Analysis of resonance characteristics of solidly mounted resonator for mass sensing applications

Solidly mounted resonators (SMRs) have recently been adopted as alternatives to quartz crystal microbalance in bio-molecular and chemical detection field. In this study, the resonance characteristics of highly c-axis-textured AlN film-based SMR were investigated to obtain better sensitivity for mass sensing applications. The resonant frequencies and quality factors of SMR with different sizes and shapes of active resonant configuration were characterized. The results show that the effect of active resonant area on the resonance frequency is insignificant. However, the quality factor is strongly dependent on the size and shape of active resonant area. Optimized resonant patterns were applied to a 2.0 GHz SMR and mass sensor. Experimental results indicate that the sensitivity of the device achieved can be as high as 6,544 Hz cm²/ng, which shows the promising application in bio-molecular and industrial detecting application.     

Exact solutions of semiclassical non-characteristic Cauchy problems for the sine-Gordon equation

The use of the sine-Gordon equation as a model of magnetic flux propagation in Josephson junctions motivates studying the initial-value problem for this equation in the semiclassical limit in which the dispersion parameter ε tends to zero. Assuming natural initial data having the profile of a moving −2π kink at time zero, we analytically calculate the scattering data of this completely integrable Cauchy problem for all ε>0 sufficiently small, and further we invert the scattering transform to calculate the solution for a sequence of arbitrarily small ε. This sequence of exact solutions is analogous to that of the well-known N-soliton (or higher-order soliton) solutions of the focusing nonlinear Schrödinger equation. We then use plots obtained from a careful numerical implementation of the inverse-scattering algorithm for reflectionless potentials to study the asymptotic behavior of solutions in the semiclassical limit. In the limit ε↓0 one observes the appearance of nonlinear caustics, i.e. curves in space-time that are independent of ε but vary with the initial data and that separate regions in which the solution is expected to have different numbers of nonlinear phases.In the appendices, we give a self-contained account of the Cauchy problem from the perspectives of both inverse scattering and classical analysis (Picard iteration). Specifically, Appendix A contains a complete formulation of the inverse-scattering method for generic L¹-Sobolev initial data, and Appendix B establishes the well-posedness for L^p-Sobolev initial data (which in particular completely justifies the inverse-scattering analysis in Appendix A).     

Radiative asymmetry around the resonance in e+e−→μ+μ−

Under the assumption that the ψ is a pure 1^?? vector particle we have calculated the angular asymmetry in the process e⁺e^?→μ⁺μ^? around the resonance. We find that the asymmetry, calculated in the soft photon limit, becomes very small around the resonance.     

Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning

Dynamical system under investigation in the current work is comprised of harmonically forced linear oscillator with attached nonlinear energy sink. External forcing frequency detuning near the main resonance (1:1) is included in the system investigation. The detailed study of the periodic and quasiperiodic regimes is done in the work via (adaptive) averaging method. Local bifurcations of the periodic regimes are revealed and fully described in the space of system parameters (amplitude of excitation, damping, and frequency detuning). Novel analytical approach for predictions of strongly modulated response (SMR) is presented. This approach provides a sufficient condition for the SMR existence contrary to the previous studies. Various possibilities of coexistence of the response regimes are predicted analytically and demonstrated numerically. Among those is a coexistence of two distinct periodic regimes together with the SMR. All findings of the simplified analytic model are verified numerically and considerable agreement is observed.     

High sensitive self-assembled monolayer modified solid mounted resonator for organophosphate vapor detection

We fabricated a self-assembled monolayer (SAM) modified solid mounted resonator (SMR) for organophosphate vapor detection. The SMR device consisted of a piezoelectric stack and an all-metal Bragg's reflector. The electrode surface is chemically modified with a Cu²⁺/11-mercaptoundecanoic acid SAM to capture organophosphate compounds. After chemical modification, both the resonance frequency and the Q-factor decrease. Fourier transform infrared external reflection spectroscopy was performed to verify the formation of SAM. Adsorption of organophosphate compounds onto the SAM increases its mass, and the resonance frequency proportionally goes down. The testing results show that the modified SMR can yield a rapid, sensitive, reversible and reproducible response to nerve-agent (dimethyl methyl phosphonate) vapor. This study proves that using the SAM modified SMR to detect trace organophosphate vapor is feasibility.     

