No abstract

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings.

We demonstrate a novel response of a nonlinear micromechanical resonator when operated in a region of strong, non-linear mode coupling. The system is excited with a single drive signal and its response is characterized by periodic amplitude modulations that occur at timescales based on system parameters. The periodic amplitude modulations of the resonator are a consequence of nonlinear mode coupling and are responsible for the emergence of a "frequency comb" regime in the spectral response. By considering a generic model for a 1:3 internal resonance, we demonstrate that the novel behavior results from a saddle node on an invariant circle (SNIC) bifurcation. The ability to control the operating parameters of the micromechanical structures reported here, makes the simple micromechanical resonator an ideal testbed to study the dynamic response of SNIC behavior demonstrated in mechanical, optical and biological systems.

In the AF-treated group a late and significant lowering of various inflammatory parameters combined with a histological recovery was demonstrated. These findings suggest that administration of AF mediates a long-lasting anti-inflammatory effect in cases of acute UC.

Experimental double loop hysteresis in dc field dependent dielectric permittivity in bulk single crystal SrTiO3 is reported. Small signal measurements of the permittivity are performed in the frequency range 0.5–1.5 GHz at temperatures below 77 K using electrically thin circular parallel-plate resonators. The dielectric permittivity is extracted form the measured resonant frequency. The double loop hysteresis may be caused by field induced local paraelectric/ferroelectric phase transitions, and/or switching (polarization reversal) in local opposing ferroelectric domains associated with symmetry breaking impurities/structural defects.