Non-resonant Conditions Research Articles

Probing Thermal Magnon Current Mediated by Coherent Magnon via Nitrogen-Vacancy Centers in Diamond

Currently, thermally excited magnons are being intensively investigated owing to their potential in computing devices and thermoelectric conversion technologies. We report the detection of thermal magnon current propagating in a magnetic insulator yttrium iron garnet under a temperature gradient using a quantum sensor: electron spins associated with nitrogen-vacancy (NV) centers in diamond. Thermal magnon current was observed as modified Rabi oscillation frequencies of NV spins hosted in a beam-shaped bulk diamond that resonantly coupled with coherent magnon propagating over a long distance. Additionally, using a nanodiamond, alteration in NV spin relaxation rates depending on the applied temperature gradient were observed under a non-resonant NV excitation condition. The demonstration of probing thermal magnon current mediated by coherent magnon via NV spin states serves as a basis for creating a device platform hybridizing spin caloritronics and spin qubits.

Existence of exponentially spatially localized breather solutions for lattices of nonlinearly coupled particles: Schauder’s fixed point theorem approach

The problem of showing the existence of localized modes in nonlinear lattices has attracted considerable efforts not only from the physical but also from the mathematical viewpoint where a rich variety of methods have been employed. In this paper, we prove that a fixed point theory approach based on the celebrated Schauder’s fixed point theorem may provide a general method to concisely establish not only the existence of localized structures but also a required rate of spatial localization. As a case study, we consider lattices of coupled particles with a nonlinear nearest neighbor interaction and prove the existence of exponentially spatially localized breathers exhibiting either even-parity or odd-parity symmetry under necessary non-resonant conditions accompanied with the proof of energy bounds of solutions.

Spatial Relative Equilibria and Periodic Solutions of the Coulomb $$(n+1)$$-Body Problem

We study a classical model for the atom that considers the movement of n charged particles of charge \(-1\) (electrons) interacting with a fixed nucleus of charge \(\mu >0\). We show that two global branches of spatial relative equilibria bifurcate from the n-polygonal relative equilibrium for each critical value \(\mu =s_{k}\) for \(k\in [2,\ldots ,n/2]\). In these solutions, the n charges form n/h-groups of regular h-polygons in space, where h is the greatest common divisor of k and n. Furthermore, each spatial relative equilibrium has a global branch of relative periodic solutions for each normal frequency satisfying some nonresonant condition. We obtain computer-assisted proofs of existence of several spatial relative equilibria on global branches away from the n-polygonal relative equilibrium. Moreover, the nonresonant condition of the normal frequencies for some spatial relative equilibria is verified rigorously using computer-assisted proofs.

Rigorous verification of Hopf bifurcations in functional differential equations of mixed type

We propose a rigorously validated numerical method to prove the existence of Hopf bifurcations in functional differential equations of mixed type. The eigenvalue transversality and steady state conditions are verified using the Newton–Kantorovich theorem. The non-resonance condition and simplicity of the critical eigenvalues are verified by either computing a pair of generalized Morse indices of the step map, or by applying the argument principle to the characteristic equation and a suitable contour in the complex plane, computing the contour integral using the equivalence with a winding number. As a first application and test problem, we prove the existence of Hopf bifurcations in the Lasota–Wazewska–Czyzewska model and a pair of two such coupled equations. We then use our method to prove the existence of periodic traveling waves in the Fisher equation with nonlocal reaction. These periodic traveling waves are solutions of an ill-posed functional differential equation of mixed type.

Role of pre-ionization in NBI plasma start-up of Heliotron J using non-resonant microwave heating

Here, we report on role of pre-ionization using non-resonant 2.45 GHz microwave heating (P 2.45 GHz < 20 kW) in plasma start-up of neutral beam injection (NBI) for heliotron configurations in low beam power (P NB) under non-resonant heating condition. A rapid electron heating towards burn-through of the low-Z impurities was observed experimentally in the early phase of beam injection when the seed plasma density produced by the non-resonant heating was enough for the plasma start-up. Beam heating time to the burn-through increased with decreasing the seed plasma density and a critical density condition of the seed plasma for successful start-up was observed experimentally. Proper timing of the gas fuelling is critical for plasma expansion because the beam fuelling is not significant. A 0-dimensional (0D) model analysis of the NBI start-up developed in this study well reproduces the experimental results. The 0D model clarifies the physical mechanism of the NBI start-up using pre-ionization described as follows: (1) the seed plasma produces sufficient beam ions immediately after beam injection, (2) the beam ions heat up electrons that promote the ionization/dissociation of the background neutrals, (3) this process acts as a positive feedback loop resulting in further electron heating towards burn-through. The 0D model analysis shows that the critical density corresponds to the state at which the electron heating by the beam ions is equal to electron power loss due to conduction and ionization/dissociation.

