Natural frequency of beams with embedded piezoelectric sensors and actuators

A mathematical model is developed to study the natural frequency of beams with embedded piezoelectric sensors and actuators. The piezoelectric sensors/actuators in a non-piezoelectric matrix (host beam) are analyzed as two inhomogeneity problems by using Eshelby’s equivalent inclusion method. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form, which is expressed as functions of the elastic strain energy and dielectric energy of the piezoelectric sensors/actuators. The Euler-Bernoulli beam theory and Rayleigh-Ritz approximation technique are used in the present analysis. Parametric studies show that the size, volume fraction and location of the piezoelectric inclusions significantly influence the natural frequency of the beam

Stimulated plasmon polariton scattering

The plasmon and phonon polaritons of two-dimensional (2d) and van-der-Waals materials have recently gained substantial interest. Unfortunately, they are notoriously hard to observe in linear response because of their strong confinement, low frequency and longitudinal mode symmetry. Here, we propose a fundamentally new approach of harnessing nonlinear resonant scattering that we call stimulated plasmon polariton scattering (SPPS) in analogy to the opto-acoustic stimulated Brillouin scattering (SBS). We show that SPS allows to excite, amplify and detect 2d plasmon and phonon polaritons all across the THz-range while requiring only optical components in the near-IR or visible range. We present a coupled-mode theory framework for SPS and based on this find that SPS power gains exceed the very top gains observed in on-chip SBS by at least an order of magnitude. This opens exciting new possibilities to fundamental studies of 2d materials and will help closing the THz gap in spectrocopy and information technology.Comment: 7 pages, 3 figure

Luminosity function, sizes and FR dichotomy of radio-loud AGN

The radio luminosity function (RLF) of radio galaxies and radio-loud quasars is often modelled as a broken power-law. The break luminosity is close to the dividing line between the two Fanaroff-Riley (FR) morphological classes for the large-scale radio structure of these objects. We use an analytical model for the luminosity and size evolution of FRII-type objects together with a simple prescription for FRI-type sources to construct the RLF. We postulate that all sources start out with an FRII-type morphology. Weaker jets subsequently disrupt within the quasi-constant density cores of their host galaxies and develop turbulent lobes of type FRI. With this model we recover the slopes of the power laws and the break luminosity of the RLF determined from observations. The rate at which AGN with jets of jet power $Q$ appear in the universe is found to be proportional to $Q^{-1.6}$. The model also roughly predicts the distribution of the radio lobe sizes for FRII-type objects, if the radio luminosity of the turbulent jets drops significantly at the point of disruption. We show that our model is consistent with recent ideas of two distinct accretion modes in jet-producing AGN, if radiative efficiency of the accretion process is correlated with jet power.Comment: 13 pages, 1 figure, accepted by MNRA

Statistics of 3-dimensional Lagrangian turbulence

We consider a superstatistical dynamical model for the 3-d movement of a Lagrangian tracer particle embedded in a high-Reynolds number turbulent flow. The analytical model predictions are in excellent agreement with recent experimental data for flow between counter-rotating disks. In particular, we calculate the Lagrangian scaling exponents zeta_j for our system, and show that they agree well with the measured exponents reported in [X. Hu et al., PRL 96, 114503 (2006)]. Moreover, the model correctly predicts the shape of velocity difference and acceleration probability densities, the fast decay of component correlation functions and the slow decay of the modulus, as well as the statistical dependence between acceleration components. Finally, the model explains the numerically [P.K. Yeung and S.B. Pope, J. Fluid Mech. 207, 531 (1989)] and experimentally observed fact [B.W. Zeff et al., Nature 421, 146 (2003)] that enstrophy lags behind dissipation.Comment: 5 pages, 3 figures. Replaced by final version accepted by Phys. Rev. Let

Enhanced ponderomotive force in graphene due to interband resonance

We analyze intrinsic nonlinearities in two-dimensional polaritonic materials interacting with an optical wave. Focusing on the case of graphene, we show that the second-order nonlinear optical conductivity due to carrier density fluctuations associated with the excitation of a plasmon polariton is closely related to the ponderomotive force due to the oscillating optical field. This relation is first established through an elegant thermodynamic approach for a Drude-like plasma, in the frequency range where intraband scattering is the dominant contribution to conductivity. Subsequently, we extend our analysis to the interband regime, and show that for energies approximately half the Fermi energy, the intraband contribution to the ponderomotive force diverges. In practice, thermal broadening regularizes this divergence as one would expect, but even at room temperature typically leaves a strong ponderomotive enhancement. Finally, we study the impact of nonlocal corrections and find that nonlocality does not lead to further broadening (as one would expect in the case of Landau damping), but rather to a splitting of the ponderomotive interband resonance. Our analysis should prove useful to the open quest for exploiting nonlinearities in graphene and other two-dimensional polaritonic materials, through effects such as second harmonic generation and photon drag.Comment: 7 pages, 2 figures, 1 appendi