Interplay of plasmon resonances in binary nanostructures

By introducing the difference permittivity ratio η=(ε ₂?ε ₀)/(ε ₁?ε ₀), the Green matrix method for computing surface plasmon resonances is extended to binary nanostructures. Based on the near field coupling, the interplay of plasmon resonances in two closely packed nanostrips is investigated. At a fixed wavelength, with varying η the resonances exhibit different regions: the dielectric effect region, resonance chaos region, collective resonance region, resonance flat region, and new branches region. Simultaneously, avoiding crossing and mode transfer phenomena between the resonance branches are observed. These findings will be helpful to design hybrid plasmonic subwavelength structures.     

FMR in thin ferromagnetic granular film

The ferromagnetic resonance is considered for a thin granular film consisting of spherical metal particles. It is shown that the interparticle dipole interactions lead to a noticeable shift of the resonance field and a strong asymmetry of absorption line. The free induction signal is time modulated and its envelopem _ind(t) obeys the law ln (m _ind) ≈t ^2/3. The role of the particle shape in considered system is also discussed.     

Speculations on a strongly interacting Higgs sector

Using the 1/N expansion, we argue that the O_2N Higgs-Goldstone model may be a good indicator of the behavior of the standard SU₂ ? U₁ electroweak model in the non-perturbative limit of a strongly interacting Higgs sector. We emphasize that there remains a physical scalar particle or resonance σ (Higgs remnant), whose mass (and width) will be set by the weak scale. However, its coupling to vector bosons is expected to be much stronger than the standard model Higgs of comparable mass. This provides evidence that there is an upper limit to the Higgs mass in the hundreds of GeV, regardless of whether naturalness constraints are imposed on the parameters of the effective lagrangian. We conclude with some comments about the possible relevance of this particle to the radiative events observed at the CERN $\text{p}\text{p}$ collider.     

Application of He's variational iteration method to nonlinear heat transfer equations

Instead of finding a small parameter for solving nonlinear problems through perturbation method, a new analytical method called He's variational iteration method (VIM) is introduced to be applied to solve nonlinear heat transfer equations in this Letter. In this research, variational iteration method is used to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative-conduction equation containing two small parameters of ε₁ and ε₂ and evaluate the efficiency of straight fins. VIM can apply to the nonlinear equations with boundary or initial conditions defined in different points just with developing the correction functional using the extra parameters such as Cn, as used in this Letter.     

A rotating mass embedded in an Einstein-Gödel universe

A metric containing a parameterε(ε ²=1) has been obtained which represents a Kerr metric in the background of a static Einstein universe whenε is put equal to +1. The same metric will represent the external field of a mass embedded in a rotating Gödel universe whenε is set equal to ?1.     

Enhancing the dynamic range of targeted energy transfer in acoustics using several nonlinear membrane absorbers

In order to enhance the robustness and the energy range of efficiency of targeted energy transfer (TET) phenomena in acoustics, we discuss in this paper about the use of multiple nonlinear membrane absorbers (called nonlinear energy sinks or NES) placed in parallel. We show this way, mainly thanks to an experimental set-up with two membranes, that the different absorbers have additional effects that extend the efficiency and the possibilities of observation of TET. More precisely, we present the different behavior of the system under sinusoidal forcing and free oscillations, characterizing the phenomena for all input energies. The frequency responses are also presented, showing successive clipping of the original resonance peak of the system, and strongly modulated regimes (SMR). A model is finally used to generalize these results to more than two NES and to simulate the case of several very similar membranes in parallel which shows how to extend the existence zone of TET.     

The Crossover Regime for the Weakly Asymmetric Simple Exclusion Process

We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0–1 step initial condition. Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location. One expects a crossover from Gaussian to Tracy-Widom distributed fluctuations. The appropriate crossover scale is an asymmetry of order \(\sqrt{\varepsilon}\), times of order ε ^?2, and a spatial location of order ε ^?3/2. For this parameter window we obtain the limiting distribution function of the integrated current in terms of an integral over the difference of two Fredholm determinants. For large times, on the scale ε ^?2, this distribution function converges to the one of Tracy-Widom.     

Bifurcations and chaos in register transitions of excised larynx experiments

Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure.     

