Nonresonant States Research Articles

Experimental study on a pitching wave energy converter with adjustable natural period

This paper proposed a pitching wave energy converter with adjustable natural period (called C-WEC), which is achieved by moving the movable mass block. A prototype was fabricated and tested in a wave flume to study the performance of the C-WEC. Free decay tests demonstrated that the natural period of the prototype can be adjusted between 1.60 s and 3.30 s. The wave flume tests showed that for regular and irregular waves, the prototype can capture high mechanical power and exhibit large response amplitude operator (RAO) as well as high capture width ratio (CWR) across a wide range of wave periods, avoiding poor performance in non-resonant states. The Froude scaling law was used to assess the annual average power of a 1:16th full-scale C-WEC in real seas off the Canary Islands based on the measured mechanical power in irregular waves. The result showed that the annual average power of the C-WEC using tuning control can be up to 29.8 kW, an increase of 67.4% compared to the WEC with a constant natural period. The experimental results showed that the C-WEC is a promising pitching wave energy converter and its natural period adjustment method can be easily applied to other pitching WECs.

Determination of atomic multiphoton-ionization phases by trichromatic multichannel wave-packet interferometry

We present the unambiguous determination of quantum phases in the multiphoton ionization (MPI) of potassium atoms by using a multichannel photoelectron interferometry scheme based on trichromatic pulse shaping. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the $3d$ state resulting in a $(2+1)$ resonance-enhanced MPI (REMPI), a $(1+2)$ REMPI occurs via the nonresonant intermediate $4p$ state with an initial green or blue pulse. We show that ionization via a nonresonant intermediate state lifts the degeneracy of photoelectron interferograms from pathways consisting of permutations of the colors. The analysis of the interferograms reveals a phase shift of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ depending on the sign of the detunings in the $(1+2)$ REMPI pathways. In addition, we demonstrate that the photoionization time delay in the resonant $(2+1)$ REMPI pathway gives rise to a linear spectral phase in the photoelectron spectra. Insights into the underlying MPI processes are gained through an analytic perturbative description and numerical simulations of a trichromatic driven three-level system coupled to the continuum.

Non-resonant piezoelectric linear motor with alternating normal contact force.

A non-resonant piezoelectric linear motor with alternating normal contact force is developed to realize a piezoelectric linear motor with high precision, large stroke, and strong thrust. The motor employs four piezoelectric stacks to excite the non-resonant state vibration of two driving feet, which alternately push the mover to generate unidirectional motion. Through the analysis of the working principle of the motor, the structure of the motor is designed and manufactured. The test results show the feasibility of the motor. Furthermore, the operating results show that the flatness of the contact surface strongly affects the performance of the motor. The design criteria of the motor are proposed, thus providing a basis for the optimization of the motor.

Investigation of multistep effects for proton inelastic scattering to the 21+ state in He6

Multistep effects among bound, resonant, and nonresonant states have been investigated by the continuum-discretized coupled-channels method (CDCC). In the CDCC, a resonant state is treated as multiple states fragmented in a resonance energy region, although it is described as a single state in usual coupled-channels calculations. For such the fragmented resonant states, one-step, and multistep contributions to the cross sections should be carefully discussed because the cross sections obtained by the one-step calculation depend on the number of those states, which corresponds to the size of the model space. To clarify the role of the multistep effects, we propose the one-step calculation without model-space dependence for the fragmented resonant states. Furthermore, we also discuss the multistep effects among the ground, ${2}_{1}^{+}$ resonant, and nonresonant states in $^{6}\mathrm{He}$ for proton inelastic scattering.

Resonant interaction in chiral Eshelby-twisted van der Waals atomic layers

We study the electronic structures of chiral, Eshelby-twisted van der Waals atomic layers with a particular focus on a chiral twisted graphite (CTG), a graphene stack with a constant twist angle $\theta$ between successive layers. We show that each CTG can host infinitely many resonant states which arise from the interaction between the degenerate monolayer states of the constituent layers. Each resonant state has a screw rotational symmetry, and may have a smaller reduced Brillouin zone than other non-resonant states in the same structure. And each CTG can have the resonant states with up to four different screw symmetries. We derive the energies and wave functions of the resonant states in a universal form of a one-dimensional chain regardless of $\theta$, and show that these states exhibit a clear optical selection rule for circularly polarized light. Finally, we discuss the uniqueness and existence of the exact center of the lattice and the self-similarity of the wave amplitudes of the resonant states.

