, we mainly discuss analytical expressions of positive definiteness for a special 4th order 3-dimensional symmetric tensor defined by the constructed model for a physical phenomenon. Firstly, an analytically necessary and sufficient conditions of 4th order 2-dimensional symmetric tensors are given to test its positive definiteness. Furthermore, by means of such a result, a necessary and sufficient condition of positive definiteness is obtained for a special 4th order 3-dimensional symmetric tensor. Such an analytical conditions can be used for verifying the vacuum stability of general scalar potentials of two real singlet scalar fields and the Higgs boson. The positive semi-definiteness conclusions are presented too.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematical Physics submitted time 2019-11-23
Abstract： " The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of 4th order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity of 3th order 2 dimensional (3 dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th order tensors, the analytically sufficient conditions of copositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for $\mathbb{Z}_3$ scalar dark matter. "
Peer Review Status:Awaiting Review
Subjects: Physics >> The Physics of Elementary Particles and Fields Subjects: Mathematics >> Mathematical Physics submitted time 2018-10-08
Abstract： In the present paper, we have systematically explored the general rules for all kinds of combination of Hodge star and exterior differentiation operators. We have derived the unified forms of the non-vanishing and independent operators made up of arbitrary numbers of Hodge star and exterior differentiation operators. On basis of this, we have explicitly investigated the interaction of all the combined operators. What is more, all the operators have been classified according to the ranks of the newly generated differential forms. As an application, it has been demonstrated that the Maxwell’s equations for U(1) gauge field can be constructed from the linear combinations of two (n-1)-forms. "
Peer Review Status:Awaiting Review
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