Journal articles on the topic 'Resonance'
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1
Malhotra, Renu. "New results on orbital resonances." Proceedings of the International Astronomical Union 15, S364 (October 2021): 85–101. http://dx.doi.org/10.1017/s1743921321001411.
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AbstractPerturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called “low-eccentricity resonant bridges” connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some – though not necessarily entire – resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.
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ALAM, MOHAMMAD-REZA, YUMING LIU, and DICK K. P. YUE. "Bragg resonance of waves in a two-layer fluid propagating over bottom ripples. Part I. Perturbation analysis." Journal of Fluid Mechanics 624 (April 10, 2009): 191–224. http://dx.doi.org/10.1017/s0022112008005478.
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We investigate, via perturbation analyses, the mechanisms of nonlinear resonant interaction of surface-interfacial waves with a rippled bottom in a two-layer density-stratified fluid. As in a one-layer fluid, three classes of Bragg resonances are found to exist if nonlinear interactions up to the third order in the wave/ripple steepness are considered. As expected, the wave system associated with the resonances is more complicated than that in a one-layer fluid. Depending on the specifics of the resonance condition, the resonance-generated wave may be a surface or internal mode and may be transmitted or reflected. At the second order, class I Bragg resonance occurs involving two surface and/or internal waves and one bottom-ripple component. The interaction of an incident surface/internal wave with the bottom ripple generates a new surface or internal wave that may propagate in the same or the opposite direction as the incident wave. At the third order, class II and III Bragg resonances occur involving resonant interactions of four wave/ripple components: two surface and/or internal waves and two bottom-ripple components for class II resonance; three surface and/or internal waves and one bottom-ripple components for class III resonance. As in class I resonance, the resonance-generated wave in class II resonance has the same frequency as that of the incident wave. For class III resonance, the frequency of the resonant wave is equal to the sum or difference of the two incident wave frequencies. We enumerate and represent, using Feynman-like diagrams, the possible cases and combinations for Bragg resonance up to the third order (in two dimensions). Analytical regular perturbation results are obtained and discussed for all three classes of Bragg resonances. These are valid for limited bottom patch lengths and initial/finite growth of the resonant waves. For long bottom patches, a uniformly valid solution using multiple scales is derived for class I resonance. A number of applications underscoring the importance and implication of these nonlinear resonances on the evolution of ocean waves are presented and discussed. For example, it is shown that three internal/surface waves co-propagating over bottom topography are resonant under a broad range of Bragg conditions. The present study provides the theoretical basis and understanding for the companion paper (Alam, Liu & Yue 2008), where a direct numerical solution for the general nonlinear problem is pursued.
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Kovernikova, Lidiia I. "Resonance Modes at Harmonics Frequencies in Electrical Networks." E3S Web of Conferences 209 (2020): 07006. http://dx.doi.org/10.1051/e3sconf/202020907006.
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Resonance modes at harmonic frequencies in electrical networks are a serious problem. They arise due to the availability of electrical equipment with capacitive and inductive elements. The values of the harmonics of currents and voltages increase at resonances. The voltage quality indices in resonant modes exceed the limit values. Harmonics cause energy losses in electrical equipment, reduce its service life, create economic damage. Capacitor banks are often damaged by resonances. Network nodes with resonant circuits and resonant harmonics can be determined using the frequency characteristics of the nodal reactance (susceptance). The paper presents an algorithm and HARMONICS software for the analysis and forecasting of resonance modes, the results of studies of resonance modes in the high-voltage networks of Eastern Siberia.
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Quinn, Tyler, and Mariah G. MacDonald. "Confirming Resonance in Three Transiting Systems." Astronomical Journal 166, no. 2 (July 13, 2023): 58. http://dx.doi.org/10.3847/1538-3881/ace049.
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Abstract Although resonant planets have orbital periods near commensurability, resonance is also dictated by other factors, such as the planets’ eccentricities and masses, and therefore must be confirmed through a study of the system’s dynamics. Here, we perform such a study for five multiplanet systems: Kepler-226, Kepler-254, Kepler-363, Kepler-1542, and K2-32. For each system, we run a suite of N-body simulations that span the full parameter space that is consistent with the constrained orbital and planetary properties. We study the stability of each system and look for resonances based on the libration of the critical resonant angles. We find strong evidence for a two-body resonance in each system; we confirm a 3:2 resonance between Kepler-226c and Kepler-226d, confirm a 3:2 resonance between Kepler-254c and Kepler-254d, and confirm a three-body 1:2:3 resonant chain between the three planets of Kepler-363. We explore the dynamical history of two of these systems and find that these resonances most likely formed without migration. Migration leads to the libration of the three-body resonant angle, but these angles circulate in both Kepler-254 and Kepler-363. Applying our methods to additional near-resonant systems could help us identify which systems are truly resonant or nonresonant and which systems require additional follow-up analysis.
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Namouni, F., and M. H. M. Morais. "Resonance libration and width at arbitrary inclination." Monthly Notices of the Royal Astronomical Society 493, no. 2 (February 6, 2020): 2854–71. http://dx.doi.org/10.1093/mnras/staa348.
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ABSTRACT We apply the analytical disturbing function for arbitrary inclination derived in our previous work to characterize resonant width and libration of mean motion resonances at arbitrary inclination obtained from direct numerical simulations of the three-body problem. We examine the 2:1 and 3:1 inner Jupiter and 1:2 and 1:3 outer Neptune resonances and their possible asymmetric librations using a new analytical pendulum model of resonance that includes the simultaneous libration of multiple arguments and their second harmonics. The numerically derived resonance separatrices are obtained using the mean exponential growth factor of nearby orbits (megno chaos indicator). We find that the analytical and numerical estimates are in agreement and that resonance width is determined by the first few fundamental resonance modes that librate simultaneously on the resonant time-scale. Our results demonstrate that the new pendulum model may be used to ascertain resonance width analytically, and more generally, that the disturbing function for arbitrary inclination is a powerful analytical tool that describes resonance dynamics of low as well as high inclination asteroids in the Solar system.
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Lari, Giacomo, Melaine Saillenfest, and Marco Fenucci. "Long-term evolution of the Galilean satellites: the capture of Callisto into resonance." Astronomy & Astrophysics 639 (July 2020): A40. http://dx.doi.org/10.1051/0004-6361/202037445.
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Context. The Galilean satellites have very complex orbital dynamics due to the mean-motion resonances and the tidal forces acting in the system. The strong dissipation in the couple Jupiter–Io is spread to all the moons involved in the so-called Laplace resonance (Io, Europa, and Ganymede), leading to a migration of their orbits. Aims. We aim to characterize the future behavior of the Galilean satellites over the Solar System lifetime and to quantify the stability of the Laplace resonance. Tidal dissipation permits the satellites to exit from the current resonances or be captured into new ones, causing large variation in the moons’ orbital elements. In particular, we want to investigate the possible capture of Callisto into resonance. Methods. We performed hundreds of propagations using an improved version of a recent semi-analytical model. As Ganymede moves outwards, it approaches the 2:1 resonance with Callisto, inducing a temporary chaotic motion in the system. For this reason, we draw a statistical picture of the outcome of the resonant encounter. Results. The system can settle into two distinct outcomes: (A) a chain of three 2:1 two-body resonances (Io–Europa, Europa–Ganymede, and Ganymede–Callisto), or (B) a resonant chain involving the 2:1 two-body resonance Io–Europa plus at least one pure 4:2:1 three-body resonance, most frequently between Europa, Ganymede, and Callisto. In case A (56% of the simulations), the Laplace resonance is always preserved and the eccentricities remain confined to small values below 0.01. In case B (44% of the simulations), the Laplace resonance is generally disrupted and the eccentricities of Ganymede and Callisto can increase up to about 0.1, making this configuration unstable and driving the system into new resonances. In all cases, Callisto starts to migrate outward, pushed by the resonant action of the other moons. Conclusions. From our results, the capture of Callisto into resonance appears to be extremely likely (100% of our simulations). The exact timing of its entrance into resonance depends on the precise rate of energy dissipation in the system. Assuming the most recent estimate of the dissipation between Io and Jupiter, the resonant encounter happens at about 1.5 Gyr from now. Therefore, the stability of the Laplace resonance as we know it today is guaranteed at least up to about 1.5 Gyr.
