Non-resonant System Research Articles

On evolution of the planet's obliquity in a non-resonant planetary system

On evolution of the planet's obliquity in a non-resonant planetary system

Generalized method of Feynman-Pines diagram technique in the theory of energy spectrum of two-level quasiparticle renormalized due to multi-phonon processes at cryogenic temperature

Theory of the spectrum of localized two-level quasi-particle renormalized due to interaction with polarization phonons at cryogenic temperature is developed using the generalized method of Feynman-Pines diagram technique. Using the procedure of partial summing of infinite ranges of the main diagrams, mass operator is obtained as a compact branched chain fraction, which effectively takes into account multi-phonon processes. It is shown that multi-phonon processes and interlevel interaction of quasiparticle and phonons cardinally change the renormalized spectrum of the system depending on the difference of energies of two states, which either resonates with phonon energy or does not. The spectrum of non-resonant system contains renormalized energies of the main states and two similar infinite series of groups of phonon satellite levels. The spectrum of a resonant system contains a renormalized ground state and infinite series of satellite groups.

Dynamical reliability of internally resonant or non-resonant strongly nonlinear system under random excitations

Abstract The dynamical reliability of multi-degrees-of-freedom (MDOF) strongly nonlinear system under Gaussian white noise excitations is studied, including resonance and non-resonance. Firstly, the equations of motion of the original system with or without internal resonance are reduced to a set of Ito stochastic differential equations after stochastic averaging. Then, the backward Kolmogorov equation and the Pontryagin equation associated with the resonantly or non-resonantly averaged Ito stochastic differential equations, which determine the conditional reliability function and the mean first-passage time of the original random system, are constructed under appropriate boundary and (or) initial conditions, respectively. In particular, if the non-resonantly averaged system is completely decoupled, the conditional reliability function and the mean first-passage time of the original non-resonant system can be obtained by solving a set of simplified backward Kolmogorov equations. A system comprising two weakly coupled and strongly nonlinear mechanical oscillators is given as a concrete example to show the application of the proposed method. The 1:1 internal resonance or non-resonance is discussed. The corresponding high-dimensional backward Kolmogorov equation and Pontryagin equation are established and solved numerically. All theoretical results are validated by a Monte Carlo digital simulation.

Experimental investigation on burr formation in vibration-assisted micro-milling of Ti-6Al-4V

Titanium alloys have been widely used in aerospace, marine and medical industries, due to their high strength, good corrosion resistance and excellent heat resistance. High tool wear rate and low machining accuracy limits conventional micro-milling to meet increasing stringent demand. In this paper, a prototype of two-directional vibration stage and its control system are developed for non-resonant mode vibration-assisted micro-milling system. A series of slot milling experiments are carried out to investigate the effects of vibration parameters on burr generation. The results show that vibration-assisted micro-milling is an effective way to reduce burr size when choosing appropriate vibration parameters and directions.

A periodic configuration of the Kepler-25 planetary system

We study proximity of the Kepler-25 planetary system to a periodic configuration, which is known to be the final state of a system that undergoes smooth migration resulting from the planet-disc interaction. We show that the system is close to the periodic configuration of 2:1 mean motion resonance (MMR) what indicates that its past migration was neither disturbed significantly by turbulence in the disc nor the orbits were perturbed by planetesimals that left after the disc dispersal. We show that, because of the TTV model degeneracy, a periodic configuration is difficult to be found when the standard modelling of the transit timing variations (TTVs) is used. The TTV signal of a periodic configuration (with anti-aligned apsidal lines) may be misinterpreted as an aligned non-resonant system. We demonstrate that the standard MCMC modelling of the Kepler-25 TTVs is very sensitive to an a~priori information on the eccentricities (prior probability distributions). Wide priors (of the order of the ones typically used in the literature) result in favouring the aligned non-resonant configurations with small planets' masses and moderate eccentricities, while for the narrower priors the most likely are the anti-aligned resonant systems with larger masses and very low eccentricities.

