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Register a new userUnified Expressions Of All Differential Variational Principles
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This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.
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In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, H{o}lder, Maupertuis-Lagrange variational principles of integral style, the invariant quantities of the general, Voss, H{o}lder, Maupertuis-Lagrange variational principles are given, finally the Noether conservation charges of the general, Voss, H{o}lder, Maupertuis-Lagrange variational principles are deduced, and the intrinsic relations among the invariant quantities and the Noether conservation charges of the all integral variational principles are achieved.
This paper has been withdrawn by the authors because the paper is largely revised and improved.
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition matrices, the latter of which was used in early definitions of characteristic modes and is uniquely defined for all scattering scenarios. This also makes it possible to extend the known application domain of characteristic mode decomposition to any other frequency-domain solver capable of generating transition matrices, such as finite difference or finite element methods. The formulation of characteristic modes using a transition matrix allows for the decomposition of induced currents and scattered fields from arbitrarily shaped objects, providing high numerical dynamics and increased stability, removing the issue of spurious modes, offering good control of convergence, and significantly simplifying modal tracking. Algebraic properties of the transition matrix are utilized to show that characteristic mode decomposition of lossy objects fails to deliver orthogonal far fields. All aforementioned properties and steps are demonstrated on several numerical examples for both surface- and volume-based method-of-moment formulations.
We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution to the energy, which is intrinsically non-local. Under minimal assumptions, we establish three distinct variational principles for the stray field energy: a minimax principle involving magnetic scalar potential and two minimization principles involving magnetic vector potential. We then apply our formulations to the dimension reduction problem for thin ferromagnetic shells of arbitrary shapes.
In the past hundred years, chaos has always been a mystery to human beings, including the butterfly effect discovered in 1963 and the dissipative structure theory which won the chemistry Nobel Prize in 1977. So far, there is no quantitative mathematical-physical method to solve and analyze these problems. In this paper, the idea of using field theory to study nonlinear systems is put forward, and the concept of generalized potential is established mathematically. The physical essence of generalized potential promoting the development of nonlinear field is extended and the spatiotemporal evolution law of generalized potential is clarified. Then the spatiotemporal evolution law of conservative system and pure dissipative system is clarified. Acceleration field, conservative vector field and dissipation vector field are established to evaluate the degree of conservation and dissipation of physical field. Finally, the development route of new field research and the precondition of promoting engineering application in the future are discussed.
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