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Malhotra, Renu, and Nan Zhang. "On the divergence of first-order resonance widths at low eccentricities." Monthly Notices of the Royal Astronomical Society 496, no. 3 (June 19, 2020): 3152–60. http://dx.doi.org/10.1093/mnras/staa1751.
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ABSTRACT Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first-order mean motion resonances diverge for nearly circular orbits. Here, we examine the nature of this divergence with a non-perturbative analysis of a few first-order resonances interior to a Jupiter-mass planet. We show that a first-order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centres of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of ‘bridges’ between adjacent first-order resonances: at low eccentricities, the apocentric libration zone of a first-order resonance smoothly connects with the pericentric libration zone of the neighbouring first-order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low-eccentricity regime.
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Pang, Zhaojun, Zhonghua Du, Chun Cheng, and Qingtao Wang. "Dynamics and Control of Tethered Satellite System in Elliptical Orbits under Resonances." International Journal of Aerospace Engineering 2020 (September 21, 2020): 1–12. http://dx.doi.org/10.1155/2020/8844139.
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This paper studies resonance motions of a tethered satellite system (TSS) in elliptical orbits. A perturbation analysis is carried out to obtain all possible resonance types and corresponding parameter relations, including internal resonances and parametrically excited resonances. Besides, a resonance parametric domain is given to provide a reference for the parameter design of the system. The bifurcation behaviors of the system under resonances are studied numerically. The results show that resonant cases more easily enter chaotic motion than nonresonant cases. The extended time-delay autosynchronization (ETDAS) method is applied to stabilize the chaotic motion to a periodic one. Stability analysis shows that the stable domains become smaller in resonance cases than in the nonresonance case. Finally, it is shown that the large amplitudes of periodic solutions under resonances are the main reason why the system is difficult to control.
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Pan, Shanshan, and Xiyun Hou. "Analysis of Resonance Transition Periodic Orbits in the Circular Restricted Three-Body Problem." Applied Sciences 12, no. 18 (September 6, 2022): 8952. http://dx.doi.org/10.3390/app12188952.
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Resonance transition periodic orbits exist in the chaotic regions where the 1:1 resonance overlaps with nearby interior or exterior resonances in the circular restricted three-body problem (CRTBP). The resonance transition periodic orbits have important applications for tour missions between the interior and the exterior regions of the system. In this work, following the increase of the mass parameter μ in the CRTBP model, we investigate the breakup of the first-order resonant periodic families and their recombination with the resonance transition periodic families. In this process, we can describe in detail how the 1:1 resonance gradually overlaps with nearby first-order resonances with increasing strength of the secondary’s perturbation. Utilizing the continuation method, features of the resonance transition periodic families are discussed and characterized. Finally, an efficient approach to finding these orbits is proposed and some example resonance transition periodic orbits in the Sun–Jupiter system are presented.
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HE, J. J., J. HU, L. Y. ZHANG, L. LI, S. W. XU, X. Q. YU, and M. L. LIU. "REEXAMINATION OF ASTROPHYSICAL RESONANCE-REACTION-RATE EQUATIONS FOR AN ISOLATED, NARROW RESONANCE." International Journal of Modern Physics E 20, no. 01 (January 2011): 165–72. http://dx.doi.org/10.1142/s0218301311017399.
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The well-known astrophysical resonant-reaction-rate (RRR) equations for an isolated narrow resonance induced by the charged particles have been reexamined. The validity of those assumptions used in deriving the classical analytic equations has been checked, and found that these analytic equations only hold for certain circumstances. It shows the customary definition of "narrow" is inappropriate or ambiguous in some sense, and it awakes us not to use those analytic equations without caution. As a suggestion, it is better to use the broad-resonance equation to calculate the RRR numerically even for a narrow resonance of a few keV width. The present conclusion may influence some work in which the classical narrow-resonant equations were used for calculating the RRRs, especially at low stellar temperatures for those previously defined "narrow" resonances.
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DOROBANTU, V., and C. HATEGAN. "APPROACH TO QUASI-RESONANT PROCESSES." Modern Physics Letters A 06, no. 27 (September 7, 1991): 2463–66. http://dx.doi.org/10.1142/s021773239100289x.
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An approach to quasi-resonant processes is presented, by developing a method of generalized reduced (K)- and collision-matrices. It is proved that a single channel resonance can induce, via direct interaction coupling, quasi-resonant structures in competing reaction channels. The magnitude of the quasi-resonant process is proportional both to strengths of single channel resonance and of direct coupling. A direct compression of the quasi-resonance's width is evidenced. Its width is smaller than the width of originating single channel resonance.
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MacDonald, Mariah G., Michael S. Polania Vivas, Skylar D’Angiolillo, Ashley N. Fernandez, and Tyler Quinn. "exoMMR: A New Python Package to Confirm and Characterize Mean Motion Resonances." Astronomical Journal 166, no. 3 (August 7, 2023): 94. http://dx.doi.org/10.3847/1538-3881/ace69d.
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Abstract The study of orbital resonances allows for the constraint of planetary properties of compact systems. We can predict a system’s resonances by observing the orbital periods of the planets, as planets in or near mean motion resonance (MMR) have period ratios that reduce to a ratio of small numbers. However, a period ratio near commensurability does not guarantee a resonance; we must study the system’s dynamics and resonant angles to confirm resonance. Because resonances require in-depth study to confirm, and because two-body resonances require a measurement of the eccentricity vector which is quite challenging, very few resonant pairs or chains have been confirmed. We thus remain in the era of small-number statistics, not yet able to perform large population synthesis or informatics studies. To address this problem, we build a python package to find, confirm, and analyze MMRs, primarily through N-body simulations. We then analyze all near-resonant planets in the Kepler/K2 and TESS catalogs, confirming over 60 new resonant pairs and various new resonant chains. We additionally demonstrate the package’s functionality and potential by characterizing the mass–eccentricity degeneracy of Kepler-80g, exploring the likelihood of an exterior giant planet in Kepler-80, and constraining the masses of planets in Kepler-305. We find that our methods overestimate the libration amplitudes of the resonant angles and struggle to confirm resonances in systems with more than three planets. We identify various systems that are likely resonant chains but that we are unable to confirm, and highlight next steps for exoplanetary resonances.
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Li, Miao, and Shengping Gong. "Dynamics of Polar Resonances and Their Effects on Kozai–Lidov Mechanism." Applied Sciences 12, no. 13 (June 28, 2022): 6530. http://dx.doi.org/10.3390/app12136530.