Optimization of time reversal focusing in resonant and non-resonant systems through various signal processing techniques

This research optimizes a time reversal focus of energy in terms of amplitude and quality by exploring several signal processing techniques applied to the reversed impulse response. Techniques explored here include deconvolution or inverse filtering [M. Tanter et al., J. Acoust. Soc. Am. 108, 223-234 (2000)], one-bit time reversal [A. Derode et al., J. Appl. Phys. 85, 6343-6352 (1999)], and a new technique termed “clipping.” A parameterization study comparing the maximum focal amplitude and focal temporal quality of time reversal focal signals for these techniques with different settings will be presented. Focal signals are explored in two different systems. The first is a resonant system comprised of a steel sample with a piezoelectric transducer and a scanning laser Doppler vibrometer (SLDV). The second, nominally non-resonant system, comprises a studio monitor loudspeaker and a precision microphone in a reverberant space above the Schroeder frequency. Comparing the focal quality of various time reversal techniques in two starkly different systems shows the optimal conditions for focusing in each system.

Особенности устойчивости конечномерной системы, описываемой безрезонансным уравнением с линейным дифференциальным оператором

The linear system represented in a normal form with the material measurable elements of coefficient system is considered by the uniform linear equation and are offered aspects of stability of the finite-dimensional version of non-resonant system described by the linear equation resolved ralatively derivative with the constant positive elements of the coefficient system in a decimal numeral system at the example of the test of the known dynamic model resources of the portable personal computer are constructive.

Directional algorithms for the frequency isolation problem in undamped vibrational systems

A new algorithm is presented to solve the frequency isolation problem for vibrational systems with no damping: given an undamped mass-spring system with resonant eigenvalues, the system must be re-designed, finding some close-by non-resonant system at a reasonable cost. Our approach relies on modifying masses and stiffnesses along directions in parameter space which produce a maximal variation in the resonant eigenvalues, provided the non-resonant ones do not undergo large variations. The algorithm is derived from first principles, implemented, and numerically tested. The numerical experiments show that the new algorithms are considerably faster and more robust than previous algorithms solving the same problem.

Dual Active Bridge Converter動作を応用した非共振形非接触給電システムの基礎検証

Dual Active Bridge Converter動作を応用した非共振形非接触給電システムの基礎検証

The disruption of multiplanet systems through resonance with a binary orbit.

Most exoplanetary systems in binary stars are of S-type, and consist of one or more planets orbiting a primary star with a wide binary stellar companion. Planetary eccentricities and mutual inclinations can be large, perhaps forced gravitationally by the binary companion. Earlier work on single planet systems appealed to the Kozai-Lidov instability wherein a sufficiently inclined binary orbit excites large-amplitude oscillations in the planet's eccentricity and inclination. The instability, however, can be quenched by many agents that induce fast orbital precession, including mutual gravitational forces in a multiplanet system. Here we report that orbital precession, which inhibits Kozai-Lidov cycling in a multiplanet system, can become fast enough to resonate with the orbital motion of a distant binary companion. Resonant binary forcing results in dramatic outcomes ranging from the excitation of large planetary eccentricities and mutual inclinations to total disruption. Processes such as planetary migration can bring an initially non-resonant system into resonance. As it does not require special physical or initial conditions, binary resonant driving is generic and may have altered the architecture of many multiplanet systems. It can also weaken the multiplanet occurrence rate in wide binaries, and affect planet formation in close binaries.

Molecular-Shape-Dependent Luminescent Behavior of Dye Aggregates: Bent versus Linear Benzocoumarins

Aggregation patterns of dye molecules can govern their photophysical properties in the solid state. The linear and bent shaped dipolar benzocoumarins showed contrasting luminescence behavior in solution and in the solid state. Single crystal structures of both compounds showed π-stacking patterns with eclipsing but opposite dipole moments when viewed orthogonal to the stacking plane. Although the bent molecules are stacked in parallel in the solid state, they behave as independent molecules owing to the unfavorable excited state resonance interaction and hence emit strong fluorescence because each dipolar molecule now is in a hydrophobic environment surrounded by other molecules. This is an unusual example where the shape-dependent stacking governs the solid-state luminescence of dyes, being suggested here as a nonresonant π-stacking system.

Stochastic averaging of quasi-integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitations

A stochastic averaging method for predicting the response of quasi-integrable and non-resonant Hamiltonian systems to combined Gaussian and Poisson white noise excitations is proposed. First, the motion equations of a quasi-integrable and non-resonant Hamiltonian system subject to combined Gaussian and Poisson white noise excitations is transformed into stochastic integro-differential equations (SIDEs). Then \(n\)-dimensional averaged SIDEs and generalized Fokker–Plank–Kolmogrov (GFPK) equations for the transition probability densities of \(n\) action variables and \(n\)- independent integrals of motion are derived by using stochastic jump–diffusion chain rule and stochastic averaging principle. The probability density of the stationary response is obtained by solving the averaged GFPK equation using the perturbation method. Finally, as an example, two coupled non-linear damping oscillators under both external and parametric excitations of combined Gaussian and Poisson white noises are worked out in detail to illustrate the application and validity of the proposed stochastic averaging method.