Operating characteristics of a linear compressor in the cryocooler

l A new efficiency map under the total impedance is proposed. l Displacement and current cannot affect maximum efficiency (0.86 at 963+0i N s m −1 ). l Non-resonant state may have higher efficiency than resonant state. l Different routines of achieving impedance matching are verified by experiments. Linear compressors have been widely used in the cryocoolers and refrigerators due to the advantages of high efficiency, low vibration level and compact construction. However, due to the complicated dynamic characteristics of the linear compressor, the impedance matching of the cryocooler is still an issue. In this study, the operating characteristics of a linear compressor are studied based on the electrical and mechanical impedance. The influences of the load impedance on the displacement and efficiency are analyzed. A new efficiency map under the total impedance is proposed. Experiments on a pulse tube cryocooler with a linear compressor are conducted to verify the theoretical analyses. The maximum theoretical efficiency of 0.86 is obtained at 963+0i N s m −1 . It is not affected by the displacement or the current. Two different routines by fixing the current at 20 A or fixing the voltage at 50 V are tested on the new efficiency map. The results show the feasibility of using the new map to find a better impedance matching and to achieve an efficiency of 0.68. The research is helpful to improve the whole cryocooler performance.

Cobalt ions doped PNN-PHT ceramics with excellent piezoelectric properties

In this study, Co-doped 0.49 Pb(Ni1/3Nb2/3)O3-0.51 Pb(Hf0.3Ti0.7)O3 ceramics with high piezoelectric constants, electromechanical coupling coefficients, and low dielectric losses were prepared by conventional solid-phase reaction method for use as piezoelectric energy harvesters in both resonant and non-resonant working states. XRD results showed the dissolution of Co ions in the crystal lattice, thereby replacing B-sites and transforming the crystal phase into tetragonal phase. Valence states of Co obtained from fitted XPS data confirmed the existence of Co as Co2+ in the lattice. The introduction of Co2+ effectively increased grain size, improved ferroelectric properties, reduced leakage current density, and enhanced electromechanical coupling coefficient kp. Impacts of Co-doping on properties of the as-obtained ceramics were discussed. The optimal performances were obtained at x = 1.25, with piezoelectric constant d33~780 pC/N, electromechanical coupling coefficient kp~0.62, and dielectric loss tan δ = 0.78%. In sum, the excellent piezoelectric properties of Co-doped PNN-PHT ceramics look promising for use as piezoelectric energy harvesters.

A partial similitude method for vibration responses of rotor systems: Numerical and experimental verification

Similitude theory provides the necessary conditions to predict the structural responses of the full-scale prototype through the scaled model, and is widely used in full-scale experiments of large structures. However, the prediction accuracy is insufficient in partial similitude. Aiming at this issue, this paper proposes the frequency adjustment laws to predict vibration responses of full-scale rotor in non-resonant state, since the rotating machinery usually works in non-resonant state. On this basis, a partial similitude method is presented by combining the frequency adjustment laws with the current method. The proposed method provides several scaling laws in the whole range of rotating speed, while only one scaling factor is used to predict the vibration responses in existing methods. The accuracy of the proposed method is verified by the numerical and experimental case studies, where the geometrical distortion is considered. In the numerical case study, the scaling laws of a rotor system are obtained by the proposed method and existing methods. The predicted results of the proposed method are compared with those of the existing methods. It is found the proposed method accurately predicts the displacements and accelerations of prototypes through those of scaled model. Moreover, the proposed method achieves a higher accuracy. The experimental study carries out the testing for the prototype and model test rigs. The experimental results show that the proposed method provides better results in predicting the displacement and acceleration compared with the existing methods. The proposed method allows designers to design a scaled model and to reproduce the vibratory behavior of the full-size prototype, which reduces the difficulty, costs and time of experimental test. Moreover, the proposed partial similitude method has a better performance than the existing methods.

