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Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.


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Journal ArticleDOI
TL;DR: In this paper, the same principle applied to the angular momentum balance proves the emergence, at the mesoscale, of an antisymmetric component of the volume-averaged hydrodynamic stress irrespective of the particle Reynolds number.
Abstract: The paper begins by showing how standard results on the average hydrodynamic stress in a uniform fluid-particle system follow from a direct, elementary application of Cauchy’s stress principle. The same principle applied to the angular momentum balance proves the emergence, at the mesoscale, of an antisymmetric component of the volume-averaged hydrodynamic stress irrespective of the particle Reynolds number. Several arguments are presented to show the physical origin of this result and to explain how the averaging process causes its appearance at the mesoscale in spite of the symmetry of the microscale stress. Examples are given for zero and finite Reynolds number, and for potential flow. For this last case, the antisymmetric stress component vanishes, but the Cauchy principle proves nevertheless useful to derive in a straightforward way known results and to clarify their physical nature.

40 citations

Journal ArticleDOI
TL;DR: In this paper, the authors derived an equation of motion for a homogeneous, isotropic, elastic plate by an antisymmetric expansion in the thickness coordinate of the displacement components.

40 citations

Journal ArticleDOI
TL;DR: In this article, explicit expressions for the matrix elements of unitary group generators between geminally antisymmetric spin-adapted N-electron configurations in terms of the orbital occupancies and spin factors are derived by use of many-body time-independent diagrammatic techniques.
Abstract: The explicit expressions for the matrix elements of unitary group generators between geminally antisymmetric spin-adapted N-electron configurations in terms of the orbital occupancies and spin factors, given as spin function matrix elements of appropriate orbital permutations, are derived by use of the many-body time-independent diagrammatic techniques. It is also shown how this approach can be conveniently combined with graphical methods of spin algebras to obtain explicit expressions for the spin factors, once a definite coupling scheme is chosen. This method yields explicit expressions for the orbital permutations defining the spin factors. However, if desired, the explicit determination of line-up permutations can be avoided in this approach, since they are implicitly contained in the orbital diagrams. It also clearly indicates why the geminally antisymmetric spin functions have to be used when a simple formalism is desired. 5 figures.

40 citations

Journal ArticleDOI
TL;DR: It is demonstrated that a symmetric system of two linearly coupled waveguides, with Kerr nonlinearity and resonant grating in both of them, gives rise to a family of symmetric and antisymmetric solitons in an exact analytical form, a part of which exists outside of the bandgap in the system's spectrum.
Abstract: We demonstrate that a symmetric system of two linearly coupled waveguides, with Kerr nonlinearity and resonant grating in both of them, gives rise to a family of symmetric and antisymmetric solitons in an exact analytical form, a part of which exists outside of the bandgap in the system's spectrum, i.e., they may be regarded as embedded solitons (ES's, i.e., the ones partly overlapping with the continuous spectrum). Parameters of the family are the soliton's amplitude and velocity. Asymmetric ES's, unlike the regular (nonembedded) gap solitons (GS's), do not exist in the system. Moreover, ES's exist even in the case when the system's spectrum contains no bandgap. The main issue is the stability of the solitons. We demonstrate that some symmetric ES's are stable, while all the antisymmetric solitons are unstable; an explanation is given to the latter property, based on the consideration of the system's Hamiltonian. We produce a full stability diagram, which comprises both embedded and regular solitons, quiescent and moving. A stability region for ES's is found around the point where the constant of the linear coupling between the two cores is equal to the Bragg-reflectivity coefficient accounting for the linear conversion between the right- and left-traveling waves in each core, i.e., the ES's are the ``most endemic'' solitary solitons in this system. The stability region quickly shrinks with the increase of the soliton's velocity $c$, and completely disappears when $c$ exceeds half the maximum velocity. Collisions between stable moving solitons of various types are also considered, with a conclusion that the collisions are always quasielastic.

40 citations

Journal ArticleDOI
TL;DR: In this article, the calculations presented in Part I of this paper have been extended so as to include vibrations which are antisymmetric with respect to the central plane of the disk, and curves showing the normal components of the displacements at the boundary surfaces are also drawn, to get the vibration patterns according to the theoretical assumptions made.
Abstract: The calculations presented in Part I of this paper have been extended so as to include vibrations, which are antisymmetric with respect to the central plane of the disk. Curves showing the normal components of the displacements at the boundary surfaces are also drawn, to get the vibration patterns according to the theoretical assumptions made.

40 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023145
2022286
2021109
2020112
2019118
2018122