Time flies when you are in a groove: using entrainment to mechanical resonance to teach a desired movement distorts the perception of the movement’s timing

The human motor system quickly entrains rhythmic limb movement to the resonant frequency of mechanical systems with which it interacts, suggesting that entrainment to an appropriately designed training device might be a convenient way to teach desired movements. We tested this possibility by asking healthy subjects (N = 30) to learn to move with a desired movement timing using a simple resonating arm training device: a lever attached to a manual wheelchair. The subjects tried to learn to roll the lever-driven wheelchair back and forth in place at a target frequency initially presented using a series of auditory beeps. One-third of the subjects trained without resonance and with no further feedback about rolling frequency; their performance did not improve. Another group trained with continual visual feedback of frequency error but no resonance; they quickly learned to roll the chair at the target frequency, as evidenced at both short-term and long-term (1 day later) retention tests. A third group trained with elastic bands attached to the lever that caused the system to resonate at the target frequency, providing a timing template. While these participants quickly entrained to the target frequency during training, they did not accurately reproduce this frequency when the system was no longer resonant, moving too slowly with the same systematic error at both the short-term and long-term retention tests. They also did not exhibit a timing aftereffect on the initial movements made when they transitioned from a resonant to non-resonant system or vice versa. This suggests they did not realize they were performing the task with a temporal error. Entrainment to mechanical resonance conveys usable information about movement timing, but seems to cause that movement timing to be perceived as slower than it actually is, as if a putative internal clock speeds up, which is a factor to consider in designing machine-assisted motor training.

Multinuclear nanoliter one-dimensional and two-dimensional NMR spectroscopy with a single non-resonant microcoil

Nuclear magnetic resonance (NMR) spectroscopy is a powerful analytical technique, but its low sensitivity and highly sophisticated, costly, equipment severely constrain more widespread applications. Here we show that a non-resonant planar transceiver microcoil integrated in a microfluidic chip (detection volume 25 nl) can detect different nuclides in the full broad-band range of Larmor frequencies (at 9.4 T from 61 to 400 MHz). Routine one-dimensional (1D) and two-dimensional (2D), homo- and heteronuclear experiments can be carried out using the broad-band coil set-up. Noteworthy, heteronuclear 2D experiments can be performed in a straightforward manner on virtually any combination of nuclides (from classical ¹H-¹³C to more exotic combinations like ¹⁹F-³¹P) both in coupled and decoupled mode. Importantly, the concept of a non-resonant system provides magnetic field-independent NMR probes; moreover, the small-volume alleviates problems related to field inhomogeneity, making the broad-band coil an attractive option for, for example, portable and table-top NMR systems.

Decarboxylative Palladium(II)‐Catalyzed Synthesis of Aryl Amidines from Aryl Carboxylic Acids: Development and Mechanistic Investigation

A fast and convenient synthesis of aryl amidines starting from carboxylic acids and cyanamides is reported. The reaction was achieved by palladium(II)-catalysis in a one-step microwave protocol using [Pd(O2CCF3)2], 6-methyl-2,2′-bipyridyl and trifluoroacetic acid (TFA) in N-methylpyrrolidinone (NMP), providing the corresponding aryl amidines in moderate to excellent yields. The protocol is very robust with regards to the cyanamide coupling partner but requires electron-rich ortho-substituted aryl carboxylic acids. Mechanistic insight was provided by a DFT investigation and direct ESI-MS studies of the reaction. The results of the DFT study correlated well with the experimental findings and, together with the ESI-MS study, support the suggested mechanism. Furthermore, a scale-out (scale-up) was performed with a non-resonant microwave continuous-flow system, achieving a maximum throughput of 11 mmol h−1 by using a glass reactor with an inner diameter of 3 mm at a flow rate of 1 mL min−1.

On the Galois group of some Fuchsian systems

The aim of this paper is to give a new result of the differential Galois theory of linear ordinary differential equations. In particular, we compute differential Galois group for special type non-resonant Fuchsian system.