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The research on highly inclined mean motion resonances (MMRs), even retrograde resonances, has drawn more attention in recent years. However, the dynamics of polar resonance with inclination i≈90∘ have received much less attention. This paper systematically studies the dynamics of polar resonance and their effects on the Kozai–Lidov mechanism in the circular restricted three-body problem (CRTBP). The maps of dynamics are obtained through the numerical method and semi-analytical method, by mutual authenticating. We investigate the secular dynamics inside polar resonance. The phase-space portraits on the e−ω plane are plotted under exact polar resonance and considering libration amplitude of critical angle σ. Simultaneously, we investigate the evolution of 5000 particles in polar resonance by numerical integrations. We confirm that the e−ω portraits can entirely explain the results of numerical experiments, which demonstrate that the phase-space portraits on the e−ω plane obtained through the semi-analytical method can represent the real Kozai–Lidov dynamics inside polar resonance. The resonant secular dynamical maps can provide meaningful guidance for predicting the long-term evolution of polar resonant particles. As a supplement, in the polar 2/1 case, we analyze the pure secular dynamics outside resonance, and confirm that the effect of polar resonance on secular dynamics is pronounced and cannot be ignored. Our work is a meaningful supplement to the general inclined cases and can help us understand the evolution of asteroids in polar resonance with the planet.
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Niganova, E. N., O. M. Syusina, O. N. Letner, and T. Yu Galushina. "Influence of the Yarkovsky effect on mean motion resonances of asteroids with small perihelion distances." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 5 (2022): 105–12. http://dx.doi.org/10.17223/00213411/65/5/105.
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The paper presents the study results of the Yarkovsky effect influence on the resonant characteristics of asteroids with small perihelion distances. Out of 52 studied objects, 27 asteroids were identified that move in the vicinity of stable and unstable low-order mean motion resonances with major planets. The evolution of the asteroids orbits is constructed with and without the Yarkovsky effect, and the behavior of the resonance characteristics in both cases is analyzed. The effect was taken into account by including the perturbation from the transversal acceleration A2, the values of which for the presented objects were obtained earlier by the authors of this work. It is shown that the Yarkovsky effect influence on stable resonances is insignificant and leads to small changes in the libration amplitude of the resonance characteristics. The stability of the resonance is preserved. With unstable resonant interaction, the number of passages through the exact commensurability changes, and for some asteroids the resonance becomes more stable.
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Lei, Hanlun, and Jian Li. "Multiharmonic Hamiltonian models with applications to first-order resonances." Monthly Notices of the Royal Astronomical Society 499, no. 4 (October 9, 2020): 4887–904. http://dx.doi.org/10.1093/mnras/staa3115.
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ABSTRACT In this work, two multiharmonic Hamiltonian models for mean motion resonances are formulated and their applications to first-order resonances are discussed. For the kp:k resonance, the usual critical argument φ = kλ − kpλp + (kp − k)ϖ is taken as the resonant angle in the first model, while the second model is characterized by a new critical argument σ = φ/kp. Based on canonical transformations, the resonant Hamiltonians associated with these two models are formulated. It is found that the second Hamiltonian model holds two advantages in comparison with the first model: (i) providing a direct correspondence between phase portraits and Poincaré sections, and (ii) presenting new phase-space structures where the zero-eccentricity point is a visible saddle point. Then, the second Hamiltonian model is applied to the first-order inner and outer resonances, including the 2:1, 3:2, 4:3, 2:3, and 3:4 resonances. The phase-space structures of these first-order resonances are discussed in detail and then the libration centres and associated resonant widths are identified analytically. Simulation results show that there are pericentric and apocentric libration zones where the libration centres diverge away from the nominal resonance location as the eccentricity approaches zero and, in particular, the resonance separatrices do not vanish at arbitrary eccentricities for both the inner and outer (first-order) resonances.
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ALAM, MOHAMMAD-REZA, YUMING LIU, and DICK K. P. YUE. "Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples." Journal of Fluid Mechanics 643 (January 15, 2010): 437–47. http://dx.doi.org/10.1017/s0022112009992850.
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We consider a class of higher order (quartet) Bragg resonance involving two incident wave components and a bottom ripple component (so called class III Bragg resonance). In this case, unlike class I/II Bragg resonance involving a single incident wave and one/two bottom ripple components, the frequency of the resonant wave, which can be reflected or transmitted, is a sum or difference of the incident wave frequencies. In addition to transferring energy across the spectrum leading to potentially significant spectral transformation, such resonances may generate long (infragravity) waves of special importance to coastal processes and engineering applications. Of particular interest here is the case where the incident waves are oblique to the bottom undulations (or to each other) which leads to new and unexpected wave configurations. We elucidate the general conditions for such resonances, offering a simple geometric construction for obtaining these. Perturbation analysis results are obtained for these resonances predicting the evolutions of the resonant and incident wave amplitudes. We investigate special cases using numerical simulations (applying a high-order spectral method) and compare the results to perturbation theory: infragravity wave generation by co- and counter-propagating incident waves normal to bottom undulations; longshore long waves generated by (bottom) oblique incident waves; and propagating–standing resonant waves due to (bottom) parallel incident waves. Finally, we consider a case of multiple resonance due to oblique incident waves on bottom ripples which leads to complex wave creation and transformations not easily tractable with perturbation theory. These new wave resonance mechanisms can be of potential importance on continental shelves and in littoral zones, contributing to wave spectral evolution and bottom processes such as sandbar formation.
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Ren, Xiao bin, Kun Ren, Ying Zhang, Cheng guo Ming, and Qun Han. "Multiple Fano resonances with flexible tunablity based on symmetry-breaking resonators." Beilstein Journal of Nanotechnology 10 (December 11, 2019): 2459–67. http://dx.doi.org/10.3762/bjnano.10.236.
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A symmetry-breaking nanostructure is proposed to achieve multiple Fano resonances. The nanostructure consists of an asymmetric ring resonator coupled to a plasmonic waveguide. The broken symmetry is introduced by deviating the centers of regular ring. New resonant modes that are not accessible through a regular symmetric ring cavity are excited. Thus, one asymmetric cavity can provide more than one resonant mode with the same mode order. As a result, the interval of Fano resonances is greatly reduced. By combining different rings with different degrees of asymmetry, multiple Fano resonances are generated. Those Fano resonances have different dependences on structural parameters due to their different physical origin. The resonance frequency and resonance peak number can be arbitrarily adjusted by changing the degree of asymmetry. This research may provide new opportunities to design on-chip optical devices with great tuning performance.
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Marzari, Francesco, and Gennaro D’Angelo. "Dust distribution around low-mass planets on converging orbits." Astronomy & Astrophysics 641 (September 2020): A125. http://dx.doi.org/10.1051/0004-6361/202038297.
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Context. Super-Earths can form at large orbital radii and migrate inward due to tidal interactions with the circumstellar disk. In this scenario, convergent migration may occur and lead to the formation of resonant pairs of planets. Aims. We explore the conditions under which convergent migration and resonance capture take place, and what dynamical consequences can be expected on the dust distribution surrounding the resonant pair. Methods. We combine hydrodynamic planet–disk interaction models with dust evolution calculations to investigate the signatures produced in the dust distribution by a pair of planets in mean-motion resonances. Results. We find that convergent migration takes place when the outer planet is the more massive. However, convergent migration also depends on the local properties of the disk, and divergent migration may result as well. For similar disk parameters, the capture in low degree resonances (e.g., 2:1 or 3:2) is preferred close to the star where the resonance strength can more easily overcome the tidal torques exerted by the gaseous disk. Farther away from the star, convergent migration may result in capture in high degree resonances. The dust distribution shows potentially observable features typically when the planets are trapped in a 2:1 resonance. In other cases, with higher degree resonances (e.g., 5:4 or 6:5) dust features may not be sufficiently pronounced to be easily observable. Conclusions. The degree of resonance established by a pair of super-Earths may be indicative of the location in the disk where capture occurred. There can be significant differences in the dust distribution around a single super-Earth and a pair of super-Earths in resonance.