Photostability of organic electro-optic polymer under practical high intensity continuous-wave 1550 nm laser irradiation

Information on the photochemical stabilities of organic electro-optic (EO) polymers under laser irradiation at 1550 nm, in the optical communication wavelength band (C-band), is crucial for understanding the long-term stability of various optical devices that employ EO polymers and providing guidelines for extending the devices’ lifetime. Thus, in this study, we constructed a pump–probe photostability evaluation system with an intensity of as high as 1.49 MW cm−2 and intensively investigated the photochemical stability of an EO polymer at 85 °C under irradiation by using a continuous-wave (CW) 1550 nm laser. We found that the photobleaching rate was proportional to the square of the pump intensity, suggesting that the dominant photodegradation pathway was associated with two-photon absorption. Our findings provide new insights into a photobleaching mechanism under non-resonant CW laser excitation conditions.

A systematic approach to nonresonance conditions for periodically forced planar Hamiltonian systems

In the first part of the paper we consider periodic perturbations of some planar Hamiltonian systems. In a general setting, we detect conditions ensuring the existence and multiplicity of periodic solutions. In the second part, the same ideas are used to deal with some more general planar differential systems.

Broadband SERS Enhancement by DNA Origami Assembled Bimetallic Nanoantennas with Label-Free Single Protein Sensing.

Engineering hotspots in surface-enhanced Raman spectroscopy (SERS) through precisely controlled assembly of plasmonic nanostructures capable of expanding intense field enhancement are highly desirable to enhance the potentiality of SERS as a label-free optical tool for single molecule detection. Inspired by DNA origami technique, we constructed plasmonic dimer nanoantennas with a tunable gap decorated with Ag-coated Au nanostars on origami. Herein, we demonstrate the single-molecule SERS enhancements of three dyes with emission in different spectral regions after incorporation of single dye molecules in between two nanostars. The enhancement factors (EFs) achieved in the range of 109-1010 for all the single dye molecules, under both resonant and nonresonant excitation conditions, would enable enhanced photostability during time-series measurement. We further successfully explored the potential of our designed nanoantennas to accommodate and detect a single thrombin protein molecule after selective placement in the wide nanogap of 10 nm. Our results suggest that such nanoantennas can serve as a broadband SERS enhancer and enable specific detection of target biological molecules with single-molecule sensitivity.

Green’s Function Related to a n-th Order Linear Differential Equation Coupled to Arbitrary Linear Non-Local Boundary Conditions

In this paper, we obtain the explicit expression of the Green’s function related to a general n-th order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, an n dimensional parameter dependence is also assumed. Moreover, some comparison principles are obtained. The explicit expression depends on the value of the Green’s function related to the two-point homogeneous problem; that is, we are assuming that when all the parameters involved on the boundary conditions take the value zero then the problem has a unique solution, which is characterized by the corresponding Green’s function g. The expression of the Green’s function G of the general problem is given as a function of g and the real parameters considered at the boundary conditions. It is important to note that, in order to ensure the uniqueness of the solution of the considered linear problem, we must assume a non-resonant additional condition on the considered problem, which depends on the non-local conditions and the corresponding parameters. We point out that the assumption of the uniqueness of the solution of the two-point homogeneous problem is not a necessary condition to ensure the existence of the solution of the general case. Of course, in this situation, the expression we are looking for must be obtained in a different manner. To show the applicability of the obtained results, a particular example is given.

Transits close to the Lagrangian solutions L 1, L 2 in the elliptic restricted three-body problem

In the last decades a peculiar family of solutions of the circular restricted three body problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit close to the Lagrangian points L 1, L 2 of the CRTBP, have been classified using the values of approximate local integrals and of the Jacobi constant. The use for small bodies of the Solar System requires to consider a hierarchical extension of the model, from the CRTBP to the full N planetary problem. The elliptic restricted three body, which is the first natural extension of the CRTBP, represents already a challenge, since global first integrals such as the Jacobi constant are not known for this problem. In this paper we extend the classification of the transits occurring close to the Lagrangian points L 1, L 2 of the ERTBP using a combination of the Floquet theory and Birkhoff normalizations. Provided that certain non-resonance conditions are satisfied, we conjugate the Hamiltonian of the problem to an integrable normal form Hamiltonian with remainder, which is used to define approximate local first integrals and to classify the transits of orbits through a neighbourhood of the Lagrange equilibria according to the values of these integrals. We provide numerical demonstrations for the Earth–Moon ERTBP.

