Nontrivial Resonance Research Articles

Mechanical Detection of the De Haas-van Alphen Effect in Graphene.

In our work, we study the dynamics of a graphene Corbino disk supported by a gold mechanical resonator in the presence of a magnetic field. We demonstrate here that our graphene/gold mechanical structure exhibits a nontrivial resonance frequency dependence on the applied magnetic field, showing how this feature is indicative of the de Haas-van Alphen effect in the graphene Corbino disk. Relying on the mechanical resonances of the Au structure, our detection scheme is essentially independent of the material considered and can be applied for dHvA measurements on any conducting 2D material. In particular, the scheme is expected to be an important tool in studies of centrosymmetric transition metal dichalcogenide (TMD) crystals, shedding new light on hidden magnetization and interaction effects.

A perfect probe: Resonance of underdamped scaled Brownian motion

We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function and mean squared displacement of a single particle, we find that for the steady state, diffusions are free ballistic motion in short time, become the transitions between superdiffusion and subdiffusion in intermediate time, and converge to zero at long times. Via the power spectrum density corresponding to the transitions between superdiffusion and subdiffusion, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles.

The first integrals and rational solutions of some fourth-order differential equations

The object of this research is fourth-order differential equations. The aim of the research is to study the analytical properties of the solutions of these differential equations. The general form of the considered equations is indicated, and also the choice of the research object is justified. Herein we studied fourth-order differential equations for which sets of resonances with all positive nontrivial resonances are absent. Besides, three of these equations satisfy the conditions of absence in the solutions of moving multivalued singular points. The solutions of the next three equations have movable special points of multivalued character. Moreover, we also investigated the analytical properties of one more fourth-order differential equation of another general form for which it is also possible to construct a two-parameter rational solution as there is a nontrivial negative resonance in the related set of resonances. The first integrals of the equations under study are found and their rational solutions are constructed from negative non-trivial resonances. The resonance method was used in this study. The obtained results can be used in the analytical theory of differential equations.

Well-posedness issues on the periodic modified Kawahara equation

This paper is concerned with the Cauchy problem of the modified Kawahara equation (posed on T), which is well-known as a model of capillary-gravity waves in an infinitely long canal over a flat bottom in a long wave regime [26]. We show in this paper some well-posedness results, mainly the global well-posedness in L2(T). The proof basically relies on the idea introduced in Takaoka-Tsutsumi's works [60,69], which weakens the non-trivial resonance in the cubic interactions (a kind of smoothing effect) for the local result, and the global well-posedness result immediately follows from L2 conservation law. An immediate application of Takaoka-Tsutsumi's idea is available only in Hs(T), s>0, due to the lack of L4-Strichartz estimate for arbitrary L2 data, a slight modification, thus, is needed to attain the local well-posedness in L2(T). This is the first low regularity (global) well-posedness result for the periodic modified Kwahara equation, as far as we know. A direct interpolation argument ensures the unconditional uniqueness in Hs(T), s>12, and as a byproduct, we show the weak ill-posedness below H12(T), in the sense that the flow map fails to be uniformly continuous.

On rational solutions of two differential equations with а moving singular line

The study is devoted to the analytical theory of ordinary differential equations. In the introduction, it is said that the object of investigation is nonlinear third-order autonomous differential equations with a moving singular line, and whose two-parameter rational solutions are known. The study aims to clarify how to obtain two-parameter rational solutions from the general solutions of these equations. In the analytical theory of differential equations, as a rule, nonlinear differential equations have negative resonances. Among these resonances is the resonance equal to –1 (trivial case). However, it is asserted in some of the researchers’ papers that the nature of these negative resonances has not been found until now. The equations only with non-trivial negative resonance arose the interest of researchers. And it appears that the rational solutions of the equations can be constructed by their negative resonances. In this paper, a necessary and sufficient condition is indicated, at which the two-parameter rational solution of the equation with a moving singular line can be obtained from its general solution.

Modeling and control of resonance effects in steel casting mold oscillators

A methodology for capturing resonance in a continuous-casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beams is proposed. The mechanism of the mold motion distortion generation in the mold oscillator is clearly delineated. Nontrivial damped natural frequency and resonance frequency calculations are carried out. Then, for a finite-difference analytical beam model approximation, a discovery of monotonic dependence on spatial approximation accuracy of the beam resonance frequency under the fixed mass and of the mass under the fixed resonance frequency is demonstrated numerically. Based on these findings, a novel beam parameters selection procedure for the precise attainment of the desired resonance and damped natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the beam model parameters to match the actual resonance frequencies exhibited by thin and thick slab casting mold oscillators at, respectively, the Nucor Decatur and the AK Steel Dearborn steel mills, is demonstrated. The resulting resonance frequency value for the latter is then used to guide the internal-model-principle-based controller design for resonance suppression in the software testbed for the AK Steel caster mold oscillator.