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Barik, Saroj, Arun Kumar Kanakati, Saurav Dutta, Nihar Ranjan Behera, Rajesh Kumar Kushawaha, and G. Aravind. "Low-lying Dipole Resonances in FeCN−: A Viable Formation Pathway for FeCN− in Space." Astrophysical Journal 931, no. 1 (May 1, 2022): 47. http://dx.doi.org/10.3847/1538-4357/ac6757.
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Abstract A low-lying resonance in FeCN− anion was identified through abrupt changes in the spectral dependence of the photoelectron angular distribution. Non-Franck–Condon transitions from the resonance to the neutral FeCN (4Δ), and the corresponding photoelectron angular distributions revealed that the resonance is a dipole scattering state. Significant thermionic electron emission was observed in the resonant photoelectron spectra, indicating a strong coupling of the resonance with the ground state of this triatomic anion and its competition over autodetachment. This low-lying resonance is identified to be an efficient pathway for the formation of FeCN− anion in the outer envelope of IRC+10216. The results in general reveal formation pathways in space for anions with low-lying resonances and large permanent dipole moment.
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Vaillant, Timothée, and Alexandre C. M. Correia. "Eviction-like resonances for satellite orbits." Astronomy & Astrophysics 657 (January 2022): A103. http://dx.doi.org/10.1051/0004-6361/202141213.
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The motion of a satellite can experience secular resonances between the precession frequencies of its orbit and the mean motion of the host planet around the star. Some of these resonances can significantly modify the eccentricity (evection resonance) and the inclination (eviction resonance) of the satellite. In this paper, we study in detail the secular resonances that can disturb the orbit of a satellite, in particular the eviction-like ones. Although the inclination is always disturbed while crossing one eviction-like resonance, capture can only occur when the semi-major axis is decreasing. This is, for instance, the case of Phobos, the largest satellite of Mars, that will cross some of these resonances in the future because its orbit is shrinking owing to tidal effects. We estimate the impact of resonance crossing in the orbit of the satellite, including the capture probabilities, as a function of several parameters, such as the eccentricity and the inclination of the satellite, and the obliquity of the planet. Finally, we use the method of the frequency map analysis to study the resonant dynamics based on stability maps, and we show that some of the secular resonances may overlap, which leads to chaotic motion for the inclination of the satellite.
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MA, ZHONG-YU, BAO-QIU CHEN, JUN LIANG, and LI-GANG CAO. "GIANT RESONANCES AND ASYMMETRY ENERGY." International Journal of Modern Physics E 15, no. 07 (October 2006): 1347–56. http://dx.doi.org/10.1142/s0218301306004934.
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A microscopic analysis of the asymmetry energy is performed through the investigation of nuclear giant resonances in the relativistic approach. Nuclear ground state properties are calculated in an extended relativistic mean-field theory plus BCS method, where the contribution of the resonant continuum to pairing correlations is properly treated. The nuclear giant resonances are investigated in the relativistic random phase approximation (RRPA) or quasi-particle RRPA. Special emphases are paid to the correlation between the giant dipole resonance or pygmy resonance and the density dependence of the asymmetry energy.
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Ferraz-Mello, S. "Slow and Fast Diffusion in Asteroid-Belt Resonances: A Review." International Astronomical Union Colloquium 172 (1999): 25–37. http://dx.doi.org/10.1017/s0252921100072389.
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AbstractThis paper reviews recent advances in several topics of resonant asteroidal dynamics as the role of resonances in the transportation of asteroids and asteroidal debris to the inner and outer solar system; the explanation of the contrast of a depleted 2/1 resonance (Hecuba gap) and a high-populated 3/2 resonance (Hilda group); the overall stochasticity created in the asteroid belt by the short-period perturbations of Jupiter’s orbit, with emphasis in the formation of significant three-period resonances, the chaotic behaviour of the outer asteroid belt, and the depletion of the Hecuba gap.
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Gomes, Rodney S. "Trapping of Dust Particles into Internal Resonances with the Inner Planets." International Astronomical Union Colloquium 150 (1996): 39–42. http://dx.doi.org/10.1017/s0252921100501249.
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AbstractTrapping of dust particles into external resonances with the inner planets is a quite relevant phenomenon, which induces the formation of rings of dust around the planets' orbits, there being observational evidence of the Earth's resonant ring (Dermott et al., 1994). On the other hand, notwithstanding it is a less probable event, capture into internal resonance (diverging orbits) is predicted in numerical integrations of dust particles' orbits subject to Poynting-Robertson drag with one or two disturbing planets. Average theories, which give a good explanation for resonance trapping when the orbits are converging, do not allow capture for diverging orbits. Close approaches with the perturbing planet disallow the application of average theories, and numerical examples show that resonance trapping for internal resonances must have a chaotic origin. As expected from analytical theories, for the case of one disturbing planet, the particle's eccentricity decreases continually after capture and resonance is eventually broken. When two disturbing planets are present, however, there is not necessarily a decrease of the eccentricity, but it may increase, decrease or oscillate, although escape from resonance always occurs anyway.
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Graham, Severance, and Kathryn Volk. "Uranus’s Influence on Neptune’s Exterior Mean-motion Resonances." Planetary Science Journal 5, no. 6 (June 1, 2024): 135. http://dx.doi.org/10.3847/psj/ad4707.
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Abstract Neptune’s external mean-motion resonances play an important role in sculpting the observed population of trans-Neptunian objects (TNOs). The population of scattering TNOs is known to “stick” to Neptune's resonances while evolving in semimajor axis (a), though simulations show that resonance sticking is less prevalent at a ≳ 200–250 au. Here we present an extensive numerical exploration of the strengths of Neptune's resonances for scattering TNOs with perihelion distances q = 33 au. We show that the drop-off in resonance sticking for the large a scattering TNOs is not a generic feature of scattering dynamics but can instead be attributed to the specific configuration of Neptune and Uranus in our solar system. In simulations with just Uranus removed from the giant planet system, Neptune's resonances are strong in the scattering population out to at least ∼300 au. Uranus and Neptune are near a 2:1 period ratio, and the variations in Neptune's orbit resulting from this near-resonance are responsible for destabilizing Neptune's resonances for high-e TNO orbits beyond the ∼20:1 resonance at a ≈ 220 au. Direct interactions between Uranus and the scattering population are responsible for slightly weakening Neptune's closer-in resonances. In simulations where Neptune and Uranus are placed in their mutual 2:1 resonance, we see almost no stable libration of scattering particles in Neptune's external resonances. Our results have important implications for how the strengths of Neptune's distant resonances varied during the epoch of planet migration when the Neptune–Uranus period ratio was evolving. These strength variations likely affected the distant scattering, resonant, and detached TNO populations.
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Popandopulo, Nikita A., Anna G. Aleksandrova, and Tat’yana V. Bordovitsyna. "Analysis of a dynamic structure of secular resonances in circumlunar orbital space." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 77 (2022): 110–24. http://dx.doi.org/10.17223/19988621/77/9.