Response Solutions for Wave Equations with Variable Wave Speed and Periodic Forcing

We consider a model of nonlinear wave equations with periodically varying wave speed and periodic external forcing. By imposing non-resonance conditions on the frequency, we establish the existence of response solutions (i.e., periodic solutions with the same frequency as the forcing) for such a model in a Cantor set of asymptotically full measure. The proof relies on a Lyapunov–Schmidt reduction together with the Nash–Moser iteration.

Periodic Vibrations of a Beam with Rigidly Sealed Ends

We study the problem of searching periodic solutions to the Euler–Bernoulli equation governing vibrations of a beam with the boundary conditions corresponding to the case of rigidly sealed beam ends. The nonlinear term satisfies the nonresonance condition at infinity. We establish the existence and uniqueness of a solution. To prove the results, we use topological methods (the Leray–Schauder principle) as well as variational methods (the mountain pass theorem).

Development of high-efficiency capacitive discharge using magnetic resonance wireless power transfer systems

We developed a high-efficiency source in a capacitively coupled plasma using magnetic resonance wireless power transfer (MRWPT) systems, which has the advantage that the matcher efficiency is very high at low gas pressures (2 mTorr to 20 mTorr) and high density plasmas (about 1 × 1010 cm−3 to 5 × 1010 cm−3). At the non-resonance conditions, most of the RF power is dissipated by the transmitter coil and the plasma is not discharged. However, at the resonance condition, the plasma is discharged as the current flowing through the transmitter coil rapidly decreases, and the matcher efficiency is higher than 90% in all experiments. For analysis, the transformer model with MRWPT systems is developed. The experimental result is consistent with the model, and the results are discussed with the relevant physical mechanisms.

A Versatile DNA Origami-Based Plasmonic Nanoantenna for Label-Free Single-Molecule Surface-Enhanced Raman Spectroscopy.

DNA origami technology allows for the precise nanoscale assembly of chemical entities that give rise to sophisticated functional materials. We have created a versatile DNA origami nanofork antenna (DONA) by assembling Au or Ag nanoparticle dimers with different gap sizes down to 1.17 nm, enabling signal enhancements in surface-enhanced Raman scattering (SERS) of up to 1011. This allows for single-molecule SERS measurements, which can even be performed with larger gap sizes to accommodate differently sized molecules, at various excitation wavelengths. A general scheme is presented to place single analyte molecules into the SERS hot spots using the DNA origami structure exploiting covalent and noncovalent coupling schemes. By using Au and Ag dimers, single-molecule SERS measurements of three dyes and cytochrome c and horseradish peroxidase proteins are demonstrated even under nonresonant excitation conditions, thus providing long photostability during time-series measurement and enabling optical monitoring of single molecules.

Non-resonance and Double Resonance for a Planar System via Rotation Numbers

We consider a planar system $$z'=f(t,z)$$ under non-resonance or double resonance conditions and obtain the existence of $$2\uppi $$ -periodic solutions by combining a rotation number approach together with Poincare-Bohl theorem. Firstly, we allow that the angular velocity of solutions of $$z'=f(t,z)$$ is controlled by the angular velocity of solutions of two positively homogeneous system $$z'=L_i(t,z),i=1,2$$ , whose rotation numbers satisfy $$\rho (L_1)>n$$ and $$\rho (L_2)<n+1$$ , namely, nonresonance occurs in the sense of the rotation number. Secondly, we prove the existence of $$2\uppi $$ -periodic solutions when the nonlinearity is allowed to interact with two positively homogeneous system $$z'=L_i(t,z),i=1,2$$ , with $$\rho (L_1)\ge n$$ and $$\rho (L_2)\le n+1$$ , which gives rise to double resonance, and some kind of Landesman–Lazer conditions are assumed at both sides.