Direct Transition from Triplet Excitons to Hybrid Light-Matter States via Triplet-Triplet Annihilation.

Strong light–matter coupling generates hybrid states that inherit properties of both light and matter, effectively allowing the modification of the molecular potential energy landscape. This phenomenon opens up a plethora of options for manipulating the properties of molecules, with a broad range of applications in photochemistry and photophysics. In this article, we use strong light–matter coupling to transform an endothermic triplet–triplet annihilation process into an exothermic one. The resulting gradual on–off photon upconversion experiment demonstrates a direct conversion between molecular states and hybrid light–matter states. Our study provides a direct evidence that energy can relax from nonresonant low energy molecular states directly into hybrid light–matter states and lays the groundwork for tunable photon upconversion systems that modify molecular properties in situ by optical cavities rather than with chemical modifications.

Dimuons in LHC

In a hadron collider like the Large Hadron Collider (LHC), the dimuon channel provides an ideal tool for the discovery of many predicted particles from Beyond Standard Model (BSM) theories such as high mass resonant, or non-resonant states. The high mass resonances like Z’ and the high mass non-resonant like contact in- teractions or extra dimensions should appear in the high mass tail of dimuon dis- tributions. The Drell-Yan process is the main source of high mass opposite sign muon pairs in the Standard Model (SM) which act as the irreducible background of signals of the above mentioned BSM models in proton-proton collisions. Therefore, it is important to study with the highest possible accuracy the Drell-Yan process. In this paper, we study in detail the expectations of the Drell-Yan process in the dimuon channel at next-to-next-to-leading order in QCD and next-to-leading order in the electroweak corrections. In our study, we considered a typical generic detector acceptance such as CMS or ATLAS at the LHC at center of mass energy 14 TeV. At the end of this study we gave estimates of the expected backgrounds for new physics searches in the dimuon final states.

Multiscale Heterogeneity Strategy in Piezoceramics for Enhanced Energy Harvesting Performances.

Piezoelectric energy harvesters (PEHs) with piezoceramics as the core can convert low-frequency vibration energy that is ubiquitous in the environment into electrical energy and are at the frontier of research in the field of energy. The high piezoelectric charge coefficient (d) together with the large piezoelectric voltage coefficient (g) are essential for enhancing the energy harvesting performances of PEHs working on a nonresonant state. However, conventional doping and solid solution design strategies lead to the same increase or decrease trend of d and dielectric permittivity ε, making it difficult to obtain a high g value because g = d/ε. Herein, exceptionally well-balanced performances of high d and large g are achieved simultaneously in modified Pb(Zr, Ti)O3(PZT)-based ceramics via a multiscale heterogeneity strategy, which involves coordination among the defect dipole, hierarchical domain, and composite. The electromechanical parameters of the optimal specimen are not only superior to those of many state-of-the-art commercial counterparts but also exhibit good thermal stability. Most importantly, the assembled PEH with the optimal specimen shows excellent variable temperature power generation characteristics. This work provides a paradigm for building PEH material through a multiscale heterogeneity strategy, expected to benefit a wide range of electromechanical coupling materials.

Impact of Absorbers on the Shielding Effectiveness of Metallic Rooms with Apertures

An electromagnetic field penetrating through an aperture or slot of a metallic enclosure generates many standing-waves due to the resonance inside the metallic enclosure, which results in reduced shielding performance. This paper examines the effect of absorbent material (absorber) to improve shielding effectiveness (SE) of large metallic rooms with apertures or slots. First, a theoretical formulation to extract the Q-factor of an absorber with any shape is proposed. Using this, the contribution of the absorber to the SE improvement of a shielded room with different sized circular apertures was investigated. Second, the resonant mode density inside the shielded room was classified into non-resonant, under-moded, and over-moded states with an increase in frequency, and the effect of the absorber in each frequency range was examined. The analysis was conducted through numerical simulation using a commercial full-wave simulator and experimental measurement using a fabricated actual shielded room and commercial absorbers. The accuracy of the analysis results was verified through the comparison of simulated and measured results. The analysis results ensured that the absorber was not effective in improving the SE in the non-resonant state of the metallic room. It was also confirmed that the absorber was effective in improving the SE in the over-moded state of the metallic room where a severe standing-wave occurs. In addition, the SE improvement level differed depending on the location of the absorber in the room.