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When developing new circumlunar satellite systems for various purposes, it is necessary to know the dynamic features of various regions of circumlunar space. It is noted that one of the main features of the dynamics of artificial Moon satellites (AMS) is the increase in the eccentricity of their orbits. It is known that such orbital evolution of objects can be caused by resonant perturbations. In this regard, the purpose of this paper is to study the influence of secular and half-secular resonances occurring on the AMS. The results are obtained by means of the processing of data from an extensive numerical experiment to study the orbital evolution of the uniformly distributed circumlunar objects moving in the range of large semi-axes from 1911.8 to 26070 km and with inclinations from 0 to 180°. The study of the influence of secular and half-secular resonances on the orbital evolution of the AMS is carried out using numerical and analytical techniques. Both techniques have advantages and disadvantages and are used in the study. Maps of secular and half-secular resonances are of great practical importance. They clearly demonstrate the areas of influence of secular resonances on the orbital evolution of circumlunar objects depending on the initial values of the semimajor axis and inclination of the orbits of objects. The analysis of each particular resonance consists in the revealing of a resonant characteristic type, which is determined by the nature of the change in a critical argument: libration - stable resonance, libration/circulation - unstable resonance, and circulation - no resonance. To estimate the whole range of the influence of resonances on the AMS dynamics, maps of their overlaps are built. The maps allow one to determine areas with significant influence of the resonances on the orbital evolution of circumlunar objects. The obtained results show that the reason for a large increase in the eccentricity in a vast area of circumlunar orbital space is the presence of the stable apsidal resonance of the Kozai-Lidov type.
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Grimshaw, R. "Resonant wave interactions near a critical level in a stratified shear flow." Journal of Fluid Mechanics 269 (June 25, 1994): 1–22. http://dx.doi.org/10.1017/s0022112094001461.
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Resonant interactions between internal gravity waves propagating in a stratified shear flow are considered for the case when the background density and shear flow vary slowly with respect to the waves. In Grimshaw (1988) triad resonances were considered, and interaction equations derived for the case when the resonance conditions are met only on certain space-time surfaces, being resonance sites. Here this analysis is extended to include higher-order resonances, with the aim of studying resonant wave interactions near a critical level. It is shown that a secondary resonant interaction between two incoming waves, in which two harmonic components of one incoming wave interact with a single harmonic component of another incoming wave, produces a reflected wave. This result is shown to agree with the study of Brown & Stewartson (1980, 1982a, b) who obtained this same result by a different approach.
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Chen, Xing-Yan, Andreas Schindewolf, Sebastian Eppelt, Roman Bause, Marcel Duda, Shrestha Biswas, Tijs Karman, Timon Hilker, Immanuel Bloch, and Xin-Yu Luo. "Field-linked resonances of polar molecules." Nature 614, no. 7946 (February 1, 2023): 59–63. http://dx.doi.org/10.1038/s41586-022-05651-8.
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AbstractScattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances1, which have been extensively studied in various platforms1–7, are not expected to exist in most ultracold polar molecules because of the fast loss that occurs when two molecules approach at a close distance8–10. Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules. The so-called field-linked resonances11–14 occur in the scattering of microwave-dressed molecules because of stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium–potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole–dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids15 and molecular supersolids16, as well as assembling ultracold polyatomic molecules.
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Froeschle, Christiane, and Alessandro Morbidelli. "The Secular Resonances in the Solar System." Symposium - International Astronomical Union 160 (1994): 189–204. http://dx.doi.org/10.1017/s0074180900046544.
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In the last three years new studies on secular resonances have been done. The second–order and fourth–degree secular perturbation theory of Milani and Knežević allowed to point out the effect of mean motion resonances on the location of the linear and non linear secular resonances. Moreover this theory improved the knowledge of the exact location of the g = g6 (i.e. ν6) resonance at low inclination. Morbidelli and Henrard revisited the semi–numerical method of Williams, taking into account the quadratic terms in the perturbing masses. They computed not only the location of secular resonances, but also provided a global description of the resonant dynamics in the main secular resonances namely g = g5 (i.e. ν5), g = g6 (i.e. ν6) and s = s6 (i.e. ν16). The resonant proper element algorithm developed by Morbidelli allows to identify the dynamical nature of resonant objects, and is a powerful tool to study the mechanisms of meteorite transport to the inner Solar System. Purely numerical experiments have been done, which show: (i) the complexity of the dynamics when two resonances overlap; (ii) the efficiency of successive crossings of non linear resonances in pumping up the inclination of small bodies; (iii) the efficiency of the secular resonance ν6 as a source of meteorites up to 2.4 AU.
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Halas, Naomi. "Playing with Plasmons: Tuning the Optical Resonant Properties of Metallic Nanoshells." MRS Bulletin 30, no. 5 (May 2005): 362–67. http://dx.doi.org/10.1557/mrs2005.99.
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AbstractNanoshells, concentric nanoparticles consisting of a dielectric core and a metallic shell, are simple spherical nanostructures with unique, geometrically tunable optical resonances. As with all metallic nanostructures, their optical properties are controlled by the collective electronic resonance, or plasmon resonance, of the constituent metal, typically silver or gold. In striking contrast to the resonant properties of solid metallic nanostructures, which exhibit only a weak tunability with size or aspect ratio, the optical resonance of a nanoshell is extraordinarily sensitive to the inner and outer dimensions of the metallic shell layer. The underlying reason for this lies beyond classical electromagnetic theory, where plasmon-resonant nanoparticles follow a mesoscale analogue of molecular orbital theory, hybridizing in precisely the same manner as the individual atomic wave functions in simple molecules. This plasmon hybridization picture provides an essential “design rule” for metallic nanostructures that can allow us to effectively predict their optical resonant properties. Such a systematic control of the far-field optical resonances of metallic nanostructures is accomplished simultaneously with control of the field at the surface of the nanostructure. The nanoshell geometry is ideal for tuning and optimizing the near-field response as a stand-alone surface-enhanced Raman spectroscopy (SERS) nanosensor substrate and as a surface-plasmon-resonant nanosensor.Tuning the plasmon resonance of nanoshells into the near-infrared region of the spectrum has enabled a variety of biomedical applications that exploit the strong optical contrast available with nanoshells in a spectral region where blood and tissue are optimally transparent.
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Stuchlík, Zdeněk, Andrea Kotrlová, and Gabriel Török. "Multi-resonance orbital model of HF QPOs." Proceedings of the International Astronomical Union 8, S290 (August 2012): 315–16. http://dx.doi.org/10.1017/s1743921312020182.
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AbstractUsing known frequencies of the twin peak high-frequency quasiperiodic oscillations (HF QPOs) and known mass M of the central black hole, the black-hole dimensionless spin a can be determined assuming a concrete version of the resonance model. However, large range of observationally limited values of the black hole mass implies a low precision of the spin estimates. We discuss the possibility of higher precision of the black hole spin a measurements in the framework of multi-resonance model inspired by observations of more than two HF QPOs in some black hole sources. We determine the spin and mass dependence of the twin peak frequencies with a general rational ratio n:m assuming a non-linear resonance of oscillations with the epicyclic and Keplerian frequencies or their combinations. In the multi-resonant model, the twin peak resonances are combined properly to give the observed frequency set. We focus on the special case of duplex frequencies, when the top, bottom, or mixed frequency is common at two different radii where the resonances occur giving triple frequency sets.
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Veksler, Naum, Jean-Louis Izbicki, Jean-Marc Conoir, and Pascal Rembert. "Methods of Isolation of Modal Resonances." Applied Mechanics Reviews 51, no. 7 (July 1, 1998): 449–74. http://dx.doi.org/10.1115/1.3099015.
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The scattering problem by immersed targets involves the resonance phenomenon. Different methods of isolation of modal resonances are discussed: the Resonant Scattering Theory (the different backgrounds used in this method are considered), the phase gradient method (which is partly independent of the background choice), and the Argand diagram method (leading to both theoretical and experimental determination of the frequency and the width of resonances) and an exact description of the resonance components of partial modes (involving the determination of the roots of the characteristic equation in the complex frequency plane). The results provided by these methods are compared, their validity domain is discussed. Whatever the method, the resonant components appear as Breit-Wigner functions: this is the common point between the different methods. This review article includes 119 references.