Efficient Cementing of CH3NH3PbBr3 Nanoparticles to Upconversion Nanoparticles Visualized by Confocal Microscopy

Upconversion‐perovskite nanohybrids are prepared by assembling CH3NH3PbBr3 perovskite nanoparticles (PK) with naked NaYF4:Yb3+,Tm3+ nanoparticles (UCn) via an innovative strategy consisting of using cucurbit[7]uril (CB[7]) to anchor the perovskite nanoparticles firmly and closely to the upconversion nanoparticles, thus leading to UCn@PKCB nanohybrids. A commercial multiphoton laser scanning confocal microscope is used to demonstrate the successful assembly. This technique proves to be useful to evaluate luminescence lifetime in the range of several tens of μs and allows visualization of the extraordinarily efficient nontrivial resonance energy transfer from the upconversion nanoparticle to the perovskite after near‐infrared (NIR) excitation of the nanohybrid as well as the homogeneity of the UCn@PKCB sample. The considerable photostability of the perovskite in these nanohybrids is demonstrated by prolonged irradiation of the nanohybrid under UV light as well as under NIR light.

Resonances at COSY — the dibaryon issue

The cooler synchrotron COSY at the research center Jülich has been dedicated to the investigation of nucleon-nucleon collisions. Together with appropriate detector setups it has been particularly well suited for the search of resonances in the baryonbaryon system. Hence it is of no surprise that the observation of the first non-trivial dibaryon resonance has been established at this machine. A review on this issue is given - including the quest for dibaryons in nuclear matter.

Renormalized dispersion relations of β-Fermi-Pasta-Ulam chains in equilibrium and nonequilibrium states.

We study the nonlinear dispersive characteristics in β-Fermi-Pasta-Ulam (FPU) chains in both thermal equilibrium and nonequilibrium steady state. By applying a multiple scale analysis to the FPU chain, we analyze the contribution of the trivial and nontrivial resonance to the renormalization of the dispersion relation. Our results show that the contribution of the nontrivial resonance remains significant to the renormalization, in particular, in strongly nonlinear regimes. We contrast our results with the dispersion relations obtained from the Zwanzig-Mori formalism and random phase approximation to further illustrate the role of resonances. Surprisingly, these theoretical dispersion relations can be generalized to describe dispersive characteristics well at the nonequilibrium steady state of the FPU chain with driving-damping in real space. Through numerical simulation, we confirm that the theoretical renormalized dispersion relations are valid for a wide range of nonlinearities in thermal equilibrium as well as in nonequilibrium steady state. We further show that the dispersive characteristics persist in nonequilibrium steady state driven-damped in Fourier space.

Justification of the NLS approximation for a quasilinear water wave model

We show how for a quasilinear water wave model the NLS approximation can be justified. The model presents several new difficulties due to the quadratic terms which have to be eliminated by a normal-form transformation. Due to the quasilinearity of the problem there is some loss of regularity associated with the normal-form transformation and there is a nontrivial resonance present in the problem. The loss of regularity is dealt with by using a Cauchy–Kowalevskaya-like method to treat the initial value problem and the nontrivial resonance is dealt with via a rescaling argument.

Bounds for the nonlinear Schrödinger approximation of the Fermi–Pasta–Ulam system

We prove that the evolution of a slowly varying envelope of small amplitude of an underlying oscillating wave packet in the Fermi–Pasta–Ulam (FPU) system can be described approximately by the nonlinear Schrödinger equation. In contrast to other lattice equations for which this question has been addressed in the existing literature, the FPU system possesses a nontrivial quadratic resonance due to the curves of eigenvalues which vanish at the wave number k = 0. The proof of the error estimates is based on normal form transforms and a wave number-dependent scaling of the error function.

Multinets, resonance varieties, and pencils of plane curves

We show that a line arrangement in the complex projective plane supports a nontrivial resonance variety if and only if it is the underlying arrangement of a ‘multinet’, a multi-arrangement with a partition into three or more equinumerous classes which have equal multiplicities at each inter-class intersection point, and satisfy a connectivity condition. We also prove that this combinatorial structure is equivalent to the existence of a pencil of plane curves, also satisfying a connectivity condition, whose singular fibers include at least three products of lines, which comprise the arrangement. We derive numerical conditions which impose restrictions on the number of classes, and the line and point multiplicities that can appear in multinets, and allow us to detect whether the associated pencils yield nonlinear fiberings of the complement.

Parametric amplification of metric fluctuations during reheating in two field models

We study the parametric amplification of super-Hubble-scale scalar metric fluctuations at the end of inflation in some specific two-field models of inflation, a class of which is motivated by hybrid inflation. We demonstrate that there can indeed be a large growth of fluctuations due to parametric resonance and that this effect is not taken into account by the conventional theory of isocurvature perturbations. Scalar field interactions play a crucial role in this analysis. We discuss the conditions under which there can be nontrivial parametric resonance effects on large scales.

Nontrivial stochastic resonance temperature for the kinetic Ising model

The kinetic Ising model in a weak oscillating magnetic field is studied in the context of stochastic resonance. The signal-to-noise ratio calculated with simulations is found to peak at a nontrivial resonance temperature above the equilibrium critical temperature ${T}_{c}.$ We argue that its appearance is closely related to the vanishing of the kinetic coefficient at ${T}_{c}.$ Comparisons with various theoretical results in one and higher dimensions are made.