Complex scaling: Physics of unbound light nuclei and perspective

Abstract The complex scaling method (CSM) is one of the most powerful methods of describing the resonances with complex energy eigenstates based on non-Hermitian quantum mechanics. We present the basic application of CSM to the properties of the unbound phenomena of light nuclei. In particular, we focus on many-body resonant and non-resonant continuum states observed in unstable nuclei. We also investigate the continuum level density (CLD) in the scattering problem in terms of the Green’s function with CSM. We discuss the explicit effects of resonant and non-resonant contributions in CLD and transition strength functions.

Nonlinear dynamical response of interacting bosons to synthetic electric field

We theoretically study the non-linear response of interacting neutral bosonic gas in a synthetically driven one-dimensional optical lattice. In particular, we examine the bosonic analogue of electronic higher harmonic generation in a strong time-dependent synthetic vector potential manifesting itself as the synthetic electric field. We show that the vector potential can generate reasonably high harmonics in the insulating regime, while the superfluid regime exhibits only a few harmonics. In the insulating regime, the number of harmonics increases with the increase in the strength of the vector potential. This originates primarily due to the field-driven resonant and non-resonant excitations in the neutral Mott state and their recombination with the ground state. If the repulsive interaction between two atoms ($U$) is close to the strength of the gauge potential ($A_0$), the resonant quasiparticle-quasihole pairs on nearest-neighbor sites, namely dipole states are found to a play a dominant role in the generating higher harmonics. However, in the strong-field limit $A_0\gg U$, the nonresonant states where quasiparticle-quasihole pairs are not on nearest-neighbor sites give rise to higher harmonics.

Investigation of contributions of the 22+ resonance in He6 via analysis of the He6(p, p′) reaction

We investigate the contribution of the $2^{+}_{2}$ resonance in $^6$He to observables via analysis of the $^6$He($p,p'$) reaction by using the continuum-discretized coupled channels method combined with the complex-scaling method. In this study, we obtain the $2^{+}_{2}$ state with the resonant energy 2.25 MeV and the decay width 3.75 MeV and analyse contributions of resonances and nonresonant continuum states to the cross section separately. It is found that the $2^{+}_{2}$ state plays an important role in the energy spectrum. Furthermore, contributions of nonresonant continuum states are also important to clarify the properties of the $2^{+}_{2}$ state.

Gamow-shell-model description of Li isotopes and their mirror partners

Background: Weakly bound and unbound nuclei close to particle drip lines are laboratories of new nuclear structure physics at the extremes of neutron/proton excess. The comprehensive description of these systems requires an open quantum system framework that is capable of treating resonant and nonresonant many-body states on equal footing. Purpose: In this work, we construct the minimal complex-energy configuration interaction approach to describe binding energies and spectra of selected 5 $\leq$ A $\leq$ 11 nuclei. Method: We employ the complex-energy Gamow shell model (GSM) assuming a rigid $^4$He core. The effective Hamiltonian, consisting of a core-nucleon Woods-Saxon potential and a simplified version of the Furutani-Horiuchi-Tamagaki interaction with the mass-dependent scaling, is optimized in the sp space. To diagonalize the Hamiltonian matrix, we employ the Davidson method and the Density Matrix Renormalization Group technique. Results: Our optimized GSM Hamiltonian offers a good reproduction of binding energies and spectra with the root-mean-square (rms) deviation from experiment of 160 keV. Since the model performs well when used to predict known excitations that have not been included in the fit, it can serve as a reliable tool to describe poorly known states. A case in point is our prediction for the pair of unbound mirror nuclei $^{10}$Li-$^{10}$N in which a huge Thomas-Ehrman shift dramatically alters the pattern of low-energy excitations. Conclusion: The new model will enable comprehensive studies of structure and reactions aspects of light drip-line nuclei.