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Pichierri, Gabriele, and Alessandro Morbidelli. "The onset of instability in resonant chains." Monthly Notices of the Royal Astronomical Society 494, no. 4 (April 26, 2020): 4950–68. http://dx.doi.org/10.1093/mnras/staa1102.
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ABSTRACT There is evidence that most chains of mean motion resonances of type k:k − 1 among exoplanets become unstable once the dissipative action from the gas is removed from the system, particularly for large N (the number of planets) and k (indicating how compact the chain is). We present a novel dynamical mechanism that can explain the origin of these instabilities and thus the dearth of resonant systems in the exoplanet sample. It relies on the emergence of secondary resonances between a fraction of the synodic frequency 2π(1/P1 − 1/P2) and the libration frequencies in the mean motion resonance. These secondary resonances excite the amplitudes of libration of the mean motion resonances, thus leading to an instability. We detail the emergence of these secondary resonances by carrying out an explicit perturbative scheme to second order in the planetary masses and isolating the harmonic terms that are associated with them. Focusing on the case of three planets in the 3:2–3:2 mean motion resonance as an example, a simple but general analytical model of one of these resonances is obtained, which describes the initial phase of the activation of one such secondary resonance. The dynamics of the excited system is also briefly described. Finally, a generalization of this dynamical mechanism is obtained for arbitrary N and k. This leads to an explanation of previous numerical experiments on the stability of resonant chains, showing why the critical planetary mass allowed for stability decreases with increasing N and k.
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Zangwill, Gilad, and Er’el Granot. "Multiple Fano Resonances in Dynamic Resonant Tunneling Processes." Applied Sciences 13, no. 11 (June 2, 2023): 6767. http://dx.doi.org/10.3390/app13116767.
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The existence of Fano resonances in dynamic resonant tunneling (RT) systems has been investigated. Fano resonances are characterized by the appearance of a 100% reflection coefficient in proximity to a high transmission coefficient. For a Fano resonance to appear, a bound state must exist. On the other hand, a resonant tunneling process is characterized by a high transmission and the existence of a quasi-bound state (QBS) instead of a bound one. It has been shown that, by narrowing the width of the barrier, the resonance energy of the QBS gradually decreases and eventually turns into a bound state. Consequently, in a dynamic RT process, there are two scenarios: either a bound state exists, in which case, Fano resonances exist for any barrier width, or a QBS exists, and the barrier should be narrow enough for the Fano resonance to appear. In both cases, the incoming particle’s frequency must be lower than the oscillating well’s frequency. In this work, these resonances are investigated in detail, and both exactly numerically and approximated analytical expressions are derived for both the weak and strong oscillating amplitude regimes. One of the conclusions is that, when the oscillating frequency is low enough, multiple Fano resonances can appear by varying the barrier’s width. Since these resonances are very sharp and zero transmission can easily be detected, this property can be used as a very accurate method for measuring the barrier’s width, even when the particle’s de-Broglie wavelength is much larger than the barrier’s width.
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Kholostova, O. V. "On Nonlinear Oscillations of a Time-Periodic Hamiltonian System at a 2:1:1 Resonance." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd221101.
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We consider the motions of a near-autonomous Hamiltonian system $2\pi$-periodic in time, with two degrees of freedom, in a neighborhood of a trivial equilibrium. A multiple parametric resonance is assumed to occur for a certain set of system parameters in the autonomous case, for which the frequencies of small linear oscillations are equal to two and one, and the resonant point of the parameter space belongs to the region of sufficient stability conditions. Under certain restrictions on the structure of the Hamiltonian of perturbed motion, nonlinear oscillations of the system in the vicinity of the equilibrium are studied for parameter values from a small neighborhood of the resonant point. Analytical boundaries of parametric resonance regions are obtained, which arise in the presence of secondary resonances in the transformed linear system (the cases of zero frequency and equal frequencies). The general case, for which the parameter values do not belong to the parametric resonance regions and their small neighborhoods, and both cases of secondary resonances are considered. The question of the existence of resonant periodic motions of the system is solved, and their linear stability is studied. Two- and three-frequency conditionally periodic motions are described. As an application, nonlinear resonant oscillations of a dynamically symmetric satellite (rigid body) relative to the center of mass in the vicinity of its cylindrical precession in a weakly elliptical orbit are investigated.
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Dvorak, R. "New Results on the Motions of Asteroids in Resonances." Symposium - International Astronomical Union 152 (1992): 145–52. http://dx.doi.org/10.1017/s0074180900091051.
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In this article we present a numerical study of the motion of asteroids in the 2:1 and 3:1 resonance with Jupiter. We integrated the equations of motion of the elliptic restricted 3-body problem for a great number of initial conditions within this 2 resonances for a time interval of 104 periods and for special cases even longer (which corresponds in the the Sun-Jupiter system to time intervals up to 106 years). We present our results in the form of 3-dimensional diagrams (initial a versus initial e, and in the z-axes the highest value of the eccentricity during the whole integration time). In the 3:1 resonance an eccentricity higher than 0.3 can lead to a close approach to Mars and hence to an escape from the resonance. Asteroids in the 2:1 resonance with Jupiter with eccentricities higher than 0.5 suffer from possible close approaches to Jupiter itself and then again this leads in general to an escape from the resonance. In both resonances we found possible regions of escape (chaotic regions), but only for initial eccentricities e > 0.15. The comparison with recent results show quite a good agreement for the structure of the 3:1 resonance. For motions in the 2:1 resonance our numeric results are in contradiction to others: high eccentric orbits are also found which may lead to escapes and consequently to a depletion of this resonant regions.
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Rahman, Atta Ur, Junping Geng, Richard W. Ziolkowski, Tao Hang, Qaisar Hayat, Xianling Liang, Sami Ur Rehman, and Ronghong Jin. "Photoluminescence Revealed Higher Order Plasmonic Resonance Modes and Their Unexpected Frequency Blue Shifts in Silver-Coated Silica Nanoparticle Antennas." Applied Sciences 9, no. 15 (July 26, 2019): 3000. http://dx.doi.org/10.3390/app9153000.
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Higher order plasmonic resonance modes and their frequency blue shifts in silver-coated silica nanoparticle antennas are studied. Synthesizing them with a wet chemistry method, silica (SiO2) nanoparticles were enclosed within silver shells with different thicknesses. A size-dependent Drude model was used to model the plasmonic shells and their optical losses. Two higher order plasmonic resonances were identified for each case in these simulations. The photoluminescence spectroscopy (PL) experimental results, in good agreement with their simulated values, confirmed the presence of those two higher order resonant modes and their resonance frequencies. When compared with pure metallic Ag nanoparticles, size-induced blue shifts were observed in these resonance frequencies.
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LIU, YUMING, and DICK K. P. YUE. "On generalized Bragg scattering of surface waves by bottom ripples." Journal of Fluid Mechanics 356 (February 10, 1998): 297–326. http://dx.doi.org/10.1017/s0022112097007969.