Dynamics of Coupled Thermoacoustic Oscillators Under Asymmetric Forcing

Quenching of limit cycle oscillations (LCO), either through mutual coupling or external forcing, has attracted wide attention in several fields of science and engineering. However, the simultaneous utilization of these coupling schemes in quenching of LCO has rarely been studied despite its practical applicability. We study the dynamics of two thermoacoustic oscillators simultaneously subjected to mutual coupling and asymmetric external forcing through experiments and theoretical modeling. We investigate the forced response of both identical and non-identical thermoacoustic oscillators for two different amplitudes of LCO. Under mutual coupling alone, identical thermoacoustic oscillators display the occurrence of partial amplitude death and amplitude death, whereas under forcing alone, asynchronous quenching of LCO is observed at non-resonant conditions. When the oscillators are simultaneously subjected to mutual coupling and asymmetric forcing, we observe a larger parametric region of oscillation quenching than when the two mechanisms are utilized individually. This enhancement in the region of oscillation quenching is due to the complementary effect of amplitude death and asynchronous quenching. However, a forced response of coupled non-identical oscillators shows that the effect of forcing is insignificant on synchronization and quenching of oscillations in the oscillator which is not directly forced. Finally, we qualitatively capture the experimental results using a reduced-order theoretical model of two coupled Rijke tubes which are coupled through dissipative and time-delay coupling and asymmetrically forced. We believe that these findings offer fresh insights into the combined effects of mutual and forced synchronization in a system of coupled nonlinear oscillators.

Adaptive Damping – An Improved Resonance Mitigation Scheme for Shunt Capacitors

Adding a damping unit to a shunt capacitor is an effective way to mitigate capacitor-caused resonance. However, damping units suffer from power loss issues. This shortcoming is amplified further in cases where resonance has a low possibility of occurring. In view of this, an adaptive damping method is proposed to improve the existing scheme. The damping unit is capable of mitigating resonance and eliminating the power loss under the non-resonance condition. The core idea of the proposed approach is to add a breaker so that the damping unit can be switched on or off depending on whether resonance occurs. The design of and control mechanism for the proposed switchable damping unit are presented. The performances of the new resonance mitigation scheme in terms of harmonic mitigation, loading, switching transient and cost are verified for an actual capacitor application case.

Normal forms for strong magnetic systems on surfaces: trapping regions and rigidity of Zoll systems

AbstractWe prove a normal form for strong magnetic fields on a closed, oriented surface and use it to derive two dynamical results for the associated flow. First, we show the existence of invariant tori and trapping regions provided a natural non-resonance condition holds. Second, we prove that the flow cannot be Zoll unless (i) the Riemannian metric has constant curvature and the magnetic function is constant, or (ii) the magnetic function vanishes and the metric is Zoll. We complement the second result by exhibiting an exotic magnetic field on a flat two-torus yielding a Zoll flow for arbitrarily weak rescalings.

Effective Electrochemical Modulation of SERS Intensity Assisted by Core-Shell Nanoparticles.

An effective and reversible tuning of the intensity of surface-enhanced Raman scattering (SERS) of nonelectroactive molecules at nonresonance conditions by electrochemical means has been developed on plasmonic molecular nanojunctions formed between Au@Ag core-shell nanoparticles (NPs) and a gold nanoelectrode (AuNE) modified with a self-assembled monolayer. The Au@Ag nanoparticle on nanoelectrode (NPoNE) structures are formed in situ by the electrochemical deposition of Ag on AuNPs adsorbed on the AuNE and can be monitored by both the electrochemical current and SERS signals. Instead of introducing molecular changes by the applied electrode potential, the highly effective SERS intensity tuning was achieved by the chemical composition transformation of the ultrathin Ag shell from metallic Ag to insulating AgCl. The electrode potential-induced electromagnetic enhancement (EME) tuning in the Au@Ag NPoNE structure has been confirmed by finite-difference time-domain simulations. Moreover, the specific Raman band associated with Ag-molecule interaction can also be tuned by the electrode potential. Therefore, we demonstrated that the electrode potential could effectively and reversibly modulate both EME and chemical enhancement in Au@Ag NPoNE structures.

Response solutions for strongly dissipative quasi-periodically forced systems with arbitrary nonlinearities and frequencies

We consider quasi-periodically systems in the presence of dissipation and study the existence of response solutions, i.e. quasi-periodic solutions with the same frequency vector as the forcing term. When the dissipation is large enough and a suitable function involving the forcing has a simple zero, response solutions are known to exist without assuming any non-resonance condition on the frequency vector. We analyse the case of non-simple zeroes and, in order to deal with the small divisors, we confine ourselves to two-dimensional frequency vectors, so as to use the properties of continued fractions. We show that, if the order of the zero is odd (if it is even, in general no response solution exists), a response solution still exists provided the inverse of the parameter measuring the dissipation belongs to a set given by the union of infinite intervals depending on the convergents of the ratio of the two components of the frequency vector. The intervals may be disjoint and as a consequence we obtain the existence of response solutions in a set with “holes”. If we want the set to be connected we have to require some non-resonance condition on the frequency: in fact, we need a condition weaker than the Bryuno condition usually considered in small divisors problems.