The origins of nearly coplanar, non-resonant systems of close-in super-Earths

ABSTRACT Some systems of close-in ‘super-Earths’ contain five or more planets on non-resonant but compact and nearly coplanar orbits. The Kepler-11 system is an iconic representative of this class of system. It is challenging to explain their origins given that planet–disc interactions are thought to be essential to maintain such a high degree of coplanarity, yet these same interactions invariably cause planets to migrate into chains of mean motion resonances. Here, we mine a large data set of dynamical simulations of super-Earth formation by migration. These simulations match the observed period ratio distribution as long as the vast majority of planet pairs in resonance become dynamically unstable. When instabilities take place resonances are broken during a late phase of giant impacts, and typical surviving systems have planet pairs with significant mutual orbital inclinations. However, a subset of our unstable simulations matches the Kepler-11 system in terms of coplanarity, compactness, planet-multiplicity, and non-resonant state. This subset has dynamical instability phases typically much shorter than ordinary systems. Unstable systems may keep a high degree of coplanarity post-instability if planets collide at very low orbital inclinations (≲1○) or if collisions promote efficient damping of orbital inclinations. If planetary scattering during the instability takes place at low orbital inclinations (i ≲ 1○), orbital inclinations are barely increased by encounters before planets collide. When planetary scattering pumps orbital inclinations to higher values (≳1○) planets tend to collide at higher mutual orbital inclinations, but depending on the geometry of collisions mergers’ orbital inclinations may be efficiently damped. Each of these formation pathways can produce analogues to the Kepler-11 system.

An Electron Propagator Approach Based on a Multiconfigurational Reference State for the Investigation of Negative-Ion Resonances Using a Complex Absorbing Potential Method.

Negative-ion resonances are important metastable states that result from the collision between an electron and a neutral target. The course of many chemical processes in nature is often dictated by how an intermediate resonance state falls apart. This article reports on the development of an electron propagator (EP) based on a Hamiltonian Ĥ perturbed by a complex absorbing potential (CAP) and a multiconfigurational self-consistent field (MCSCF) initial state to study these resonances. Perturbation of Ĥ by a CAP makes the resonances amenable to a bound-state method like MCSCF. Resonances stand out among the non-resonant states as persistent complex eigenvalues of the perturbed Ĥ when the strength (η) of the CAP is varied. The MCSCF method gives a reliable and accurate description of the target states, especially when the non-dynamical correlations are dominant. The resonance energies are obtained from the poles of the EP. We propose three variants of our EP depending on how the effect of the CAP is introduced. We find that the computationally most efficient variant is the one in which the reference state of the EP is an unperturbed MCSCF wavefunction and a non-zero CAP is defined only on the virtual orbital subspace of the reference state. The onset of the CAP is carefully optimized in order to minimize the artifacts due to reflections from the CAP. An extrapolation method (based on a Padé approximant) and a de-perturbation method are adopted in order to account for the limitations of finite basis sets used and determine the resonance energy in the limit of η → 0. 2P Be-, 2Πg N2-, and 2Π CO- shape resonances are investigated. The position and width of these resonances computed in this study agree well with those reported earlier in the literature.