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We study the generalized Bragg scattering of surface waves over a wavy bottom. We consider the problem in the general context of nonlinear wave–wave interactions, and write down and provide geometric constructions for the Bragg resonance conditions for second-order triad (class I) and third-order quartet (class II and class III) wave– bottom interactions. Class I resonance involving one bottom and two surface wave components is classical. Class II resonance manifests bottom nonlinearity (it involves two bottom and two surface wave components), and has been studied in the laboratory. Class III Bragg resonance is new and is a result of free-surface nonlinearity involving resonant interaction among one bottom and three surface wave components. The amplitude of the resonant wave is quadratic in the surface wave slope and linear in the bottom steepness, and, unlike the former two cases, the resonant wave may be either reflected or transmitted (relative to the incident waves) depending on the wave–bottom geometry. To predict the initial spatial/temporal growth of the Bragg resonant wave for these resonances, we also provide the regular perturbation solution up to third order. To confirm these predictions and to obtain an efficient computational tool for general wave–bottom problems with resonant interactions, we extend and develop a powerful high-order spectral method originally developed for nonlinear wave–wave and wave–body interactions. The efficacy of the method is illustrated in high-order Bragg resonance computations in two and three dimensions. These results compare well with existing experiments and perturbation theory for the known class I and class II Bragg resonance cases, and obtain and elucidate the new class III resonance. It is shown that under realistic conditions with moderate to small surface and bottom steepnesses, the amplitudes of third-order class II and class III Bragg resonant waves can be comparable in magnitude to those resulting from class I interactions and appreciable relative to the incident wave.
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Sangoi Mendonça, Lucas, and Fábio Ecke Bisogno. "RESONANCE-BASED NORMALIZATION THEORY FOR ANALYSIS AND DESIGN OF RESONANT POWER CONVERTERS." Eletrônica de Potência 24, no. 3 (September 30, 2019): 356–65. http://dx.doi.org/10.18618/rep.2019.3.0018.
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Jinhua Hu, Jinhua Hu, Xiuhong Liu Xiuhong Liu, Jijun Zhao Jijun Zhao, and and Jun Zou and Jun Zou. "Investigation of Fano resonance in compound resonant waveguide gratings for optical sensing." Chinese Optics Letters 15, no. 3 (2017): 030502–30505. http://dx.doi.org/10.3788/col201715.030502.
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Mustill, Alexander J., and Mark C. Wyatt. "Hamiltonian model of capture into mean motion resonance." Proceedings of the International Astronomical Union 6, S276 (October 2010): 300–303. http://dx.doi.org/10.1017/s1743921311020357.
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AbstractMean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. The model is applicable to many scenarios, including (i) Planet migration through gas discs trapping other planets or planetesimals in resonances; (ii) Planet migration through a debris disc; (iii) Dust migration through PR drag. The Hamiltonian model will allow quick interpretation of the resonant properties of extrasolar planets and Kuiper Belt Objects, and will allow synthetic images of debris disc structures to be quickly generated, which will be useful for predicting and interpreting disc images made with ALMA, Darwin/TPF or similar missions. Full details can be found in Mustill & Wyatt (2011).
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Zhang, Dayong, Li Cheng, and Zuochun Shen. "Formation Laws of Direction of Fano Line-Shape in a Ring MIM Plasmonic Waveguide Side-Coupled with a Rectangular Resonator and Nano-Sensing Analysis of Multiple Fano Resonances." Crystals 11, no. 7 (July 14, 2021): 819. http://dx.doi.org/10.3390/cryst11070819.
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Plasmonic MIM (metal-insulator-metal) waveguides based on Fano resonance have been widely researched. However, the regulation of the direction of the line shape of Fano resonance is rarely mentioned. In order to study the regulation of the direction of the Fano line-shape, a Fano resonant plasmonic system, which consists of a MIM waveguide coupled with a ring resonator and a rectangle resonator, is proposed and investigated numerically via FEM (finite element method). We find the influencing factors and formation laws of the ‘direction’ of the Fano line-shape, and the optimal condition for the generation of multiple Fano resonances; and the application in refractive index sensing is also well studied. The conclusions can provide a clear theoretical reference for the regulation of the direction of the line shape of Fano resonance and the generation of multi Fano resonances in the designs of plasmonic nanodevices.
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Tung, Bui Son, Bui Xuan Khuyen, Young Joon Yoo, Joo Yull Rhee, Ki Won Kim, Vu Dinh Lam, and Young Pak Lee. "Reversibly-propagational metamaterial absorber for sensing application." Modern Physics Letters B 32, no. 04 (February 9, 2018): 1850044. http://dx.doi.org/10.1142/s0217984918500446.
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We investigated a reversibly-propagational metamaterial perfect absorber (MPA) for X band using two separated identically-patterned copper layers, which were deposited on continuous dielectric FR-4 layers. By adjusting oblique incidence, two separated resonances are excited, then come close to each other and is finally merged to be a perfect absorption peak at 10.1 GHz. The nature of resonance is the quadrupole mode instead of the fundamental resonances in common MPAs. The mechanism of perfect absorption is the coupling of two quadrupole resonances at their superposition, leading to an enhancement of energy absorption. Finally, we numerically presented the capability of sensing thin resonant substance using the proposed MPA. The characteristic resonance of substance, which does not appear on the absorption spectrum at the limited thickness of bare substance layer, is detected with a great magnitude of signal by exploiting the absorption resonance of MPA. Our work provides another way to obtain the reversibly-propagational absorption by controlling the incident angle instead of the geometrical structure, and might be useful for the potential devices based on MPA such as detectors and sensors.
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Wu, Yipeng, Hongli Ji, Jinhao Qiu, Weiqun Liu, and Jinling Zhao. "An internal resonance based frequency up-converting energy harvester." Journal of Intelligent Material Systems and Structures 29, no. 13 (May 31, 2018): 2766–81. http://dx.doi.org/10.1177/1045389x18778370.
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Frequency up-converting vibration energy harvester can bridge the gap between high-frequency response and low-frequency input, greatly increasing the efficiency of energy conversion. This article proposed a novel frequency up-converting energy harvester based on 1:3 internal resonance in 2 degree-of-freedom cubic nonlinear systems. The harvester consists of two asymmetric cantilevers corresponding to two vibration degrees-of-freedom. The ratio of cantilevers’ first-order resonances is (or close to) 1:3. When excited frequency matches the resonant frequency of the first assisting cantilever, 1:3 internal resonance of the harvester system occurs, leading to drastic vibration of the second generating cantilever at its resonance. The generated voltage frequency is then three times increased. Finally, simulated and experimental results clearly proved this frequency up-converting principle. In addition, the resonant frequency tuning and wideband behaviors of the harvester were also investigated, which increased the viability of the proposed harvester under the practical environment vibrations.
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Dong, Wei Jie, Meng Wei Liu, and Cui Yan. "Measurement and Visualization of Dynamics of Piezoelectric Microcantilever." Key Engineering Materials 437 (May 2010): 30–34. http://dx.doi.org/10.4028/www.scientific.net/kem.437.30.
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Methods for measuring the resonant frequencies and visualizing the motion of the Pb(Zr0.5Ti0.5)O3 microcantilever are investigated. Considering the two-segment structure of the microcantilever, a self-exiting self-sensing method is proposed to obtain the fundamental resonant frequency. An optical system consisting of light microscope, CCD camera and video card is established to visualize the first two vibration mode shapes. The theoretical, measured and visualized first resonance of one micocantilever is 17.28 kHz, 17 kHz and 17.8 kHz, respectively. A theoretical second resonance of 84.16 kHz is seen at 71.9 kHz. The proposed method is valid for measuring and visualizing low resonances of active micro structure.
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King, M. E., and A. F. Vakakis. "An Energy-Based Approach to Computing Resonant Nonlinear Normal Modes." Journal of Applied Mechanics 63, no. 3 (September 1, 1996): 810–19. http://dx.doi.org/10.1115/1.2823367.