Temperature dependence of the dielectric function of monolayer MoS2

An analytic expression of the dielectric function of monolayer molybdenum disulfide (MoS₂) ε?=?ε₁ + iε₂ is presented for energies from 1.4 to 6.0?eV and temperatures from 35 to 350?K. The dielectric function parametric model is used to express ε as a sum of polynomials, which naturally includes asymmetry of critical-point lineshapes. The temperature dependence is achieved by fitting model parameters. In this way, the dielectric function of MoS₂ for arbitrary temperature can be calculated. We observed the fundamental absorption peak, which occurs at the K point of the Brillouin zone. These results are expected to be useful in designing and understanding applied-device technologies based on monolayer MoS₂.     

Nonlinear Landau-Zener tunneling of Bose-Einstein condensate in a spatially magnetic modulated trap

We study tunneling of a Bose-Einstein condensates confined in a effective double-well potential (a single well with a spatially magnetic modulated scattering length, actually), called pseudo double-well trap, in which the interaction of atoms characterized by the s-wave scattering length a _s can be widely tuned with a magnetic-field Feshbach resonance. As a result, corresponding to different nonlinear parameters, the energy levels of the nonlinear Schrödinger equation can have complex structures in their dependence on the bias between the wells. We discuss the emergence of looped levels, which lead to a breakdown of adiabaticity that the Landau-Zener transition probability does not vanish even in the adiabatic limit. Moreover, we also find that the Landau-Zener tunneling in the pseudo trap show many striking properties distinguished from that of the real trap model (where the barrier is created by the external potential). Possible experimental observation in an opticallyinduced photonic lattices in a photorefractive material is suggested.     

Renormalization problem in nonrenormalizable massless Φ4 theory

Nonrenormalizable massless Φ⁴ theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers ofg andg ^2/ε obtained for the Green's functions in massless (Φ⁴)_4+ε with generic ε. For ε=1 and ε=2, these series reduce to double series in powers ofg and lng. The problems of extension to (Φ⁴)_4+ε with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed.     

Investigation of parity violation and interference effects in the angular distributions of fragments originating from 233U fission induced by resonance neutrons

Three interference asymmetry effects in the angular distributions of fragments originating from ²³³U fission induced by resonance neutrons were measured. The energy dependences of the asymmetry factors being studied show sizable irregularities that are associated, according to modern theory, with the interference of s and p resonances at the stage of a compound nucleus. The basic features of weak p-wave resonances in the low-energy region were obtained from a global theoretical analysis of the asymmetry factors as functions of energy. The first estimates of nuclear matrix elements of weak interaction were derived for a few p-wave resonances.     

Fractal diffusion in smooth dynamical systems with virtual invariant curves

Preliminary results of extensive numerical experiments with a family of simple models specified by the smooth canonical strongly chaotic 2D map with global virtual invariant curves are presented. We focus on the statistics of the diffusion rate D of individual trajectories for various fixed values of the model perturbation parameters K and d. Our previous conjecture on the fractal statistics determined by the critical structure of both the phase space and the motion is confirmed and studied in some detail. In particular, we find additional characteristics of what we earlier termed the virtual invariant curve diffusion suppression, which is related to a new very specific type of critical structure. A surprising example of ergodic motion with a “hidden” critical structure strongly affecting the diffusion rate was also encountered. At a weak perturbation (K ? 1), we discovered a very peculiar diffusion regime with the diffusion rate D=K ²/3 as in the opposite limit of a strong (K ? 1) uncorrelated perturbation, but in contrast to the latter, the new regime involves strong correlations and exists for a very short time only. We have no definite explanation of such a controversial behavior.     

Optimal Multigrid Algorithms for Variable-Coupling Isotropic Gaussian Models

A novel class of multigrid algorithms for the variable-coupling isotropic Gaussian models is presented. In addition to the elimination of the critical slowing down (which otherwise might become much worse than usual in the case of strongly varying coupling values), the “volume factor” is also eliminated. That is, the need to produce many independent fine-grid configurations for averaging out their statistical deviations is removed, by applying multigrid cycles that sample mostly on coarse grids. Thermodynamic limits can be calculated to relative accuracy ε _r in just $O(\varepsilon _r^{ - 2} )$ computer operations, where ε _r is the error relative to the standard deviation of the observable. In this paper, such an optimal algorithm is obtained for the calculation of the susceptibility in the d-dimensional variable-coupling isotropic Gaussian model (with numerical experiments for d = 1, 2). Some basic general rules for the operation of multigrid algorithms, applicable to much wider classes of models, are derived.