Sur la symétrie dans les phénomènes physiques, symétrie d'un champ électrique et d'un champ magnétique

Curie, Pierre

doi:10.1051/jphystap:018940030039300

Cited by 557 publications

(430 citation statements)

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“…It is interesting to interpret our results in the context of Curie's principle [25], which asserts that the symmetries of the causes must be found in the effects. Asymmetryinduced symmetry requires that 1) any state with the symmetry of the system be unstable and hence not observed and 2) the symmetry of the system be reduced to realize the symmetric state-both consistent with but not following from Curie's principle.…”

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confidence: 89%

Symmetric States Requiring System Asymmetry

Nishikawa

Motter

2016

Phys. Rev. Lett.

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Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here we report on the discovery of the converse of symmetry breaking-the scenario in which complete synchronization is not stable for identically-coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones.Symmetry-the property of appearing the same from different viewpoints-is so central to physics that Weyl [1] suggested that "all a priori statements in physics have their origin in symmetry"; Anderson [2] went further to propose that "physics is the study of symmetry." In the study of complex networks this tradition was for many years relegated to a secondary position, for the excellent reason that real complex systems appeared not to exhibit symmetries. Recent work has shown, however, that they not only can exhibit a myriad of symmetries [3] but also that such symmetries have direct implications for dynamical behavior (see Ref.[4] for example). Partially motivated by that, significant recent attention has been dedicated to the extreme, most symmetric case of uniform networks in which nodes are all identically coupled to the others and have no natural grouping, as in a ring or all-to-all network. It has been shown that such systems can exhibit spatiotemporal patterns of coexisting synchronous and non-synchronous behavior [5,6], for which elaborated mathematical analysis techniques are now available [7]. The emergence of these patterns can be regarded as a form of symmetry breaking, since the realized state has less symmetry than the system [8].Here we demonstrate for the first time that the converse of symmetry breaking with the roles of the system and its state reversed-which we term asymmetryinduced symmetry-is also possible. We provide examples of uniform, rotationally symmetric networks of coupled oscillators for which stable uniform states (thus rotationally symmetric states) do not exist when the nodes are identical but do exist when the nodes are not identical.In a network of coupled oscillators a uniform, symmetric state represents synchronization, in which all units swing in concert, following the exact same dynamics as a function of time [9]. Synchronization dynamics is widespread across fields-ranging from physics and engineering to biology and social sciences-and is intimately related to the twin proce...

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confidence: 89%

Symmetric States Requiring System Asymmetry

Nishikawa

Motter

2016

Phys. Rev. Lett.

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“…Then I has a Gamma-mixture distribution, which is described by a cumulant-generating function By virtue of Eqs. (12)(13), each term of the summation r j in Eq. (B2) is an independent Gamma-distributed random variable.…”

Section: Discussionmentioning

confidence: 99%

Langevin equation for systems with a preferred spatial direction

2016

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In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by the external force and alters the Gaussian structure of the system's fluctuations. By solving this extended equation, we demonstrate that the statistical properties of the fluctuations in these systems can be predicted from physical observables, such as the temperature and the hydrodynamic gradients.

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“…Although the necessity of broken symmetry was already pointed out by P. Curie in 1894 [28], it took until the 1960s that Soviet scientists found the first material exhibiting static magnetoelectric coupling [29,30]. Dzyaloshinskii found that piezoelectric Cr 2 O 3 displays long-range magnetic order and thus breaks time reversal symmetry [31].…”

Section: Development Of Mec In Insulatorsmentioning

confidence: 99%