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A formulation for computing resonant nonlinear normal modes (NNMs) is developed for discrete and continuous systems. In a canonical framework, internal resonance conditions are immediately recognized by identifying commensurable linearized natural frequencies of these systems. Additionally, a canonical formulation allows for a single (linearized modal) coordinate to parameterize all other coordinates during a resonant NNM response. Energy-based NNM methodologies are applied to a canonical set of equations and asymptotic solutions are sought. In order to account for the resonant modal interactions, it will be shown that high-order terms in the O(1) solutions must be considered (in the absence of internal resonances, a linear expansion at O(1) is sufficient). Two applications (‘3:1’ resonances in a two-degree-of-freedom system and ‘3:1’ resonance in a hinged-clamped beam) are then considered by which to demonstrate the resonant NNM methodology. It is shown that for some responses, nonlinear modal relations do not exist in the context of physical coordinates and thus a transformation to a canonical framework is necessary in order to appropriately define NNM relations.
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Li, Miao, Yukun Huang, and Shengping Gong. "Survey of asteroids in retrograde mean motion resonances with planets." Astronomy & Astrophysics 630 (September 24, 2019): A60. http://dx.doi.org/10.1051/0004-6361/201936117.
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Aims. Asteroids in mean motion resonances (MMRs) with planets are common in the solar system. In recent years, increasingly more retrograde asteroids are discovered, several of which are identified to be in resonances with planets. We here systematically present the retrograde resonant configurations where all the asteroids are trapped with any of the eight planets and evaluate their resonant condition. We also discuss a possible production mechanism of retrograde centaurs and dynamical lifetimes of all the retrograde asteroids. Methods. We numerically integrated a swarm of clones (ten clones for each object) of all the retrograde asteroids (condition code U < 7) from −10 000 to 100 000 yr, using the MERCURY package in the model of solar system. We considered all of the p/−q resonances with eight planets where the positive integers p and q were both smaller than 16. In total, 143 retrograde resonant configurations were taken into consideration. The integration time was further extended to analyze their dynamical lifetimes and evolutions. Results. We present all the meaningful retrograde resonant configurations where p and q are both smaller than 16 are presented. Thirty-eight asteroids are found to be trapped in 50 retrograde mean motion resonances (RMMRs) with planets. Our results confirm that RMMRs with giant planets are common in retrograde asteroids. Of these, 15 asteroids are currently in retrograde resonances with planets, and 30 asteroids will be captured in 35 retrograde resonant configurations. Some particular resonant configurations such as polar resonances and co-orbital resonances are also identified. For example, Centaur 2005 TJ50 may be the first potential candidate to be currently in polar retrograde co-orbital resonance with Saturn. Moreover, 2016 FH13 is likely the first identified asteroid that will be captured in polar retrograde resonance with Uranus. Our results provide many candidates for the research of retrograde resonant dynamics and resonance capture. Dynamical lifetimes of retrograde asteroids are investigated by long-term integrations, and only ten objects survived longer than 10 Myr. We confirmed that the near-polar trans-Neptunian objects 2011 KT19 and 2008 KV42 have the longest dynamical lifetimes of the discovered retrograde asteroids. In our long-term simulations, the orbits of 12 centaurs can flip from retrograde to prograde state and back again. This flipping mechanism might be a possible explanation of the origins of retrograde centaurs. Generally, our results are also helpful for understanding the dynamical evolutions of small bodies in the solar system.
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Zhang, Zhiyong, Thomas Sattel, Yujie Zhu, Xuan Li, Yawei Dong, and Xiaoting Rui. "Mechanism and Characteristics of Global Varying Compliance Parametric Resonances in a Ball Bearing." Applied Sciences 10, no. 21 (November 5, 2020): 7849. http://dx.doi.org/10.3390/app10217849.
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Varying compliance (VC) is an unavoidable form of parametric excitation in rolling bearings and can affect the stability and safety of the bearing and its supporting rotor system. To date, we have investigated VC primary resonance in ball bearings, and in this paper other parametric VC resonance types are addressed. For a classical ball bearing model with Hertzian contact and clearance nonlinearities between the rolling elements and raceway, the harmonic balance and alternating frequency/time domain (HB–AFT) method and Floquet theory are adopted to analyze the VC parametric resonances and their stabilities. It is found that the 1/2-order subharmonic resonances, 2-order superharmonic resonances, and various VC combination resonances, such as the 1-order and 2-order summed types, can be excited, thus resulting in period-1, period-2, period-4, period-8, period-35, quasi-period, and even chaotic VC motions in the system. Furthermore, the bifurcation and hysteresis characteristics of complex VC resonant responses are discussed, in which cyclic fold, period doubling, and the second Hopf bifurcation can occur. Finally, the global involution of VC resonances around bearing clearance-free operations (i.e., adjusting the bearing clearance to zero or one with low interference) are provided. The overall results extend the investigation of VC parametric resonance cases in rolling bearings.
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Zhu, Qixin, Hongli Liu, Yiyi Yin, Lei Xiong, and Yonghong Zhu. "On Numerical Simulation Approach for Multiple Resonance Modes in Servo Systems." Journal of Control Science and Engineering 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/1261495.
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Mechanical resonance is one of the most pervasive problems in servo control. Closed-loop simulations are requisite when the servo control system with high accuracy is designed. The mathematical model of resonance mode must be considered when the closed-loop simulations of servo systems are done. There will be a big difference between the simulation results and the real actualities of servo systems when the resonance mode is not considered in simulations. Firstly, the mathematical model of resonance mode is introduced in this paper. This model can be perceived as a product of a differentiation element and an oscillating element. Secondly, the second-order differentiation element is proposed to simulate the resonant part and the oscillating element is proposed to simulate the antiresonant part. Thirdly, the simulation approach for two resonance modes in servo systems is proposed. Similarly, this approach can be extended to the simulation of three or even more resonances in servo systems. Finally, two numerical simulation examples are given.
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Konenkov, NV. "A simulation study of excitation contour of a linear trap with spatial harmonics." European Journal of Mass Spectrometry 27, no. 2-4 (May 26, 2021): 94–100. http://dx.doi.org/10.1177/14690667211020153.
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The process of nonlinear resonant excitation of ion oscillations in a linear trap is studied. There is still no detailed simulation of the resonance peak in the literature. We propose to use the excitation contour to describe the collective ion resonance. The excitation contour is a resonant mass peak obtained by the trajectory method with the Gaussian distribution of the initial coordinates and velocities. The following factors are considered: excitation time, low order hexapole and octopole harmonics with amplitudes A3 and A4, the depth of the initial ion cloud position. These multipoles are used for selective ion ejection from linear ion trap. All these factors affect the ion yield and the shape of the contours. Obtained data can be useful for control of such processes as ion fragmentation, ion isolation, ion activation, and ion ejection. Simulated resonance peaks are important for the theoretical description of the ion collective nonlinear resonances.
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Bellucci, Stefano, Volodymyr Fitio, Iryna Yaremchuk, Oleksandr Vernyhor, and Yaroslav Bobitski. "Features of the Resonance in a Rectangular Dielectric Surace-Relief Gratings Illuminated with a Limited Cross Section Gaussian Beam." Nanomaterials 12, no. 1 (December 28, 2021): 72. http://dx.doi.org/10.3390/nano12010072.
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In this work the features of the resonance in a rectangular dielectric surface-relief gratings, illuminated with a limited cross-section Gaussian beam, have been studied. The rigorous coupled wave method and beam decomposition into the plane waves by the Fourier transform have been used. It is shown that there is a resonant wavelength for each thickness of the dielectric grating. The value of resonant wavelength depends on the beam angle of incidence on the gratings. Moreover, the two types of resonances can occur in the grating at certain grating parameters. The power reflection coefficient is practically equal to unity for the first type of resonance and is much smaller than unity, for the second one. The obtained results extend the knowledge regarding the nature of the waveguide resonance in the dielectric grating, considering the limited cross section beam, and they can increase its use in many applications.