Heating of Enceladus due to the dissipation of ocean tides

Given Cassini observations of a large and unexplained endogenic heat source, the subsurface ocean on Enceladus is an important test bed for modeling icy-satellite ocean tides and the dissipative heat generated. Here we revisit and expand estimates of the ocean tidal power (heating rate) to describe how the power depends on input parameter and process assumptions. The approach taken in this (and previous) work by this author is that the dissipation process in Enceladus' ocean is unknown and cannot be reliably modeled from first principles. Considered instead are generic dissipation forms that cover specific physical dissipation processes as special cases (specific cases described here include linear/nonlinear drag, eddy viscosity, viscoelastic ice coupling, and vertical wave damping). The justification for basing conclusions primarily on the generic (rather than specific) dissipation forms is that whatever the ocean dissipation process, it must draw from the stored energy (kinetic or potential) in the ocean tidal response, and this process must have an associated time scale for the dissipation to take place. By treating this time scale (as well as the Lamb number/wave speed) as free parameters, millions of tidal solutions are calculated to sample the full domain of tidal scenarios that arrive from different combinations of these two parameters, as well as the assumed dissipation form. Conclusions drawn from the general behavior in this larger solution domain are then considered to be more robust than conclusions drawn from the subdomain that assumes the validity of a specific physical dissipation process. The results show plausible states whereby the ocean tides (even if Enceladus is covered with thick ice) generate the observed heat flux. While the same results show that low-power, non-resonant states are also allowed, an argument is presented that these low-power states may not be stable in the presence of secular trends (e.g. cooling, stratification). Rather, self-tuned resonance stabilizes the tidal configuration in a near-resonant forced state with high power and dissipative heat.

Gamow shell-model calculations of neutron-rich lithium isotopes

<p indent="0mm">The calculations of neutron-rich lithium isotopes have been performed using the Gamow shell model (GSM). In the present work, the shell model basis is generated by solving the one-body Schrödinger equation of the Woods-Saxon (WS) potential in the complex momentum space. The resulting single-particle basis is composed of bound, resonant and non-resonant continuum states, which is also called the Berggren ensemble. Two-body interaction between nucleons in the Berggren ensemble is derived from the realistic nuclear force CD-Bonn potential with the many-body perturbation theory named the <inline-formula id="INLINE7" content-type="pic"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi other="0">Q</mml:mi><mml:mo other="1" stretchy="true">^</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula>-box folded diagrams. The model space consists of the 0p_3/2 bound state, 0p_1/2 resonant state and p_1/2 non-resonant continuum states for neutrons, and 0p_3/2, 0p_1/2 bound states for protons, respectively. The real and imaginary parts of the complex eigenvalues of the shell model Hamiltonian represent the excitation energies and resonance widths of resonant states, respectively. The p-shell neutron-rich lithium isotopes ^7–10Li have been studied. The results of GSM calculations with CD-Bonn potential are compared with traditional shell model with PWT interaction and GSM with surface Gaussian interaction (SGI). The low-lying spectra and resonance widths of resonant states are discussed, as well as the influences of the continuum states on these observables. In terms of the low-lying spectra of well-bound nuclei, the GSM calculations reproduce the excitation energies of ^7–9Li with good accuracy, except for the states with <sc>4 MeV</sc> or higher energies of ⁷Li, which decay through α-particle emission. In the calculation of the unbound nucleus ¹⁰Li, the GSM calculation proves that continuum effect is crucial in its low-lying spectrum. The shell model calculation with PWT interaction of ¹⁰Li overestimates the excitation energies by almost 100%, and by introducing the continuum states, GSM calculation can give more accurate values. Similar phenomenon was also observed in the shell model calculation with USDB interaction of the unbound nucleus ²⁶O, and was explained by the continuum effect as well. As for the resonance widths, the present calculations extend to higher levels of the studied nuclei compared with GSM calculations with the SGI interaction, and obtain reasonable resonance widths of the resonant states. Though the widths of the α-emitting states of ⁷Li cannot be explained by the current GSM, the resonant states among the excited states of ^8–9Li are reproduced in the present work. The GSM calculation with realistic nuclear force also gives correct resonant property of the first 1⁺ state of ¹⁰Li, while the GSM calculation with SGI yields a non-resonant state. The excited state of ¹⁰Li with unknown angular momentum and resonance width is also reproduced, which is predicted to be a 0⁺ state, with <sc>0.13 MeV</sc> width. In the present work, it is proved that the continuum effect is crucial in shell-model calculations of unbound ¹⁰Li. Through treating the continuum effect microscopically, the GSM calculations with properly renormalized realistic nuclear force can reproduce the observed low-lying spectra and resonance widths of both bound and unbound nuclei with high accuracy. On the other hand, the GSM with realistic nuclear force is based on a relatively small model space, and can thus be used to systems with more valence particles. The GSM with realistic nuclear force is proved to be a promising tool for future research on weakly bound or unbound nuclei.