scholarly journals Dynamical symmetries, coherent states and nonlinear realizations: The SO(2,4) case

2017 ◽  
Vol 15 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Andrej B. Arbuzov ◽  
Diego Julio Cirilo-Lombardo
Keyword(s):  
Symmetry Breaking ◽  
Coherent States ◽  
Dynamical Symmetry ◽  
Point Of View ◽  
Quadratic Model ◽  
Spontaneous Compactification ◽  
Dynamical Symmetries ◽  
Coset Geometry ◽  
The Stability ◽  
Nonlinear Realizations

Nonlinear realizations of the [Formula: see text] group are discussed from the point of view of symmetries. Dynamical symmetry breaking is introduced. One linear and one quadratic model in curvature are constructed. Coherent states of the Klauder–Perelomov type are defined for both cases taking into account the coset geometry. A new spontaneous compactification mechanism is defined in the subspace invariant under the stability subgroup. The physical implications of the symmetry rupture in the context of nonlinear realizations and direct gauging are analyzed and briefly discussed.

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals Asymmetry underlies stability in power grids

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ferenc Molnar ◽  
Takashi Nishikawa ◽  
Adilson E. Motter
Keyword(s):  
Symmetry Breaking ◽  
Real World ◽  
Power Grids ◽  
Stable Operation ◽  
World Systems ◽  
Symmetric State ◽  
Network Systems ◽  
Additional Improvement ◽  
The Stability ◽  
General Method

AbstractBehavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.

scholarly journals Suboptimal Disturbance Observer Design Using All Stabilizing Q Filter for Precise Tracking Control

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh
Keyword(s):  
Design Method ◽  
Industrial Applications ◽  
Point Of View ◽  
Observer Design ◽  
Linear Matrix ◽  
External Disturbances ◽  
Closed Loop Systems ◽  
Control Target ◽  
The Stability ◽  
Unified Index

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

scholarly journals Photoluminescent Coordination Polymers Based on Group 12 Metals and 1H-Indazole-6-Carboxylic Acid

Inorganics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 20
Author(s):  
Antonio A. García-Valdivia ◽  
Estitxu Echenique-Errandonea ◽  
Gloria B. Ramírez-Rodríguez ◽  
José M. Delgado-López ◽  
Belén Fernández ◽  
...  
Keyword(s):  
Carboxylic Acid ◽  
Coordination Polymers ◽  
Density Functional ◽  
Free Ligand ◽  
Emission Spectra ◽  
Point Of View ◽  
Theoretical Point ◽  
Fourier Transformed Infrared Spectroscopy ◽  
3D Network ◽  
The Stability

Two new coordination polymers (CPs) based on Zn(II) and Cd(II) and 1H-indazole-6-carboxylic acid (H2L) of general formulae [Zn(L)(H2O)]n (1) and [Cd2(HL)4]n (2) have been synthesized and fully characterized by elemental analyses, Fourier transformed infrared spectroscopy and single crystal X-ray diffraction. The results indicate that compound 1 possesses double chains in its structure whereas 2 exhibits a 3D network. The intermolecular interactions, including hydrogen bonds, C–H···π and π···π stacking interactions, stabilize both crystal structures. Photoluminescence (PL) properties have shown that compounds 1 and 2 present similar emission spectra compared to the free-ligand. The emission spectra are also studied from the theoretical point of view by means of time-dependent density-functional theory (TD-DFT) calculations to confirm that ligand-centred π-π* electronic transitions govern emission of compound 1 and 2. Finally, the PL properties are also studied in aqueous solution to explore the stability and emission capacity of the compounds.

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