Lasing properties of non-resonant single quantum dot-cavity system under incoherent excitation

Single quantum dot laser has earned extensive interest due to its peculiar properties, however, most of works are focused on the resonant case. In this paper, the lasing oscillation based on off-resonant quantum dot (QD)-cavity system is investigated detailedly through two-electrons QD model. By gradually increasing the pump rate, the typical lasing signatures are shown with and without detuning, include the spectral transition from multiple peaks to single peak, and antibunching to Poissonian distribution. It is also demonstrated how detuning factor strongly influence photon statistics and emission properties, specially, the side peak of spectra induced by the exchange energy (named "sub-peak") will go across the main peak from left to right when the detuning is gradually increased, and, furthermore, we find the "sub-peak cross of spectra" will facilitate the lasing oscillation because of the existence of exchange energy.

Formation of ‘3D’ multiplanet systems by dynamical disruption of multiple-resonance configurations

Assuming that giant planets are formed in thin protoplanetary discs, a '3D' system can form, provided that the mutual inclination is excited by some dynamical mechanism. Resonant interactions and close planetary encounters are thought to be the primary inclination-excitation mechanisms, resulting in a resonant and non-resonant system, respectively. Here we propose an alternative formation scenario, starting from a system composed of three giant planets in a nearly coplanar configuration. As was recently shown for the case of the Solar system, planetary migration in the gas disc (Type II migration) can force the planets to become trapped in a multiply resonant state. We simulate this process, assuming different values for the planetary masses and mass ratios. We show that such a triple resonance generally becomes unstable as the resonance excites the eccentricities of all planets and planet-planet scattering sets in. One of the three planets is typically ejected from the system, leaving behind a dynamically 'hot' (but stable) two-planet configuration. The resulting two-planet systems typically have large values of semimajor axial ratios (a1/a2 < 0.3), while the mutual inclination can be as high as 70{\deg}, with a median of \sim30{\deg}. A small fraction of our two-planet systems (\sim5 per cent) ends up in the stability zone of the Kozai resonance. In a few cases, the triple resonance can remain stable for long times and a '3D' system can form by resonant excitation of the orbital inclinations; such a three-planet system could be stable if enough eccentricity damping is exerted on the planets. Finally, in the single-planet resulting systems, which are formed when two planets are ejected from the system, the inclination of the planet's orbital plane with respect to the initial invariant plane -presumably the plane perpendicular to the star's spin axis- can be as large as \sim40{\deg}.

Performance Analysis and Experimental Verification of Mid-Range Wireless Energy Transfer through Non-resonant Magnetic Coupling

In this paper, the efficiency analysis of a mid-range wireless energy transfer system is performed through non-resonant magnetic coupling. It is shown that the self-resistance of the coils and the mutual inductance are critical in achieving a high efficiency, which is indicated by our theoretical formulation and verified in our experiments. It is experimentally shown that high efficiency, up to 65%, can be realized even in a non-resonant wireless energy system which employs a device part with moderate or low quality factor. We also address some aspects of a practical wireless energy transfer system and show that careful design of the de-tuned system can intrinsically minimize the power dissipated in the source part. Our non-resonant scheme presented in this paper allows flexible design and fabrication of a wireless energy transfer systems with transfer distance being several times of the coils' radius.

SYSTEMIC: A TESTBED FOR CHARACTERIZING THE DETECTION OF EXTRASOLAR PLANETS. II. NUMERICAL APPROACHES TO THE TRANSIT TIMING INVERSE PROBLEM

Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for numerically solving the so-called inverse problem, the determination of the orbital elements of a perturbing body from the transit timing variations it induces. We assume that the planetary systems under examination have a limited number of Doppler velocity measurements, and show that a more extensive radial velocity characterization with precision comparable to the semiamplitude of the perturber may remove degeneracies in the solution. We examine several configurations of interest, including (1) a prototypical non-resonant system, modeled after HD40307 b and c, which contains multiple super-Earth mass planets, (2) a hypothetical system containing a transiting giant planet with a terrestrial-mass companion trapped in low-order mean motion resonance, and (3) the HAT-P-13 system, in which forced precession by an outer perturbing body that is well characterized by Doppler radial velocity measurements can give insight into the interior structure of a perturbing planet, and for which the determination of mutual inclination between the transiting planet and its perturber is a key issue.